

Cognifront Engineering Mathematics Classroom Assistant 2014 ROBO Product Contents 
Theory Animation
Theoretical and difficult concepts of engineering subjects require a good visualization. This section includes all important concepts in subject and and provides audiovisual modules for those concepts. These modules can be played\paused. You can seek them backward and forward. You also have volume control for these audiovisual modules. The modules can also be embedded in the power point slides that teachers may prepare or the ones that are packaged with the product. The audiovisual modules provide a great source of revision for the students as well. 
Differential Equations Part 1This module talks about Historical Background of Differential Equation, what is Differential Equation and Classification of Differential Equation. 

Differential Equations Part 2Here you will learn about different types of Ordinary Differential Equation that are Single Order Differential Equation and Higher Order Differential Equation. This module also defines order of Differential Equation and degree of Differential Equation. 

Differential Equations Part 3Here you will learn about Practical Approach to Differential Equation, Formation of Differential Equation and Elimination of Arbitrary constants. 

Equations Of SphereLearn about Sphere and its equations in different coordinate systems. Here you will also learn about Software application of equations of Sphere. 

L'hospital's RuleThe objective of this module is to explain the History of L\'Hospital\'s Rule, Need of L\'Hospital\'s Rule and solve examples on L\'Hospital\'s Rule. 

Introduction to Partial DifferentiationObjectives of this session are to identify need for partial differentiation, define partial differential equations and solve an example of partial differential equation. 

 
Fourier SeriesThis module explains the Fourier series and its real life applications. 

Complex Number IntroductionThis module gives brief introduction about real numbers, imaginary numbers, complex numbers and use of complex numbers in daytoday life. 

Algebra Of Complex NumberA complex number is a number that can be expressed in the form a+bi, where a and b are real numbers and i is the imaginary unit. This module explains various operations of complex number, Argands diagram, complex conjugate and modules of complex number. 

Logarithms Of Complex NumbersThis module explains general and prinicple value of Logarithm and seperation of Real and Imaginary part of complex numbers briefly. 

Polar And Exponential Form Of Complex NumberThis modules explains polar and exponential form of complex numbers and also explains example of these forms of complex number. 

Power Of Complex NumberIn this module DeMoivre\'s theorem is explained briefly. This module also explains applications of DeMoivre\'s theorem to solve algebraic equations. 

 
Applications Of DifferentiationsIn this module application of derivatives is explained with the help of 2 real life examples. Anything that relates two values at different time most likely uses a derivative process. 

Composite Functions And Higher Order DerivativesFunction composition is the pointwise application of one function to another function to produce a third function. This module explains Composite functions and partial differentiation of second and third order derivative. 

Function With Single VariableThis module gives youe brief introduction to function with single variable. Examples of function with Single Variable is also explained in this module. 

Function With Multiple VariableThis module give brief introduction of function with multiple variable and partial differentiation. This module also explains example of function with multiple variable and partial differentiation. 

Rules Of Partial Differentiation Part 1In this module rules of partial differentiation, Derivative of Sum, Product and Quotient and the derivative of constant values are explained briefly. 

Rules Of Partial Differentiation Part 2This module covers Rules of Partial Differentiation in brief. This module also explains use of Rules of Partial Differentiation in real life. 

 
Hyperbolic FunctionsHyperbolic functions are analogs of ordinary trignometric or circular functions .This module explains real life use of Hyperbolic cos, tan functions. This module gives brief introduction of hyperbolic functions. In this module relation between Circular and Hyperbolic function is also explained. 

Leibnitz's TheoremThis module explains Leibnitz\'s theorem, need of Leibnitz\'s theorem, methods to solve example using Leibnitz\'s theorem. This module also covers example solved by using Leibnitz\'s theorem. 

Maclaurin's Series IntroductionIn this module Maclaurin\'s theorem is explained in brief. This module also explains Applications of Maclaurin\'s Theorem and the examples based on Maclaurin\'s theorem. 

Successive Differentiation And NotationThis module covers definition and notation of partial differentiation, differential coefficients of standard functions and the applications of successive differentiation in brief. 

Illustration On Successive Differentiation Part 1This module explains methods for solving successive differentiation in brief. Methods such as Higher Derivative, Trigonometric Transformation and Standard results, Partial fractions and Demovier\'s theorem. This module explains Higher Derivative, Trigonometric Transformation and Standard results methods for solving successive differentiation. 

Illustration On Successive Differentiation Part 2This module explains Partial fractions and Demovier\'s theorem methods for solving successive differentiation 

 
Expansion Of Standard FunctionsThis module covers expansion of standard functions and the methods of expansion of functions such as Substitution, Differentiation and Integration, and Leibnitz\'s theorem. 

Illustration On Expansion Of Functions Part 1This module covers use of standard function and one of the expansion method as differentiation and intergation in brief. 

Conditions For Consistency Of Homogeneous EquationsThis module explains what are the conditions of consistency of homogeneous equations and examples related to it. Conditions of solution of system such as unique solution and infinite solution is explained with the help of example. 

Expansion Of Determinants And Cramers RuleThis module gives brief introduction about expansion of determinants, varification of eigen value and cramers rule. In this module solving of given system using cramers rule is also is explained with the help of example. 

Functional Dependence Errors And ApproximationIn this module study of function dependence of functions, errors and approximation, example of errors and approximation and applications of approximation is explained in brief. 

Illustration On Expansion Of Functions Part 2This module covers expansion of standard functions by Substitution, use of complex numbers and use of Leibnitz\'s theorem in details. 

 
Jacobian Definition And Notation Part 1This module exmplains Jacobian in real world and definations and notations of Jacobian in details 

MatricesThis module covers definition and notation of matrices, applications of matrices and types of matrices in brief. Types of matrices such as row, column, symmetric, skew symmetric, scalar, unit, upper triangular, lower triangular and diagonal matrix is explained in this module. 

Matrices OperationsIn this module study of reallife example of matrices, determinant of matrices, minor and cofactor of matrix and adjoint and inverse of matix is explain in brief. 

