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MAT 207B Methods of Applied Mathematics Syllabus Page (Winter 2025)
Synopsis:
We will cover the most important and fundamental concepts in Applied Mathematics, which are rather classical yet indispensable for understanding any modern applications, such as: Calculus of Variations and Applications; Basics of PDEs; Basics of Fourier Series; Sturm-Liouville Problems;
Eigenvalue Problems via Variational Principle; Green's Functions;
and Laplacian Eigenfunctions and Applications.
N. Young: An Introduction to Hilbert Space, Cambridge Univ. Press, 1988. This is an optional textbook, but strongly recommended to get this book since this is one of the best introductory book on Hilbert spaces and basic functional analysis. I will use some chapters of this book, in particular, Chap. 8-11.
The following are good references (some of them seem to be viewable at
books.google.com):
R. Courant & D. Hilbert: Methods of Mathematical Physics, Vol.I, Wiley, 1953.
G. B. Folland: Fourier Analysis and Its Applications, AMS, 2009.
I. M. Gelfand & S. V. Fomin: Calculus of Variations,
Dover Publications, Inc., 2000.
F. B. Hildebrand: Methods of Applied Mathematics,
Dover Publications, Inc., 1992.
S. Hildebrandt & A. Tromba: The Parsimonious Universe: Shape and Form in the Natural World, Coperincus, Springer, 1996.
M. Kot: A First Course in the Calculus of Variations, Student Mathematical Library, Vol. 72, AMS, 2014.
I. Stakgold & M. J. Holst: Green's Functions and Boundary Value Problems, 3rd Ed., John Wiley & Sons, Inc., 2011.
W. A. Strauss: Partial Differential Equations: An Introduction,
2nd Ed., John Wiley & Sons, 2008.
J. L. Troutman & M. P. Bautista: Boundary Value Problems of Applied Mathematics, 2nd Ed., Dover Publications, Inc., 2017.
K. Yosida: Lectures on Differential and Integral Equations,
Dover Publications, Inc., 1991.
I will keep updating the webpages for this course (one of which you are
looking at now). In particular, please read the comments, handouts, and reference page often.
After each class, I will put relevant comments and references as well as
most of my handouts in class in this page that should
serve as a guide to further understanding of the class material.
Also, after each lecture, I will post my lecture notes at our
Lecture Notes Page.
Homework:
I will assign homework every Friday. I will collect your homework at my
Friday class after one week from the assigned date.
Please go to
our homework page. LATE HOMEWORK WILL NOT BE ACCEPTED. A subset of
these problems will be graded.
Grading Scheme:
40% Homework
60% Final Exam
Minimal Canvas Usage:
For this course, the usage of Canvas is minimal.
We will use the Canvas website mainly for communication purposes such as
important announcements, posting questions or comments that would benefit
the whole class. Also, the HW solutions will be posted on Canvas and the
gradebook will be maintained on Canvas.
All the other important information, such as lecture notes, HW problem sets,
and reference info for each lecture, etc., will use our course website
located in my own homepage.