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Calculus-That Will Break Your Fear

Give Me 10 Hours, I will Make You Master In Differential, Integral and Vector Calculus
Total Derivatives using Chain Rule
Homogenous function
Euler's theorem
Maxima and Minima for a function of one variable, two variables and three variables
Continuity of a function at a particular value and in a Closed Interval
Differentiability of a function in an Open Interval
Mean Value Theorems :
Roll's Theorem
Legrange's Mean Value Theorem
Cauchy's Mean Value Theorem
Taylor's Theorem ( Generalised Mean Value Theorem )
Definite Integrals and Properties of definite integrals
Improper Definite Integrals, Convergence and Divergence
Comparison Test, P-Series Test and Integral Test
Gamma functions
Beta functions
Applications :
Areas
Length of the arc of a curve
Volume generated by revolving the areas formed about X-Axis and about Y-Axis
Limits
VECTOR CALCULUS :
Basic Vector Algebra : Dot Product ( Scalor Product ), Cross Product ( Vector Product ), Scalor Triple Product, Vector Triple Product
Gradient, Directional derivative (d.d), Unit Normal
Divergence, Solenoidal Vector
Curl or Rotation , Irrotational or Conservative Force Field
Line Integrals, Work Done
Surface Integrals : Double Integrals evaluation techniques, Change of order of integration
Volume Integrals, Triple integrals evaluation techniques
Vector Integral Theorems :
Green's Theorem
Stoke's Theorem
Guass - Divergence Theorem

This course has detailed explanation of following Topics:

Partial Derivatives : Partial and Total Derivatives ( Chain rule), Homogeneous functions, Euler’s Theorem, Maxima and Minima for a function of One variable, Two variables and Three variables.

Mean value theorems : Continuity of a function at a particular value and in a closed interval, Differentiability of a function in an open interval, Roll’s theorem, Legrange’s Mean value theorem, Cauchy’s Mean value theorem , Taylor’s theorem ( Generalized Mean value theorem.

Definite and Improper Definite Integrals: Properties of Definite Integrals, Convergence and Divergence, Comparison Test, P-Series Test, Integral test, Gamma and Beta functions.

Limits : Limits definition, Indeterminate forms of Limits.

Vector Calculus : Basics of Vector Algebra, Dot ( Scalar ) Product , Cross ( Vector )Product , Scalar Triple Product, Vector Triple Product, Application of Partial Derivatives on Vectors :Gradient, Directional Derivative( d,d ), Unit normal, Divergence, Solenoidal vector, Curl or Rotation, Irrotational or Conservative Force Field.

Multiple Integrals : Line integrals, Work done, Surface Integrals, Double Integrals evaluation Techniques, Volume Integrals, Triple Integrals evaluation techniques.

Vector Integral Theorems : Green’s Theorem, Stoke’s Theorem and Gauss – Divergence Theorem

Introduction

1
Introduction

Students will know about the contents of the subject in detail

2
Partial Derivatives

In this lecture you will know the difference between Ordinary Derivatives and Partial Derivatives. Ypu will also know the basic method to solve partial derivatives and Will be able to solve first order partial derivative problems by the end of this video lecture.

3
Higher Order Partial Derivatives

You will learn how to solve higher order partial derivatives problems and will have crystal clear clarity in solving  problems in partial derivatives

4
Problems in Partial Derivatives

You will find some problems solved in partial derivatives.

5
Additional Problems in Partial Derivatives

You will learn some more additional problems solved in Partial Derivatives

6
Homogeneous Functions

You will know the significance and definition of Homogeneous function. You will easily identify a homogeneous function.

7
Euler's Theorem and Problems

You will understand Type 1, Type 2 and Type 3 First Order and Second Order Standard Euler's equation,for a given Homogeneous function, and find some problems solved.

8
Total Derivatives

You will know how to solve Total Derivatives problems easily by applying Chain Rule and find problems solved.

9
Total Derivatives Continuation

You will find other methods in solving Total Derivative problems

10
Maxima and Minima for a function of Single Variable

In this lecture you will understand what is Critical Point or Stationary Point and its importance. You can see increasing and decreasing functions, Maxima and Minima through Graphical explanation. You will see Necessary and Sufficient Conditions to find Maxima and Minima for a function of one variable.You will also find find problems solved. You will know how to find Point of Inflection

11
Maxima and Minima for a function of two variables.

You will know the methods to find Maxima and Minima for a function in two variables. You will understand the importance and how to find a Saddle point

12
Constrained Maxima and Minima for a function of Three Variables.

You will know the Importance of Lagrange's Multiplier's Method ( LMM ). you will also know how this procedure makes the simplification easier in finding Maxima or Minima for a function of Three variables.