Maxima And MinimaThis module gives brief introduction about maxima and minima. This also explains maxima and minima of function of several variables, applications of maxima and minima and mathematical optimization concept. 

Methods Of Expansion Of FunctionsIn this module methods of expansion of functions is explained with the help of examples in brief. 

Partial Derivatives Of Implicit FunctionsThis module explains partial derivative of Implicit function and example of partial derivative in details. 

 
Rank Of The MatrixThis module explains finding of rank of matrix using matrix reduction methods such as reduction of matrix to Echelon Form and to normal form. 

System Of Linear Algebraic EquationsThis module explains equation in matrix form, augmented matrix, conditions of consistency of nonhomogeneous equations in details 

Taylor SeriesThis module explains Taylor theorem in brief with the help of example. 

Cauchys Condensation Gausss TestThis module explains Cauchys Condensation Test and Gauss Test in details with the help of example. 

Comparison Raabes And Dalemberts Ratio TestIn this module Comparison Test, Raabes Test and DAlemberts ratio tests are explained in brief. Example for each test is also explain in this module. 

Convergent And Divergent Series In Real LifeThis module explains Convergent and divergent series in brief with the help of real life examples. 

 
Eigen Values And ApplicationsThis module covers definition, applications and methods of finding eigen values in details. This module explains applications of eigen value such as Google Page Rank, Quantum mechanics etc. 

Illustration On Partial DifferentiationThis module explains differentiation on variable to be treated as constant, homogeneous functions and Euler\'s theorem in brief. 

Infinite Series IntroductionIn this module sequences, series, Convergent and Divergent Series and Applications of Infinite Series is explained in details. This module also covers monotonic increasing sequence, monotonic decreasing sequence, alternating sequence, oscillatory series. 

Linearly Dependant And Independant VectorsThis module explains Linear dependence of vector, Linear independence of vector, linear transformation, orthogonal matrix with the help of examples in brief. 

Logarithmic DeMorgan's And Cauchy's Integral Test And Alternating SeriesThis module covers Logarithmic test, DeMorgan\'s Test, Cauchy\'s integral test, alternating series, absolute and conditional convergence in details. 

Test For Convergence And DivergenceThis module covers Cauchy\'s nth root test, P series, convergence of geometric series. This module also covers cases for determining the convergence or divergence of geometric series. 

 
Coordinate SystemsThis module covers the cartesian,polar and cylindrical coordinate systems along with their applications. 

Division Of The Join And Direction CosinesThis module describes division of the join of two given points,direction cosines and direction ratios. 

Curve TracingThis module describes the basic definitions of curves and classification of curves according to equations. 

Tracing Of Cartesian CurvesThis module describes the rules for tracing the cartesian curve 

Applications Of DE To Orthogonal TrajectoriesThis module contains basics of orthogonal trajectories and detail working rule of application of differential equation in orthogonal trajectories. 

Newton\'s Law Of Cooling 1This module contains definition and applications of newton\'s law of cooling,which is an application of differential equations. 

 
One Dimensional Conduction Of HeatThis module contains theory of heat conduction, Fourier\'s law of heat conduction illustrated with an example 

Rate Of Decay Of Radioactive MaterialsThis module illustrates the role of differential equation in rate of decay of radioactive materials 

Chemical ProblemsThis module explains role of differential equation in chemical reactions. 

Kirchoff's Law Of Electrical CircuitsThis module explains application of differential equations in LR,RC and LC circuits. 

Rectilinear Motion 01This module contains formulae for Velocity and Acceleration Meaning and Definition of rectilinear motion,newton\'s second law of motion and concept of net forces. 

Equations Of ConeThis moduel is based on Cone,Calculation of Equations of a Cone,Discussion on Applications of Equations of Cone. 

 
Centre Of GravityThis module explains the concept of centre of gravity along with its application and another related concepts. 

Simple Harmonic MotionThis module explains the role of differential equation in simple harmonic motion. 

Differentiation Under Integral SignThis module illustrates the important concept in integral calculus,i.e. differentiation under integral sign along with its two rules. 

Beta And Gamma FunctionThis module contains a theory of beta and gamma functions along with its properties.Application of these function are also described in this module. 

Limits Of IntegrationThis module contains a theory of limits of integration as weel as there is brief description on methods of finding limits of integration 

Double IntegralsThis module contains the calculus of double integrals,difference between single and double integrals and properties of double integrals. 

 
Solid Geometry The SphereThis module contains basics of sphere, their equation, and finding equations of sphere in different cases. 

Triple IntegrationThis module contains theory of extension of double integral over 3 dimansional plane i.e. triple integration as well as standard limits. 

Application Of Multiple Intgrals To Represent Area VolumeThis module contains the application of multiple integrals to represent an area and volume. 

Exact Differential EquationThis module explains the theory of exact differential equation. 

Formation Of Differential EquationThis module explains the formation and definition of differential equations,along with the applications of differential equations. 

Solid Geometry ConeThis module contains basics of cone , their equation, right circular cone and finding equations of cone in different cases. 

 
Solid Geometry CylinderThis module contains basics of cylinder, their equation, right circular cylinder and finding equations of cylinder in different cases. 

Variable Separable FormThis module contains a brief description on variable separable form,its examples and equations reducible to variable separable form. 

Area Enclosed By Plane Curves Expressed In PolarThis module contains a theory of area enclosed by plane curves expressed in polar form as well as example based on it. 

Homogeneous And Non Homogeneous Differential EquationThis module contains a theory of homogeneous and non homogeneous differential equation,an example based on it along with its different cases. 

Moment Of Inertia 1This module contains a theory of moment and torque,meaning and definition of moment of inertia and radius of gyration. 

Moment Of Inertia 2This module contains a theory on moment of inertia,moment of inertia for some standard shapes as well as solved example. 

 
Solid Geometry Plane And Straight LineThis module contains a theory of angle between two lines,projection,plane and straight line. 

