AMS 211 - Fall 2008

AMS 211 - Fall 2008

Foundations of Applied Mathematics

This class is a one-quarter accelerated course on basic mathematical methods typically used in Applied Mathematics and many physical and engineering sciences.

The intended audience is graduate students from numerous departments in all physical and engineering Sciences (e.g. Earth & Planetary Sciences, Applied Mathematics & Statistics, Astronomy & Astrophysics, Ocean Sciences, Physics, Chemistry, Electrical Engineering, etc) who need to solidify their fundamental knowledge of the tools used in Applied Mathematics.

General Class Information

Lecture times:

Tues Thurs, 12:00-01:45pm, Baskin 372

Instructor:

Name: Nic Brummell (brummell@soe.ucsc.edu)

Phone: 9-2122

Office: BE 125

Instructor Office Hours:

Tues Thurs 4-5pm

LATEST NEWS

• 09/26/2008: CLASS HAS MOVED!
  Yay! We are OUT of that tiny classroom far, far away and into Baskin Engineering 372. That's the old Engineering building, 3rd floor and it's in the North-East corner. See ya there starting Tues 30th Sept.
• 09/29/2008: WebCT site it up and running
  You can now log in to WebCT, enroll in the "AMS211_Brummell" course and get your grades through that system (when we have done some homework and I start putting up grades).

CLASS INFORMATION

Textbooks

• K.F. Riley, M.P. Hobson, & S.J. Bence, "Mathematical methods for Physics and Engineering", 3rd edition, Cambridge University Press.

Recommended further reading can be found in:

• Arfken, G., "Mathematical Methods for Physicists", Academic Press
• Strang, G., "Introduction to Applied Mathematics", Wellesley Cambridge Press
• Courant, R. & Hilbert, D., "Methods of Mathematical Physics", Wiley Interscience.

Syllabus

Week-by-week (roughly) topics are selected chapters from the main textbook:

• Week 1-4: Multivariate Calculus and Linear Algebra
  • Chapter 5: Partial Differentiation
  • Chapter 6: Multiple integrals
  • Chapter 8: Matrices and Vector spaces
  • Chapter 10: Vector Calculus
  • Chapter 11: Line, Surface and Volume Integrals
• Week 5: Fourier Series & Transforms
  • Chapter 12: Fourier Series
  • Chapter 13: Integral Transforms
• Week 6: Complex variables and applications
  • Chapter 24: Complex variables
  • Chapter 25: Applications of complex variables.
• Week 7-10: ODEs
  • Chapter 14: First order ODEs
  • Chapter 15: Higher order ODEs
  • Chapter 17: Eigenfunction methods for Differential Equations
  • Chapter 18: Special Functions

Grading

The course will be graded on a series of seven(ish) homeworks (75%) and a final exam (25%). There may be a random midterm thrown in there somewhere for good measure, but more for you to assess how you are doing.