Multivariable Calculus

Overview

Mathematics course by Dr. Sanjeev Kumar, Prof. S. K. Gupta.

Unit 1
- Functions of several variables
- Limits for multivariable functions-I
- Limits for multivariable functions-II
- Continuity of multivariable functions
- Partial Derivatives-I
Unit 2
- Partial Derivatives-II
- Differentiability-I
- Differentiability-II
- Chain rule-I
- Chain rule-II
Unit 3
- Change of variables
- Euler's theorem for homogeneous functions
- Tangent planes and Normal lines
- Extreme values-I
- Extreme values-II
Unit 4
- Lagrange multipliers
- Taylor's theorem
- Error approximation
- Polar-curves
- Multiple Integrals
Unit 5
- Change Of Order Of Integration
- Change of Variables in Multiple Integral
- Introduction to Gamma Function
- Introduction to Beta Function
- Properties of Beta and Gamma Functions-I
Unit 6
- Properties of Beta and Gamma Functions-II
- Dirichlet's Integral
- Applications of Multiple Integrals
- Vector Differentiation
- Gradient of a Scalar Field and Directional Derivative
Unit 7
- Normal Vector and Potential field
- Gradient(Identities), Divergence and Curl(Identities)
- Some Identities on Divergence and Curl
- Line Integral (I)
- Applications of Line Integrals
Unit 8
- Green's Theorem
- Surface Area
- Surface Integral
- Divergence Theorem of Gauss
- Stoke's Theorem

Taught by IIT and IISc professors, and it follows the Indian university syllabus closely.
All videos and assignments are free on NPTEL and SWAYAM.
The certificate is recognised by many Indian universities for credit transfer and by GATE aspirants.
Great for GATE and semester exam preparation.
From Indian Institute of Technology Roorkee, a well-regarded name.
Completely free.
Self-paced: start any time.
A clear syllabus (8 parts) you can see before you start.

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Free: Every video and assignment is free on NPTEL and SWAYAM. Enrol when the next run opens.
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