Fourier Series Of Periodic Function Having Arbitrary PeriodThis module contains a theroy of function having arbitrary period,even and odd function,half range expansion. 

Tracing Of Cartesian Curves 2This module explains the rules for tracing the cartesian curves. 

Reduction FormulaeThis module contains an Introduction to reduction formulae,Definition and Reduction formula for sinusoidal functions 
Animated Solved Examples
This section contains animated solved examples with audiovisual content. You can play these modules to show how any given problem is solved stepbystep. The concepts become very clear. You can use these Audio\Visual modules to understand how to solve given problem. The audiovisual modules can be played\paused, seek backward\forward. These modules are very useful for clear understanding of problem solving process. Using this examples teacher can easily explain the solution to the problem. Here the solution is explained with the help of visuals and animations that provides a deep understanding to the students. The teacher can use these animated solved solutions for teaching; also can provide these problems to the students for practice. 
Newton's Law Of CoolingThis module illustrates an example based on Newton\'s law of cooling. 

Fouriers Law Of Heat ConductionThis module illustrates an example based on Fourier\'s law of heat conduction. 

Curve TracingThis module illustrates the animated solved example based on curve tracing. 

Differentiation Under The Integral SignThis module illustrates solved example of differentiation under the integral calculus. 

Reduction FormulaeThis module contains an animated solved example on reduction formulae. 

Differential Equations Reducible To Exact FormThis module is animated solved example based on differential equation reducible to the exact form. 

 
Gamma FunctionThis module is an animated solved example which covers gamma function,use of transformation rule is described in this module. 

Homogeneous Differential EquationThis module contains an animated solved example based on homogeneous differential equation. 

Linear Differential EquationThis module contains an animated solved example based on linear differential equation. 

Multiple IntegralsThis module contains an animated solved example based on multiple integrals. 

The ConeThis module contains an animated solved example on cone. 

The CylinderThis module contains an animated solved example on cylinder. 

 
The Sphere 1This module contains an animated solved example on sphere. 

The Sphere 2This module contains an animated solved example on cylinder. 

Application Of Double Integrals To Find Area And VolumeThis module explains application of double inetgrals to find area and volume with the help of animated solved example. 

Area Volume And Root Mean SquareThis module explains application of double inetgrals to find area and volume with the help of animated solved example. 

Volume Of Solids 1This module explains an example based on volume of solids with the help of animated solution. 

Double IntegralsThis module is an animated solved example which covers Double Integrals. 

 
Volume Of Solids 2This module is an animated solved example based on Volume Of Solids. 

Triple IntegrationThis module is an animated solved example based on Triple Integration. 
Step by Step Solved Examples
This segment features solution to problem without missing any step to solve it. These set of examples covers almost all the important topics from exam point of view. The teacher can use these step by step solutions for teaching the solved problems by navigating through the module. Almost all steps have been explained and solved using the appropriate formula required. The teacher can provide these problems to the students for practice or home assignments. 
Complex Numbers Example 1This module consists of an example based on basic definition of a complex numbers. 

Complex Numbers Example 2This module consists of an example based on a complex numbers, we are asked to prove a certain relation here. 

Complex Numbers Example 3This module consists of an example based on a complex numbers which illustrates the argand diagram with the help of an example. 

Complex Numbers Example 4This module consists of an example based on a complex numbers, with the help of a argand diagram we find the complex numbers which represents vertices. 

Complex Numbers Example 5This is an solved example based on Complex Number. This module explains illustration on Demoiver\'s Theorem. 

Complex Numbers Example 6This is an solved example based on Complex Number. This module explains illustration on Demoiver\'s Theorem. 

 
Complex Numbers Example 7This is an solved example based on Complex Number. This module explains illustration on Demoiver\'s Theorem. 

Complex Numbers Example 8This is solved example based on complex number, which illustrates roots of equation consist of complex number. 

Matrices Example 1This is solved example explaining rank of matrix by matrix reduction to normal form. Here a matrix is given to find its rank by using reducing it to the normal form. 

Matrices Example 2This solved example is based on finding non singular matrices P and Q such that PAQ is in normal form. In this example matrix A is given. 

Matrices Example 3This solved example explains obtaining inverse of matrix by finding non singular matrices P and Q such that PAQ is in normal form. 

Matrices Example 4This example is based on nonhomogeneous system of equations by using method of reduction 

 
Matrices Example 5This is an example based on problems on linearly dependent, independent vectors. 

Matrices Example 6This example is based on concept of orthogonal matrix. Is given matrix is orthogonal or not is exaplined in this example. 

Partial Differentiation Example 1This solved example is based on partial differentiation. Here solution to the problem is given in step by step format. 

Partial Differentiation Example 2This solved example is based on partial differentiation. Here solution to the problem is given in step by step format. 

Partial Differentiation Example 3This solved example is based on partial differentiation. Here solution to the problem is given in step by step format. 

Partial Differentiation Example 4This solved example is based on partial differentiation. Here solution to the problem is given in step by step format. 

 
Partial Differentiation Example 5This solved example is based on partial differentiation. Here solution to the problem is given in step by step format. This is an example based on variables to be treated as constant. 

Partial Differentiation Example 6This solved example is based on partial differentiation. Here solution to the problem is given in step by step format. This is an example based on Euler\'s theorem. 

Partial Differentiation Example 7This solved example is based on partial differentiation. Here solution to the problem is given in step by step format. 

Partial Differentiation Example 8This solved example is based on partial differentiation. Here solution to the problem is given in step by step format. This is an example based on involving substitution. 

Partial Differentiation Example 9This solved example is based on partial differentiation. Here solution to the problem is given in step by step format. This is an example based on total derivatives. 

Infinite Series Example 1This solved example is based on infinite series. Here convergence of series is tested. 

 
Infinite Series Example 2This solved example is based on infinite series. Here convergence of series is tested. 

Infinite Series Example 3This solved example is based on infinite series. Here convergence of series is tested. 

