This course on Multivariable Calculus aims to teach students the concepts of vector functions, vector calculus, partial differentiation, Jacobian transformations, envelope and evolutes, first-order partial differential equations, complex analysis, contour integration, and Taylor series. The course covers topics such as line integrals, Green's theorem, Stoke's theorem, Gauss divergence theorem, maxima and minima of functions, and various methods for solving partial differential equations. The teaching method includes theoretical explanations, examples, and solutions provided by the instructor. This course is intended for students and professionals interested in advancing their knowledge and skills in multivariable calculus and its applications.
Overview
Syllabus
Concept of Vector Point Function & Vector Differentiation By GP Sir.
Gradient of a Scalar Field & Directional Derivative | Normal Vector.
Divergence and Curl of vector field | Irrotational & Solenoidal vector.
Vector Calculus - Line Integrals of Vector Field | Example & Solution.
Vector Calculus- Application of Line Integral |Scalar Potential | Work Done By Force |.
Vector Calculus - Green's Theorem | Example and Solution by GP Sir.
Vector Calculus - Stoke's Theorem | Example and Solution by GP Sir.
Vector Calculus - Gauss Divergence Theorem | Example and Solution.
Maxima And Minima of Two Variables Function | Examples And Solution.
Maxima and Minima - Langrange's Method of Undetermined Multipliers.
Partial Differentiation Example And Solution | Multivariable Calculus.
Partial Differentiation - Euler's Theorem for Homogeneous Function.
Partial Differentiation - Total Differential Coefficient Problem & Solution.
Jacobian, Jacobian Transformation, Jacobian Method, Differential Calculus.
Jacobian, Jacobian Properties,Jacobian Example, Differential Calculus.
Jacobian, Jacobian of Implicit Function, Jacobian Example Par-III.
Envelope and Evolutes, Envelope Math, Differential Calculus By GP Sir.
Envelope and Evolutes, Evolute, Evolute of Curve Differential Calculus.
First Order Partial Differential Equation -Solution of Lagrange Form.
Non Linear Partial Differential Equations Standard Form-I By GP Sir.
Non Linear Partial Differential Equations-Standard Form-II By GP Sir.
Non Linear Partial Differential Equations-Standard Form-III By GP Sir.
Non Linear Partial Differential Equation Standard form-IV | Clairaut's Form.
Charpit's Method For Non Linear Partial Differential Equation By GP.
Partial Differential Equation | Homogeneous PDE | CF & PI | Part -I.
Partial Differential Equation | Homogeneous PDE | CF & PI | Part-II.
Partial Differential Equation | Homogeneous PDE | CF & PI | Part-III.
Partial Differential Equation | Homogeneous PDE | CF & PI | Part-IV.
Partial Differential Equation | General Method To Find PI | Part-V.
Partial Differential Equation | Non Homogeneous PDE | Rules of CF & PI.
Partial Differential Equation | Non Homogeneous PDE | Rules of PI.
Complex Analysis | Analytic Function | Cauchy Riemann Equation BY GP.
Complex Analysis - Short Trick To Find Harmonic Conjugate By GP Sir.
Complex Analysis - Analytic Function | Milne Thomson Method | Example & Solutions.
Complex Analysis - Bilinear transformation | Conformal Mappings By GP.
Complex Analysis - Complex Integration Line Integral Example & Solution.
Cauchy's Integral Formula For Analytic Function | Example & Solution.
Complex Analysis - Cauchy's Residue Theorem & Its Application by GP.
Complex Analysis- Contour Integration | Application of Residue Theorem.
Complex Analysis - Contour integration | Evaluation of Improper Integrals.
Volume of Solids of Revolution | Cartesian & Parametric Form BY GP Sir.
Surface Area of Solids of Revolution | Cartesian & Parametric Form.
Double Integral & Area By Double Integration | Multiple Integral.
Double Integration - Change of Order of Integration | Cartesian & Polar.
Triple Integral | Integral Calculus | Multivariable Calculus | GP Sir.
Triple Integral | Integral Calculus | Multivariable Calculus | Volume By Triple Integral.
Triple Integral | Dirichlet Theorem | Integral Calculus | Multivariable Calculus.
Taylor Series | Taylor Series Expansion | For Function Of Two Variable | Part-I.
Taylor Series | Taylor Series Expansion | For Function Of Two Variable | Part-II.
Limit of a function | Two Variable Function | Epsilon Delta definition of Limit | Examples.
Limit of a function | Two Variable Function | Examples & Solution | Part-II.
Continuity of a Function | Two Variable Function | Multivariable Calculus.
Partial Derivative | Function Of Two Variable | Examples By Limit Definition.
Differentiability | Two Variable Function | Multivariable Calculus.
Leibnitz Rule | Differentiation Under The Integral Sign | PYQs Of IIT-JAM & GATE.
Calculus | Important formulae | Limit Continuity And Differentiability.
Calculus | Mean Value Theorem | Important formulae | Rolles, Lagrange & Cauchy.
Calculus | Taylor Series | Maclaurin Series | Important formulae.
Differentiability | Function Of Several Variable | Condition For Differentiability.
Taught by
Gajendra Purohit
