AMS 211: 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
- Instructor:
- Name: Nic Brummell (brummell@soe.ucsc.edu)
- Phone: 9-2122
- Office: BE 125
- Instructor Office Hours:
- Tues Thurs 4-5pm
LATEST NEWS
- 12/04/2009: The exam is on MONDAY, DEC 7TH, 12:00-03:00PM in the usual room
- 12/04/2009: A TYPICAL EXAM
Here is a typical exam for you to practice with. Try without the answers first! - 09/24/2009: BUDGET CRISIS
Read this about the UC budget crisis
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.