MATH5352
Mathematical Methods in Science and Engineering II
Lectures: Tuesday 06:3009:20pm, Rm 5560, Lift
2728
Office Hour: Tuesday 4:305:30pm
Announcements:
1. The two lectures on Mar. 13 and Mar. 20 are
cancelled. Makeup lectures will be arranged later on.
2. The lecture on Mar. 20 will be held normally.
3. The makeup lecture is scheduled on 20 Apr. Friday
6:309:30pm, Rm 5510.
4. See university website for the schedule of the
final exam.
Textbook and
References:
1.
Advanced
mathematical methods for scientists and engineers: asymptotic methods and
perturbation theory, C.M. Bender and S.A. Orszag, Springer, 1999
(Textbook).
2.
Introduction
to perturbation methods, M.H. Holmes, 2^{nd} edition, Springer,
2013.
3. Perturbation methods for engineers and scientists,
A.W. Bush, Boca Raton, 1992.
4. Principles of multiscale modeling, W. E, Cambridge
University Press, 2011.
Lecture 12 (May 8) 
Slow varying coefficients, one dimensional
homogenization problem 
Textbook 11.3, Holmes` book 3.3, 5.1, 5.2 

Lecture 11 (Apr.24) 
Method of strained coordinates, multiple
scale analysis 
Textbook 11.1, 11.2, Bush` book 3.1, 3.2 
Homework
4 part III Due May 8 
Lecture 10 (Apr.20) 
WKB theory, Problems with turning points,
eigenvalue problems 
Textbook 10.1, 10.2, 10.4 
Homework
4 part II Due May 8 
Lecture 9 (Apr. 17) 
Boundary layer thickness, multiple boundary
layers, internal boundary layers, boundary layers in PDE problems 
Textbook 9.4, 9.5, Holmes` book 2.3, 2.4,
5.6 
Homework
4 part I Due May 8 
Lecture 8 (Apr. 10) 
Higher order matching, location of the
boundary layer, boundary layer thickness 
Textbook 9.3, 9.4 
Homework
3 part II Due Apr. 17 
Lecture 7 (Mar. 27) 
Boundary layer problems, boundary layer
theory 
Textbook 9.1, 9.2 
Homework
3 part I Due Apr. 17 
Lecture 6 (Mar. 20) 
An application to crystal surface
morphology, regular and singular perturbation problems 
Textbook 7.1, Bush`s book 1.3 

Lecture 5 (Mar. 6) 
Method of stationary phase, method of
steepest descents, Perturbation methods and global analysis 
Textbook 6.5, 6.6, Textbook 7.1, Bush`s
book 1.1 
Homework
2 part II Due Mar. 27 
Lecture 4 (Feb. 27) 
Laplace`s method, Watson`s lemma, method of
stationary phase 
Textbook 6.4, 6.5 
Homework
2 part I Due Mar. 27 
Lecture 3 (Feb. 20) 
Asymptotic series, Asymptotic expansion of
integrals: direct expansion of integrand, integration by parts 
Textbook 3.8, 6.1, 6.2, 6.3 
Homework
1 part III Due Feb. 27 
Lecture 2 (Feb. 13) 
Method of dominant balance 
Textbook 3.4 
Homework
1 part II Due Feb. 27 
Lecture 1 (Feb. 6) 
An example of series solution, three types
of points of homogeneous linear ODEs, Frobenius
method 
Textbook 3.1, 3.2, 3.3 
Homework
1 part I Due Feb. 27 