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

__Announcements:__

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 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 |