Course Syllabus

The schedule below provides an overview of content of the course. See also the page for the  course information for intended learning outcomes. 

Schedule

Module 1. 3-dimensional geometry and functions of several variables

  • Lecture 1
    • 10.1 Analytic geometry in three dimensions 

Exercises: 11, 25, 27, 29, 31, 33, 35, 37, 39

    • 10.6 Cylindrical and spherical coordinates

Exercises: 3, 5, 9, 13 

  •  Lecture 2
    • 12.1 Vector functions of one variable

Exercises: 17, 21, 33

    • 12.2 Some applications of vector differentiation

Exercises: 3

    • 12.3 Curves and parametrizations

Exercises: 5, 7, 11, 13, 15

  • Lecture 3
    • 13.1 Functions of several variables

Exercises: 5, 9, 13,15, 17, 23, 27, 33

    • 13.2 Limits and continuity

Exercises: 5, 7, 9, 11, 15

Module 2. Partial derivatives and linear approximation

  • Lecture 4
    • 13.3 Partial derivatives

Exercises: 5, 7, 13, 23

    • 13.4 Higher-order derivatives

Exercises: 5, 7, 11, 15, 17

    • 13.5 The chain rule

Exercises: 7, 11, 17, 21

  • Lecture 5
    • 13.6 Linear approximations, differentiability and differentials

Exercises: 3, 5, 17, 19

    • 13.7 Gradient and directional derivatives

Exercises: 3, 5, 13, 17, 25

Module 3. Applications of derivatives

  • Lecture 6
    • 13.8 Implicit functions

Exercises: 13, 17

    • 13.9 Taylor's formula, Taylor series and approximations

Exercises: 1, 3, 5, 7, 11

  • Lecture 7
    • 14.1 Extreme values

Exercises: 5, 7, 9, 19, 23, 25

    • 14.2 Extreme values of functions defined on restricted domains

Exercises: 3, 5, 9, 15

  • Lecture 8
    • 14.3 Lagrange multipliers

Exercises: 3, 9, 11, 15

    • 14.4 Lagrange multipliers in LaTeX: n-space

Exercises: 1, 3

Module 4. Multiple integrals

  • Lecture 9
    • 15.1 Double integrals

Exercises: 15, 19, 21

    • 15.2 Iteration of double integrals in Cartesian coordinates

Exercises: 3, 5, 15, 23

  • Lecture 10
    • 15.3 Improper integrals and a mean-value theorem

Exercises: 1, 3, 13, 27

    • 15.4 Double integrals in polar coordinates

Exercises: 5, 9, 15, 19, 21

  • Lecture 11
    • 15.5 Triple integrals

Exercises: 5, 7, 9

    • 15.6 Change of variables in triple integrals

Exercises: 3, 7, 11

    • 15.7 Applications of multiple integrals

Exercises: 5, 9, 13, 21,27

Module 5. Curve- and surface integrals

  • Lecture 12
    • 16.1 Vector and scalar fields

Exercises: 3, 5, 17

    • 16.2 Conservative fields

Exercises: 3, 5, 7, 21

  • Lecture 13
    • 16.3 Line integrals

Exercises: 7, 11

    • 16.4 Line integrals of vector fields

Exercises: 1, 5, 7, 15

  • Lecture 14
    • 16.5 Surfaces and surface integrals

Exercises: 1, 7, 13

    • 16.6 Oriented surfaces and flux integrals

Exercises: 5, 9, 13, 15

Module 6. Vector Calculus

  • Lecture 15
    • 17.1 Gradient, divergence and curl

Exercises: 3, 7, 11

    • 17.2 Some identities involving grad, div and curl

Exercises: 9, 15, 17

  • Lecture 16
    • 17.3 Green's Theorem in the plane

Exercises: 3, 5, 9

  • Lecture 17
    • 17.4 Divergence Theorem in LaTeX: 3-space

Exercises: 5, 11, 15

    • 17.5 Stokes' Theorem

Exercises: 1, 3, 5

  • Lecture 18
    • Recap for examination

 

Study guide

There is a study guide for those that find the material in the book demanding, see here for different editions: Edition 8  and  Edition 9. The emphasis in this study guide is on those parts of the course that are necessary for getting a PASS grade at the course. Those that aim for a higher grade should consult the course syllabus. 

Note: The study guide suggested here is being revised for the new edition of the book.

Course Summary:

Date Details Due