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.
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.
When: Mondays, Wednesdays and Fridays,
from 9:30 to 10:20am
Where: CHL
015 (Chemistry Library Building)
Day | Topics | Sections | Notes |
---|---|---|---|
Jan 3 | Double integrals. Riemann sums. Fubini's theorem. | 15.1-2 | |
Jan 5 | Double integrals over general regions. | 15.3 | |
Jan 8 | Polar coordinates. Applications. | 15.4-5 | |
Jan 10 | Moments of inertia. Review of vectors. | 15.5, 14.5 | |
Jan 12 | Surface area. Triple integrals. | 15.6-7 | |
Jan 15 | No class: Martin Luther King day | ||
Jan 17 | Triple integrals. Cylindrical coordinates. | 15.7-8 | |
Jan 19 | Spherical coordinates. | 15.9 | |
Jan 22 | Change of variables (general case). | 15.10 | |
Jan 24 | Hyperbolic coordinates. Review. | ||
Jan 26 | Midterm 1 | ||
Jan 29 | Chain rule. Implicit function theorem. | 14.5 | |
Jan 31 | The gradient vector. Level sets. | 14.6 | |
Feb 2 | Vector fields. Physical interpretations. | 16.1 | |
Feb 5 | Line integrals of functions and vector fields. | 16.2 | |
Feb 7 | Line integrals. The fundamental theorem. | 16.2-3 | |
Feb 9 | Path independence. Potential functions. | 16.3 | |
Feb 12 | When is a vector field conservative? | 16.3-4 | |
Feb 14 | Green's theorem. | 16.4 | |
Feb 16 | Curl and divergence. Circulation and flux. | 16.5 | |
Feb 19 | No class: President's day | ||
Feb 21 | Review. | ||
Feb 23 | Midterm 2 | ||
Feb 26 | Div and curl in 3D. Parametrization of surfaces. | 16.5-6 | |
Feb 28 | Surface integrals. | 16.6-7 | |
Mar 2 | Surface integrals (continued). | 16.7 | |
Mar 5 | Stokes' theorem. | 16.8 | |
Mar 7 | Divergence theorem. Maxwell's equations. | 16.9 | |
Mar 9 | Course review. | ||
Mar 14 | Final Exam |
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 |
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 |
The textbook for Math 324 is Calculus: Early Transcendentals, 7th Edition, by James Stewart.
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.
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.