Calculus-That Will Break Your Fear
Give Me 10 Hours, I will Make You Master In Differential, Integral and Vector Calculus
Ratings 4.68 / 5.00
What You Will 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
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 Should Attend!
- +2, Engineering students and students preparing for Competitive exams
- GATE, PSU,S