Infinite Series Example 4This solved example is based on infinite series. Here convergence of series is tested. 

Infinite Series Example 5This solved example is based on infinite series. Here convergence of series is tested. 

Infinite Series Example 6This solved example is based on infinite series. Here convergence of series is tested. 

Infinite Series Example 7This solved example is based on infinite series. Here convergence of series is tested. 

 
Successive Differentiation Example 1This solved example is based on successive differentiation. Here illustration on Leibnitz\'s theorem is explained by step by step solution to the problem given. 

Successive Differentiation Example 2This solved example is based on successive differentiation. Here derivative using trigonometrical transformations and standard results is explained by step by step solution to the problem given. 

Successive Differentiation Example 3This solved example is based on successive differentiation. Here illustration on Leibnitz\'s theorem is explained by step by step solution to the problem given. 

Successive Differentiation Example 4This solved example is based on successive differentiation. Here derivative using trigonometrical transformations and standard results is explained by step by step solution to the problem given. 

Successive Differentiation Example 5This solved example is based on successive differentiation. Here illustration on Leibnitz\'s theorem is explained by step by step solution to the problem given. 

Indeterminate Form Example 1This module contains a solved example on indeterminate form. We start with given data of function which approaches to certain limit and we solve it step by step to arrive final answer. 

 
Indeterminate Form Example 2This module contains solved example on indeterminate form. We apply change of base formula and L\'Hospital rule to arrive at the final answer. 

Indeterminate Form Example 3This module contains solved example on indeterminate form, under the application of finite limit and L\'Hospital rule, we calculate the value of unknown variable p. 

Indeterminate Form Example 4This module contains solved example on indeterminate form, the given data consists of logarithmic functions, we apply L\'Hospital rule to evaluate the limit. 

Indeterminate Form Example 5Module contains solved example on indeterminate form, we start with identification of given form of a data,then we evaluate the final limit after applying L\'Hospital rule. 

Indeterminate Form Example 6Module contains solved example on indeterminate form. We evaluate the limit on application of L\'Hospital rule. 

Jacobian Errors And Approximation 1This module contains a solved example on jacobian which starts with the given function x and y, we then evaluate its derivative to arrive at jacobian value.This is illustration on jacobian of composite function. 

 
Jacobian Errors And Approximation 2This module contains a solved example on jacobian which starts with 3 functions,this illustrates the jacobian of implicit function. 

Jacobian Errors And Approximation 3This module contains a solved example on jacobian which starts with functions u and v , this illustrates functional dependence of a functions. 

Jacobian Errors And Approximation 4This module contains solved example on errors and approximation to find the percentage error in the area of ellipse 

Jacobian Errors And Approximation 5This module contains solved example on errors and approximation, with the help of derivatives we evaluate final answer. 

Jacobian Errors And Approximation 6This module contains an example which illustrates on maxima and minima of function of 2 variables. 

Taylors And Maclaurins Theorem 1This module contains an example based on Taylors and Maclaurins theorem which illustrates expansion of function using standard function. 

 
Taylors And Maclaurins Theorem 2This module contains an example based on Taylors and Maclaurins theorem which illustrates expansion of function using standard function with expansion upto 5th power of x. 

Taylors And Maclaurins Theorem 3This module contains an example based on Taylors and Maclaurins theorem which illustrates expansion of function using differeniation and integration 

Taylors And Maclaurins Theorem 4This module contains an example based on Taylors and Maclaurins theorem which illustrates expansion using substituitions. 

Taylors And Maclaurins Theorem 5This module contains an example based on Taylors and Maclaurins theorem which illustrates exapansion using complex numbers. 

Taylors And Maclaurins Theorem 6This Module contains solved example based on taylors series. 

Taylors And Maclaurins Theorem 7This Module contains solved example based on taylors series. 

 
Taylors And Maclaurins Theorem 8This module contains solved example based on taylors series, we evaluate the square root of a given number using series. 

The Cone And Cylinder Example 1This module contains step by step solved example based on cone and cylinder. 

The Cone And Cylinder Example 2This module contains step by step solved example based on cone and cylinder. 

The Cone And Cylinder Example 3This module contains step by step solved example based on cone and cylinder. 

The Cone And Cylinder Example 4This module contains step by step solved example based on cone and cylinder. 

The Cone And Cylinder Example 5This module contains step by step solved example based on cone and cylinder. 

 
Differential Equation Example 1This module contains solved example based on differential equation. 

Differential Equation Example 2This module contains solved example based on differential equation. 

Differential Equation Example 3This module contains solved example based on differential equation. 

Differential Equation Example 4This module contains solved example based on differential equation. 

Differential Equation Example 5This module contains solved example based on differential equation. 

Differential Equation Example 6This module contains solved example based on differential equation. 

 
Differential Equation Example 7This module contains solved example based on differential equation. 

Differential Equation Example 8This module contains solved example based on differential equation. 

Differential Equation Example 9This module contains solved example based on differential equation. 

Differential Equation Example 10This module contains solved example based on differential equation. 

Differential Equation Example 11This module contains solved example based on differential equation. 

Differential Equation Example 12This module contains solved example based on differential equation. 

 
Differential Equation Example 13This module contains solved example based on differential equation. 

Differential Equation Example 14This module contains solved example based on differential equation. 

Differential Equation Example 15This module contains solved example based on differential equation. 

Differential Equation Example 16This module contains solved example based on differential equation. 

Differential Equation Example 17This module contains solved example based on differential equation. 

Differential Equation Example 18This module contains solved example based on differential equation. 

 
Differential Equation Example 19This module contains solved example based on differential equation. 

Differential Equation Example 20This module contains solved example based on differential equation. 

Application Of Differential Equation Example 1This module contains solved example based on application of differential equation. 

Application Of Integral To Area Volume Example 1This module contains solved example based on Application Of Integral To Area Volume. 

Application Of Integral To Area Volume Example 2This module contains solved example based on Application Of Integral To Area Volume. 

Application Of Integral To Area Volume Example 3This module contains solved example based on Application Of Integral To Area Volume. 

 
Application Of Integral To Area Volume Example 4This module contains solved example based on Application Of Integral To Area Volume. 

Applications Of Differential Equations Example 2This module contains solved example based on Application Of Integral To Area Volume. 

Applications Of Differential Equations Example 3This module contains solved example based on Application Of Integral To Area Volume. 

Applications Of Differential Equations Example 4This module contains solved example based on Application Of Integral To Area Volume. 

Applications Of Differential Equations Example 5This module contains solved example based on Application Of Integral To Area Volume. 

Applications Of Differential Equations Example 6This module contains solved example based on Application Of Integral To Area Volume. 

 
Applications Of Differential Equations Example 7This module contains solved example based on Application Of Integral To Area Volume. 

Applications Of Differential Equations Example 8This module contains solved example based on Application Of Integral To Area Volume. 

Beta Function Example 1This module contains solved example based on beta function. 

Beta Function Example 2This module contains solved example based on beta function. 

Beta Function Example 3This module contains solved example based on beta function. 

Fourier Series Example 1This module contains solved example based on Fourier Series. 

 
Fourier Series Example 2This module contains solved example based on Fourier Series. 

Fourier Series Example 3This module contains solved example based on Fourier Series. 

Gamma Function Example 1This module contains solved example based on Gamma Function. 

Gamma Function Example 2This module contains solved example based on Gamma Function. 

Gamma Function Example 3This module contains solved example based on Gamma Function. 

Gamma Function Example 4This module contains solved example based on Gamma Function. 

 
Gamma Function Example 5This module contains solved example based on Gamma Function. 

Reduction Formulae Example 1This module contains solved example based on Reduction Formulae. 

Reduction Formulae Example 2This module contains solved example based on Reduction Formulae. 

Sphere Example 1This module contains solved example based on sphere. 

Sphere Example 2This module contains solved example based on Sphere. 

Sphere Example 3This module contains solved example based on Sphere. 

 
Sphere Example 4This module contains solved example based on Sphere. 
Interactive Modules
Unique Invention developed by Cognifront. This section provides interactivity for increasing the visualization ability of the students. It facilitates the teacher to virtually interact with a complex object and help learners to have a deep understanding of the concept. With the help of this feature the user can demonstrate the features of the model in classroom itself. Learners can also interact with these modules to concretize their understanding. This will help the teacher indulge students into their lectures. This section provides interactivity with the following objectives  (a) Increase the visualization ability of the students and (b) Boost their ability of learning the concepts by allowing them to interact with it. 
Argand DiagramArgand diagrams are frequently used to plot the positions of the poles and zeroes of a function in the complex plane. This is shown in this interactive module. You can use mouse to get value position in the complex plane. 

Complex Conjugate Numbercomplex conjugates are a pair of complex numbers, both having the same real part, but with imaginary parts of equal magnitude and opposite signs. User can use mouse to get complex conjugate numbers on graph plotted. 

Matrix ApplicationThis interactive explains application of Matrices. We can show matrix data in mutiple forms. In this interactive, user can change matrix values. On change of matrix value respective graph is plotted. 

Matrix NotationMatrix is commonly written in box brackets. This interactive explains notations of matrix. In this interactive user can edit either table or matrix. If user click on table fruit and their taste according change in matrix is done. If user change value of any matrix element from 0 to 1 respective change is done in table. 

Rate Of Change Of ShadowThis interactive is applications of derivative. User can use mouse to move street lamp down/up to observe the change in height of shadow of standing man. As per change of height of street lamp, rate of change of shadow is explained using equation. 

Rerpresentation Of Complex NumberComplex number is represented in three forms: Cartesian, Polar and Exponential form. This interactive show all these three forms of complex number. User can change value and sign of complex number. On change of complex number respective forms of complex number displayed on select of forms. In polar and exponential form, on click of f user can see formula applied to generate polar and exponential form. 

 
Geometrical Interpretation Of DerivativeThis is interactive tool to understand geometrical interpretation of derivative. In this interactive user can change amplitude, frequency of wave. We have provided Point position so that user can change it as get derivative at that point of curve. 

Maxima Minima Apple TreesThe value of the function at a maximum point is called the maximum value of the function and the value of the function at a minimum point is called the minimum value of the function. Calculation of value of maxima is explained in this interactive by using example of planting of apple trees. On exceeding number of apple trees number of apples from a tree will decrease. In this interactive, user can change number of apple trees, number of apples per tree and output drops per tree on increasing number of apple trees. After addition of tree, on clicking of Calculate user will get number of trees to be added to get maximum output. This calculation is given in step by step form. 

Newton's Law Of CoolingThis module is interactive problem solution based on newton\'s law of cooling. 

Rate Of Change Of Water LevelThis module is an interactive content which explains an application of integrals using example of rate of change of water level. 

Application Of IntegralThis module is an interactive solution for Application Of Integrals. 
Surface Plotter
Surface 1This is an interactive module having 3D interaction of certain equation, we can change the values from equation and accordingly the surface view changes. 

Surface 2This is an interactive module having 3D interaction of certain equation, we can change the values from equation,equation contains one of the sinusoidal function and accordingly the surface view changes. 

Sine WaveThis module is 3D interactive having trigonometric function 
Applications
Application Of MatricesThis module explains application of matrices in real life example. Here with the help of 2 examples applications of matrices is explained. 

Application Of TrigonometryThis module explains applications of trigonometry with the help of real life example. A tribute to grate Mathematicians Aryabhatta, Archimedes, Pythagoras, Euclid, S R Ramanujan, Rene Descartes, Johan Carl Friedrich Gauss, Leonhard Euler, Sir Isaac Newton, and Pierre Simon Laplace is also given in this module. 

Applications Of Complex NumbersComplex number represents the phase difference between two subsystems. This module gives you brief introduction about where complex numbers are being used in real life example. 

