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 -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 -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.