India

Calculus of Several Variables

This is a variation on 18.02 Multivariable Calculus. It covers the same topics as in 18.02, but with more focus on mathematical concepts.

Course at a Glance

Mode of learning : Online - Self Paced

Domain / Subject : Mathematics & Science

Function : Engineering

Trainer name : Prof. James McKernan

Difficulty : Basic

Calculus of Several Variables

Description
This is a variation on 18.02 Multivariable Calculus. It covers the same topics as in 18.02, but with more focus on mathematical concepts. Topics include:

  • Vector algebra, dot product, matrices, determinant.
  • Functions of several variables, continuity, differentiability, derivative.
  • Parametrized curves, arc length, curvature, torsion.
  • Vector fields, gradient, curl, divergence.
  • Multiple integrals, change of variables, line integrals, surface integrals.
  • Stokes' theorem in one, two, and three dimensions.

Course Features
Lecture notes
Assignments and solutions
Exams and solutions

Course Meeting Times
Lectures: 3x / week, 1 hour / session

Assignments
Homework assignments are due on the second day of class every week. Late problem sets are not accepted, however the lowest problem set score will be dropped.

Grading
Assignments    25%
Hour exams    45%
Final exam    30%

Lecture Topics
1    Vectors in R2 and R3
2    Dot product
3    Cross product
4    Planes and distances
5    n-dimensional space
6    Cylindrical and spherical coordinates
7    Functions
8    Limits
9    The Derivative
10    More about derivatives
11    Higher derivatives
12    Chain rule
13    Implicit functions
14    Parametrised curves
15    Arclength
16    Moving frames
17    Vector fields
18    Div grad curl and all that
19    Taylor polynomials
20    Maxima and minima: I
21    Maxima and minima: II
22    Double integrals
23    Inclusion-exclusion
24    Triple integrals
25    Change of coordinates: I
26    Change of coordinates: II
27    Line integrals
28    Manifolds with boundary
29    Conservative vector fields revisited
30    Surface integrals
31    Flux
32    Stokes theorem
33    Gauss theorem
34    Forms on Rn

 

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