Applications Of DifferentiationsThis module explains real life examples of applications of differentiation such as rate of change of volume, rate of change of radius, rate of melting, rate of growth etc 

FenceThis is an application of maxima. This module explains sloving of fence problem using Maxima 

Facts Of MathsThis module gives idea about some interesting facts about maths such as information about World Maths Day, pronunciation of Mathematics etc. 

 
Maths For Forensic And MedicineThis module explains use of math in Forensic Service and Medical Field. How math is used for image processing is alos explained in this module. 

Sunrise EquationSunrise equation is application of Trigonometry. The sunrise equation can be used to derive the time of sunrise and sunset for any solar declination and latitude in terms of local solar time. this module explains calculation of Sunrise time and Sunset Time using Trigonometry. 

Value Of PiThis module explains History of pi, application of pi, Pi Day, and Experiment to find value of pi in details. 

Application Of SphereThis module contains the real life applications of sphere,which is a part of solid geometry. 

Application Of The ConeThis module contains the real life applications of cone,which is a part of solid geometry. 

Application Of The CylinderThis module contains applications of the cylinder,which is a part of solid geometry. 

 
Application Of Differential EquationsThis module explains use of differential equation in real life and engineering applications. 

Application Of Fourier SeriesThis module explains the practical approach towards the fourier series. 

Application Of IntegrationThis module contains the application of integration in real life. 

Application Of Coordinate GeometryThis module explains us importance of study of coordinate geometry, also, how it relates to our day to day life. 

Application Of Moment Of Inertia And Center Of Mass,GravityThis module explains real life examples based on moment of inertia and centre of gravity. 
How To Use Scientific Calculator
This section contains use of scientific calculator to solve mathematical problems such as complex numbers, examples on matrices, solving polynomial etc. How these kinds of examples can be solved using calculator only is explained in this section. 
Absolute Value And Argument Of Complex NumbersThis module illustrates the absolute value and argument associated with a given complex number with the help of a calculator. 

Determinant Of MatrixThis module illustrates an important calculation of matrix i.e. determinant on calculator. 

Finding UnknownsThis module illustrates how to find an unknowns with the help of of calculator. 

FractionsThis module illustrates the fraction representation and its calculation on calculator. 

Matrix MultiplicationThis module illustrates the multiplication of matrix on calculator. 

Solving PolynomialThis module illustrates how a polynomial is solved with the help of a calculator. 

 
Integration 1This module shows how we can carry out integration operations on calculator with the help of an example. 

Integration 2This module shows how we can carry out some basic integration operations on calculator. 
Derivative Basic Practice By Games
Amazing section developed by Cognifront Software Pvt. Ltd. In this section we have provided few games based on derivative problem so that student can learn derivative concept with fun and playing games. 
Parachute Landing By GameThis game is developed by Cognifront for basic derivative practice in mathematics. In this game, the aeroplane will pass. Click in it so that the man will jump. After that click on a falling man to open the parachute. The goal is to jump on a boat carrying correct answer (derivative) for the given equation. 

Shoot Equation By GameThis game is developed by Cognifront Software Pvt. Ltd. This game will help students to improve derivatives concept. In this game there is a question whose answer can be hit by user. If correct anwer hits score will be increased and on miss hit or wrong answer lives of hitting an answer will be decrease. 

Equation Maze By GameThis game is developed by Cognifront Software Pvt. Ltd. This game will improve derivative concept of students. Here in this game there is a question of derivative whose answer have to pick up by blue answer picker. There is red answer picker also and time out to pick up correct answer. Blue picker have to reach at the equation before red picker reach at the equation. 

Equation Hunt By GameThis module contains a derivative formulae quiz in game form. 

Solid Geometry By GameThis module is a challenging game based on solid geometry,one have to hit an arrow for the right answer,question is in the form of equation,one has to determine the shape of that equation, may be in the form of sphere,cone or cylinder etc. 
Formulae
This section is a collection of formulae which will help students to learn formulae fastly. 
JacobianThis module explains details about Jacobian such as notation, jacobian of composite functions, jacobian of implicit functions, partial derivative of implicit functions, and implicit function of 6 variables. 

Logarithm Factoring Formulae IndicesThis module covers formulae related to logarithm, factoring formulae, indices, and geometry. 

Maclaurins Taylors Series And ExpansionThis module covers Maclaurins theorem, taylors theorem, Expansion of some standard functions. 

TrigonometryThis module covers trigonometrical formulae. 

Intergration FormulaeThis module contains all important rules of integration. 

Differential EquationsThis module contains differential equation formulae list. 

 
Solid Geometry FormulaeThis module contains different formulas of solid geometry 

Beta And Gamma FunctionThis module covers all the necessary formulae for Beta And Gamma Function. 

Reduction FormulaeThis module covers all the necessary formulae for Beta and Gamma Functions. 
Self Exercises
This section is prepared to involve students by challenging them to solve handfull of classic exercises. It is really a brain booster section. 
Self ExercisesThis section is for students self improvement. Here we have provide some unsolved examples which teacher can ask to students to solve it. 

Application Of Integrals To Area And VolumeThis module contains an examples on application of integrals to area and volume for the self exercise. 

Curve Tracing And Reduction Of CurvesThis module contains an examples on curve tracing and reduction of curves for the self exercise. 

Differentiation Under The Integral SignThis module contains an examples on Differentiation Under The Integral Sign for the self exercise. 

Fourier SeriesThis module contains an examples on Fourier Series for the self exercise. 

Multiple IntegralsThis module contains an examples on Multiple Integrals for the self exercise. 

 
Reduction Formula Beta Function And Gamma FunctionsThis module contains an examples on Reduction Formula Beta Function And Gamma Functions for the self exercise. 

Solid GeometryThis module contains an examples on Solid Geometry for the self exercise. 

Differential EquationsThis module contains an examples on Multiple Integrals for the self exercise. 
Team Projects
Team Projects 2This module contains the projects for maths,which can be carried out as a team projects. 