13
Continuity of a function

You will know importance of continuity and how to find Continuity of a function at a Particular value and also in a Closed Interval

14
Differentiability of a function

You will know differentiability of a function and numericals solved.

15
Rolle's Theorem

In this lecture you will find Roll's Theorem Statement, it's significance and problems solved in it.

16
Legrange's Mean Value Theorem

In this lecture you will know the importance of Legrange's Theorem and Conditions to apply Legrange's Mean Value Theorem. some problem's solved it it.

17
Cauchy's Theorem

In this lecture you will know the comparision of Legrange's Theorem and Cauchy's Theorem. The  Conditions to apply Cauchy's Mean Value Theorem. some problem's solved it it.

18
Taylor's Theorem ( Generalised Mean Value Theorem )

In this lecture you will know the importance of Taylor's Theorem and Conditions to apply Taylor's Theorem. some problem's solved it. You can see the easy tricks of solving some problems with the help of standard series.

19
Additional problems in Mean Value Theorem.

You will find some additional problems solved.

Definite and Improper Definite Integrals.

1
Definite and Improper Definite Integrals.

Graphical understanding of Definite and Improper Definite Integrals is observed

2
Properties Of Definite Integrals

You will see how properties of Definite Integrals reduces the time in solving

3
Improper Definite Integrals

You will find problems solved in Improper Definite Integrals. you will know about Convergence and Divergence

4
Comparision Test, P-Series Test and Integral Test,

In this lecture you will find Comparision Test, P-Series Test and Integral Test,

5
Gamma Function

In this lecture you will find evaluation of integrals by Gamma function

6
Beta Functions

In this lecture you will find evaluation of integrals by Beta function.

7
Application Of Integrals : Length of the Arc of the Curve

In this lecture you will find length of the arc of the curve

8
Applications Of Integrals : Areas and Volumes

You will find how to find area enclosed between the curves and volume generated by revolving the area formed about X-Axis and Y-Axis

LIMITS

1
Limits

You will know the definition of limits and problems on limits. you will also know the indeterminate forms of the limits .

2
Limts continuation.

you will know the additional methods to find indeterminate forms of the limts

VECTOR CALCULUS

1
Vector Algebra

You will know about the important basics of vectors. You will know what is Dot product, Cross product, Scalor Triple product and Vector Triple product

2
Introduction to basics of Vector Algebra continuation

In this lecture you will find the continuation of earlier lecture . you will find triple product ( Scalor Triple Product and Vector Triple Product )

3
Gradient, Directional Derivative (d.d ), Normal

In this lecture you will know about Gradient, Directional Derivative (d.d), Normal to the given surface. you will come across Del ,a vector differential operator and Laplacian operator

4
Gradient of a scalor point function continuation

You will know about Laplacian operator and additional problems in directional derivative( d.d).

5
Divergence, Curl or Rotation

In this lecture you will know about Divergence, Solenoidal , Curl or Rotation, Irrotational, Conservative force field and problems in it.

6
Line Integral

In this lecture you will know about Line Integral , Work done in moving a particle of force field 'F' along a curve 'C' and  You will also find some problems solved in it

7
Surface Integrals, Double Integrals Evaluation Techniques

In this lecture you will the techniques to solve double integrals and some problems are solved in it.

8
Change of Order of Integrals

In this lecture you will know the evaluation of integrals using change of order of Integration

9
Triple Integrals

In this lecture you will know evaluation techniques to solve triple integrals

10
Green's Theorem

You will find the evaluation of line integrals using Green's Theorem and you will also find some problems evaluated using the theorem.

11
Stoke's Theorem

You will find the evaluation of line integrals using Stoke's Theorem and you will also find some problems evaluated using the theorem.

12
Guass-Divergence Theorem

You will find the evaluation of line integrals using Guass - Divergence Theorem and you will also find some problems evaluated using the theorem.

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10 hours on-demand video
Full lifetime access
Access on mobile and TV
Certificate of Completion