Learn · NPTEL

Course11110412537 lectures

Calculus of Several Real Variables

Prof. Joydeep Dutta · IIT Kanpur

Start with lecture 1 At NPTEL

About

This course introduces the very important subject called the calculus of several real variables, which has important applications in science and engineering. The modern world would have been impossible without it. We introduce and discuss the subject in a non-traditional way taking the vector approach in most places. We start with the basics of Vectors, study continuity and partial derivatives, study multiple integrals and their applications and end with the stokes Theorem and Gauss divergence theorem.

INTENDED AUDIENCE: Any Interested Learners

PREREQUISITES: Calculus of One Real Variable

Lectures

Week 1

  1. Vectors in plane and space YouTube
  2. Inner product and distance YouTube
  3. Application to real world problems YouTube
  4. Matrices and determinants YouTube
  5. Cross product of two vectors YouTube

Week 2

  1. Higher dimensional Euclidean space YouTube
  2. Functions of more than one real-variable YouTube
  3. Partial derivatives and Continuity YouTube
  4. Vector-valued maps and Jacobian matrix YouTube
  5. Chain rule for partial derivatives YouTube

Week 3

  1. The Gradient Vector and Directional Derivative YouTube
  2. The Implicit Function Theorem YouTube
  3. Higher Order Partial Derivatives YouTube
  4. Taylor's Theorem in Higher Dimension YouTube
  5. Maxima and Minima for Several Variables YouTube

Week 4

  1. Second Derivative Test for Maximum and Minimum YouTube
  2. Constrained Optimization and The Lagrange Multiplier Rule YouTube
  3. Vector Valued Function and Classical Mechanics YouTube
  4. Arc Length YouTube
  5. Vector Fields YouTube

Week 5

  1. Multiple Integral I YouTube
  2. Multiple Integral II YouTube
  3. Multiple Integral III YouTube
  4. Multiple Integral IV YouTube
  5. Cylindrical and Spherical Coordinates YouTube

Week 6

  1. Multiple Integrals and Mechanics YouTube
  2. Line Integral-I YouTube
  3. Line Integral-II YouTube
  4. Parametrized Surfaces YouTube

Week 7

  1. Area of a surface Integral YouTube
  2. Area of parametrized surface YouTube
  3. Surface Integrals YouTube
  4. Green's Theorem YouTube

Week 8

  1. Stoke's Theorem YouTube
  2. Examples of Stoke's Theorem YouTube
  3. Gauss Divergence Theorem YouTube
  4. Facts about vector fields YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kanpur
Department
Mathematics
Teacher
Prof. Joydeep Dutta
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
Who can watch
NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed