MATH 324 B
Advanced Multivariable Calculus

Winter 2018

Course description

Multivariable calculus is the mathematics of fields and continuos media. In particular, it is the language of electromagnetism, Newtonian gravity, fluid mechanics and the theory of elasticity. In this course, you will learn about double and triple integrals; changes of variables; polar, cylindrical and spherical coordinate systems; line and surface integrals; vector fields; flux and divergence; and circulation and curl.


Instructor

Name: Lucas Braune
Website: www.math.uw.edu/~lvhb
E-mail: lvhb 'at' uw.edu
Office: Padelford C-526
Office hours: MW, from 4:30 to 6:00pm.


Time and Place

When: Mondays, Wednesdays and Fridays, from 9:30 to 10:20am
Where: CHL 015 (Chemistry Library Building)


Calendar

Day Topics Sections Notes
Jan 3 Double integrals. Riemann sums. Fubini's theorem. 15.1-2 PDF
Jan 5 Double integrals over general regions. 15.3 PDF
Jan 8 Polar coordinates. Applications. 15.4-5 PDF
Jan 10 Moments of inertia. Review of vectors. 15.5, 14.5 PDF
Jan 12 Surface area. Triple integrals. 15.6-7 PDF
Jan 15 No class: Martin Luther King day
Jan 17 Triple integrals. Cylindrical coordinates. 15.7-8 PDF
Jan 19 Spherical coordinates. 15.9 PDF
Jan 22 Change of variables (general case). 15.10 PDF
Jan 24 Hyperbolic coordinates. Review. PDF
Jan 26 Midterm 1
Jan 29 Chain rule. Implicit function theorem. 14.5 PDF
Jan 31 The gradient vector. Level sets. 14.6 PDF
Feb 2 Vector fields. Physical interpretations. 16.1 PDF
Feb 5 Line integrals of functions and vector fields. 16.2 PDF
Feb 7 Line integrals. The fundamental theorem. 16.2-3 PDF
Feb 9 Path independence. Potential functions. 16.3 PDF
Feb 12 When is a vector field conservative? 16.3-4 PDF
Feb 14 Green's theorem. 16.4 PDF
Feb 16 Curl and divergence. Circulation and flux. 16.5 PDF
Feb 19 No class: President's day
Feb 21 Review. PDF
Feb 23 Midterm 2
Feb 26 Div and curl in 3D. Parametrization of surfaces. 16.5-6 PDF
Feb 28 Surface integrals. 16.6-7 PDF
Mar 2 Surface integrals (continued). 16.7 PDF
Mar 5 Stokes' theorem. 16.8 PDF
Mar 7 Divergence theorem. Maxwell's equations. 16.9 PDF
Mar 9 Course review. PDF
Mar 14 Final Exam

Reading Suggestions

Section numbers such as 15.1 and 16.4 refer to the course textbook.

Day Reading
Jan 3 15.1 Example 3
15.2 Examples 3, 4
Jan 5 15.3 Examples 3, 5, 6
Jan 8 15.4 Example 3
15.5 Example 3
Jan 10 12.3 Theorem 3
Proof of the Law of Cosines
Jan 12 15.6 Example 2
15.7 Examples 2, 4
Jan 19 15.9 Figures 2, 3, 4
Jan 22 15.10 Examples 1, 2, 4
Jan 29 14.5 Examples 2, 7, 8
Notes: surface area in polar coordinates
Feb 5 16.2 Examples 3, 5
Feb 14 16.4 Example 5

Important dates

Jan 3 First lecture
Jan 15 No class (Martin Luther King Day)
Jan 26 Midterm 1 covering sections 15.2-10
Feb 19 No class (Presidents' Day)
Feb 23 Midterm 2 covering sections 14.5-6, 16.1-5
Mar 9 Last lecture
Mar 14 Final exam

Textbook

The textbook for Math 324 is Calculus: Early Transcendentals, 7th Edition, by James Stewart.


Homework

Homework for this class will be submitted through Webassign.

The student that wishes practice for the exams may wish to look the Math 324 Exam Archive compiled by Dr. Andrew Loveless.


Grading

Each student's final grade will consist of the following:

Homework 10%
Midterm 1 25%
Midterm 2 25%
Final Exam 40%

Grades will be published on Catalyst after each exam.