MATH5352 Mathematical Methods in Science and Engineering II

Lectures:  Tuesday 06:30--09:20pm, Rm 5560, Lift 27-28

Office Hour:  Tuesday 4:30-5:30pm

Syllabus

Academic Integrity

 

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 6:30-9:30pm, 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, 2nd 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