Team Projects 1This section contains practical and challenging math problems, which students have to solve along with the team. 
Lecture Plans
This section presents a complete lecture plan. You get a license to edit these lectures to suit your style. We respect the fact that every teacher has a different style of teaching and that is why this section is flexible to allow you to choose and edit your presentations. You can bring any additional content into these presentations. You can combine two or more presentations if you wish to cover those topics in a single lecture. 
Applications Of DE To Orthogonal TrajectoriesThis module contains theory of application of DE to orthogonal trajectories. 

Simple Harmonic MotionThis module contains theory of simple harmonic motion ,hook\'s law and formulae for time and velocity 

Rate Of Decay Of Radioactive MaterialsThis module contains theory of radioactive decay of element and rate of decay of radioactive elements 

One Dimensional Conduction Of HeatThis module contains theory of conduction of heat,laws of conduction of heat 

Application Of Differential Equations In Orthogonal TrajectriesThis module contains theory of Application of DE in orthogonal trajectry 

Applications Of DE To Chemical ProblemsThis module contains theory of Application of DE in chemical problems 

 
Rectilinear MotionThis module contains theory for Velocity and Acceleration Meaning and Definition of rectilinear motion,newton\'s second law of motion and concept of net forces. 

Centre Of Gravity 1This lecture module contains a powerpoint presentation on the theory of centre of gravity. 

Centre Of Gravity 2This lecture module contains a powerpoint presentation on the theory of centre of gravity. 

Beta And Gamma FunctionThis lecture module contains a Beta function and its properties,Gamma function and its properties,Application of these functions,Solve an example 

Co Ordinate SystemThis lecture introduces a learner to the concept of Types of coordinate systems,Relation between coordinate systems,Shift of origin and Distance formula 

Curve TracingThis lecture is based on Basic definitions of curves and Classification of curves 

 
Differentiation Under Integral SignThis lecture is an itroduction to a DUIS,DUIS rule1,Solved example,DUIS rule2 

Double IntegralsThis lecture is based on double integrals,its properties and solved example. 

Equation Of ConeThis lecture is based on Define Cone,Calculate Equations of a Cone,Discussion on Applications of Equations of Cone. 

Exact Differential EquationThis lecture explains Exact Differential Equation,Example on Exact Differential Equation,Equation Reducible to Exact Differential Equation and 4 rules. 

Formation Of Differential EquationThis lecture consists of Definition of Differential Equation,Formation of Differential Equation,Example on formation of Differential Equation,Application of Differential Equation. 

Homogeneous And Non Homogeneous Differential EquationThis lecture introduces a learner to a concept Homogeneous Differential Equation,Example on Homogeneous Differential Equation,NonHomogeneous Differential Equation and 2 cases. 

 
Limits Of IntegrationTHis lecture contains a Meaning of limits of integration,Methods for determining the limits of integration. 

Linear Differential EquationThis lecture is an introduction to a Linear Differential Equation and Equation Reducible to Linear Differential Equation 

Moment Of Inertia 1This lecture introduces to a concept of Moment and Torque,Meaning and Definition of Moment of Inertia and Radius of Gyration. 

Moment Of Inertia 2This lecture introduces to a standard limits for moment of inertia for certain shapes. 

Solid Geometry ConeThis lecture introduces a learner to the concept of Cone,Right circular cone.It also contains a Solved example 

Solid Geometry CylinderThis lecture is an introduction to a Cylinder,Right circular cylinder and an enveloping cylinder 

 
Solid Geometry Line And PlaneThis lecture is an introduction to a Angle between two lines,Projection of lines,The plane and the straight line 

Solid Geometry SphereThis lecture contains a Sphere,Equation of sphere and Different cases of sphere. 

Variable Separable FormThis lecture is an introduction to a Variable separable form,Example on Variable separable form,Equation Reducible to Variable separable form,Example on Equation Reducible to Variable separable form. 

Division Of The Join And Direction CosinesThis lecture contains a Division of the join of two given points,Direction cosines,Direction ratios. 

Reduction FormulaeThis lecture is an Introduction to reduction formulae,Definition and Reduction formula for sinusoidal functions 

Tracing Of Cartesian CurvesThis lecture explains a rules for tracing a cartesian curves. 

 
Tracing Of Cartesian Curves 2This lecture explains some more rules for tracing a cartesian curves. 

Triple IntegrationThis lecture introduces to a calculus of triple integration along with its applications. 

Application Of Multiple Intgrals To Represent Area VolumeThis lecture contains a theory of Application Of Multiple Intgrals To Represent Area Volume. 

Newton's Law Of CoolingThis lecture introduces to a concept of Newton\'s Law Of Cooling. 

Area Enclosed By Plane Curves Expressed In PolarThis lectur econtaisn a theory for Area Enclosed By Plane Curves Expressed In Polar. 

Adjoint Cofactor Inverse Of MatrixThis lecture explains calculation of determinant of Matrix, Minor of matrix, cofactor of an element, adjoint of matrix, and inverse of matrix in details. 

 
Algebra Of Complex NumbersIn this lecture leaners will introduced to complex numbers in details. This lecture also explains Algebra of complex number, Argand diagram, Complex conjugate and modulus of complex number in details. 

Cauchys Condensation Gausss TestThis lecture covers Cauchys condensation test, Convergence test for auxiliary series, Gausss test. 

Cauchys Nth Root Test P Series Convergence Of Geometric SeriesThis lecture will introduced Cauchys nth root test,P series,Convergence of geometric series in details. 

Comparison Raabes And D Alemberts Ratio TestThis lecture will introduced Comparison test, DAlemberts ratio test, Raabes test in details. 

Composite Functions Higher Order DerivativesThis lecture covers Composite function, Derivatives of composite function, Higher order derivatives in details. 

Condition For Consistency Of Homogeneous EquationsThis lecture explains Condition for consistency of homogeneous equations in details. 

 
Convergent And Divergent Series In Real LifeIn this lecture learners will introduced to Convergent and divergent series in real life. 

