Calculus-That Will Break Your Fear
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
Students will know about the contents of the subject in detail
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.
You will learn how to solve higher order partial derivatives problems and will have crystal clear clarity in solving problems in partial derivatives
You will find some problems solved in partial derivatives.
You will learn some more additional problems solved in Partial Derivatives
You will know the significance and definition of Homogeneous function. You will easily identify a homogeneous function.
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.
You will know how to solve Total Derivatives problems easily by applying Chain Rule and find problems solved.
You will find other methods in solving Total Derivative problems
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
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
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.
You will know importance of continuity and how to find Continuity of a function at a Particular value and also in a Closed Interval
You will know differentiability of a function and numericals solved.
In this lecture you will find Roll's Theorem Statement, it's significance and problems solved in it.
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.
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.
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.
You will find some additional problems solved.
Definite and Improper Definite Integrals.
Graphical understanding of Definite and Improper Definite Integrals is observed
You will see how properties of Definite Integrals reduces the time in solving
You will find problems solved in Improper Definite Integrals. you will know about Convergence and Divergence
In this lecture you will find Comparision Test, P-Series Test and Integral Test,
In this lecture you will find evaluation of integrals by Gamma function
In this lecture you will find evaluation of integrals by Beta function.
In this lecture you will find length of the arc of the curve
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
You will know the definition of limits and problems on limits. you will also know the indeterminate forms of the limits .
you will know the additional methods to find indeterminate forms of the limts
VECTOR CALCULUS
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
In this lecture you will find the continuation of earlier lecture . you will find triple product ( Scalor Triple Product and Vector Triple Product )
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
You will know about Laplacian operator and additional problems in directional derivative( d.d).
In this lecture you will know about Divergence, Solenoidal , Curl or Rotation, Irrotational, Conservative force field and problems in it.
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
In this lecture you will the techniques to solve double integrals and some problems are solved in it.
In this lecture you will know the evaluation of integrals using change of order of Integration
In this lecture you will know evaluation techniques to solve triple integrals
You will find the evaluation of line integrals using Green's Theorem and you will also find some problems evaluated using the theorem.
You will find the evaluation of line integrals using Stoke's Theorem and you will also find some problems evaluated using the theorem.
You will find the evaluation of line integrals using Guass - Divergence Theorem and you will also find some problems evaluated using the theorem.
