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

 

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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 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