Definition And Notation Nth Differential Coefficients Of Standard FunctionsThis lecture covers definition and notation of nth differential coefficients of standard functions in details. 

Definition Of Eigen Values Method Of Finding Eigen ValueThis lecture covers brief introduction about definition of eigen value and methods of finding eigen value. 

DeMoivre's TheoremThis lecture covers DeMoiver\'s theorem in details. 

Differentiation RulesThis lecture covers Function with one variable and its derivative, Function with multiple variables and its differentiation, Rules of differentiation in details. 

Errors And ApproximationIn this lecture leaners will introduced to Partial derivatives of implicit functions, Functional dependence of the functions, Errors and approximation in details. 

 
Expansion Of Determinants Verification Of Eigen Values Cramers RuleThis lecture covers Expansion of determinants, Verification of eigen values and details of Cramer\'s rule. 

Functions And Their DerivativesIn this lecture leaners will introduced to Function with one variable and its derivative, Function with multiple variables and its differentiation in details. 

Homogeneous And Non Homogeneous Equations Condition For Consistency Of Non Homogeneous EquationsThis lecture covers Homogeneous and nonhomogeneous equations, Conditions for consistency of nonhomogeneous equations. 

Hyperbolic Functions Logarithms Of Complex NumbersThis lecture explains Hyperbolic functions, Relation between trigonometric and hyperbolic functions, General and principle value of logarithm, Separation of real and imaginary part in details 

Illustration On Differentiation Homogeneous Function And Euler's TheoremThis lecture cover Differentiation on variable to be treated as constant, Homogeneous functions, Euler\'s theorem. 

Introduction To Complex NumbersThis lecture gives brief introduction to Square roots of positive and negative numbers, Imaginary number i. 

 
Jacobian Definition Jacobian Of FunctionsThis is introductory lecture about Jacobian. This lecture covers Notation of jacobian, Jacobian of composite function, Jacobian of implicit function 

Leibnitz's TheoremIn this lecture learners will introduced to Leibnitz\'s Theorem. This also explains Need of Leibnitz\'s theorem, Types to solve using Leibnitz\'s theorem, and Solve an example based on Leibnitz\'s theorem. 

Linear Dependence And Independence Of Vectors Linear Transformation Orthogonal MatrixIn this lecture learners will introducted to Conditions for consistency of homogeneous equations, Linear dependence and independence of vector, Linear transformation, and orthogonal matrix. 

Linear Transformation Orthogonal MatrixThis lecture gives brief introduction to Linear transformation, Orthogonal matrix, and example based on linera transformation and orthogonal matrix. 

Logarithmic De Morgans And Cauchys Integral Test And Alternating SeriesThis lecture covers logarithmic test, De Morgans test, cauchys integral test in details. This lecture plan also covers Alternating series, absolute and conditional convergence. 

Maclaurin's Series IntroductionThis is introductory lecture about Maclaurin\'s theorem. This lecture covers Maclaurinâ€™s theorem, Application of Maclaurinâ€™s theorem in details and example based on Maclaurin\'s theorem. 

 
Matrix Notation And TypesIn this lecture learners will learn definition and notation of matrices, applications of matrices and types of matrices in brief. Types of matrices such as row, column, symmetric, skew symmetric, scalar, unit, upper triangular, lower triangular and diagonal matrix are also cover in this lecture. 

Maxima And MinimaThis lecture covers Maxima and minima of function of single and multiple variable in details. 

Optimization Finding Maxima And MinimaMathematical optimization is the selection of a best element from some set of available alternatives. The concept of Mathematical optimization is explained in this lecture. This lecture covers Optimization, Maxima and minima concepts. 

Partial Derivatives Of Implicit Functions Functional Dependence Of The FunctionsThis lecture covers Partial derivatives of implicit functions, Functional dependence of the functions in details. 

Polar Exponential And Cartesian FormThis lecture will give brief introduction about forms in Complex number such as cartesian form, polar form and exponential form in details. 

Rank Augmented MatrixThis lecture explains Rank of a matrix, Find the rank by reducing the matrix to Echelon form and normal form, Augmented matrix in details. 

 
Sequences Series Convergent And Divergent Series And Applications Of Infinite SeriesIn this lecture learners will introduced to sequences, series, Convergent and Divergent Series and Applications of Infinite Series in details. This lecture also covers monotonic increasing sequence, monotonic decreasing sequence, alternating sequence, oscillatory series. 

Taylor SeriesThis lecture covers Taylor series and examples based on Taylor Series 
3D Stereographic
New feature developed by Cognifront. The first time ever in Engineering field there is 3D Stereos for learning. 3D Stereos are used in Entertainment media only but Cognifront come up with this 3D Stereo module for engineering education to make teaching and learning joyful. 
Application Of TrigonometryThis module describes the application of trigonometry in real life with 3D view. 

Maxima And MinimaThis module describes the global and local maxima,minima in 3D view. 

Transformation MatrixThis module describes transformation matrix in 3D view. 

Hyperbolic FunctionThis module gives a graphical 3D view of a trigonometrical and hyperbolic function. 

Application Of Partial DifferentiationThis module describes the traffic flow analysis in 3D view which can be explained with the help of partial differentiation. 

CartesianThis module contains a 3D view of cartesian coordinate system 

 
CylindricalThis module contains a 3D view of cylindrical coordinate system 

PolarThis module contains a 3D view of polar coordinate system 

CuspThis module shows the graph of cusp in 3 dimensional view. 

Equation Of ConeThis module contains 3 dimensional visualozation of cones. 

Equation Of Elliptical ConeThis module contains 3dimensional visualization of elliptical cone with its equation 

Equation Of FrustumThis module contains 3dimensional visualization of Frustum with its equation 

 
Equation Of Parabolic ConeThis module contains 3dimensional visualization of Parabolic Cone with its equation 

Surface By Equation 1This module contains 3 Dimensional view of surface. 

Surface By Equation 2This module contains 3 Dimensional view of surface. 

Surface By Equation 3This module contains 3 Dimensional view of surface. 
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