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Calculus-That Will Break Your Fear
Rating: 4.7 out of 5(3 ratings)
56 students

Calculus-That Will Break Your Fear

Give Me 10 Hours, I will Make You Master In Differential, Integral and Vector Calculus
Created byAmarender Reddy Byreddy
Last updated 8/2020
English

What you'll learn

  • 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

Explore related topics

Course content

4 sections • 41 lectures • 10h 12m total length

  • Introduction7:30

    Students will know about the contents of the subject in detail

  • Partial Derivatives16:22

    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.

  • Higher Order Partial Derivatives11:05

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

  • Problems in Partial Derivatives17:25

    You will find some problems solved in partial derivatives.

  • Additional Problems in Partial Derivatives15:07

    You will learn some more additional problems solved in Partial Derivatives

  • Homogeneous Functions10:53

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

  • Euler's Theorem and Problems14:43

    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.

  • Total Derivatives10:20

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

  • Total Derivatives Continuation16:15

    You will find other methods in solving Total Derivative problems

  • Maxima and Minima for a function of Single Variable16:50

    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

  • Maxima and Minima for a function of two variables.19:16

    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

  • Constrained Maxima and Minima for a function of Three Variables.15:56

    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.

  • Continuity of a function18:44

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

  • Differentiability of a function15:59

    You will know differentiability of a function and numericals solved.

  • Rolle's Theorem13:30

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

  • Legrange's Mean Value Theorem7:27

    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.

  • Cauchy's Theorem10:27

    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.

  • Taylor's Theorem ( Generalised Mean Value Theorem )19:20

    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.

  • Additional problems in Mean Value Theorem.16:47

    You will find some additional problems solved.

Requirements

  • Basic formulae in differentiation and integration

Description

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

Who this course is for:

  • +2, Engineering students and students preparing for Competitive exams
  • GATE, PSU,S

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