Boyce, W.E. & DiPrima, R.C. 2005 Elementary differential equations and ...
Bronson, R. 1993 Schaum's outline of theory and problems of differential
equations.
The University of Western Australia
School of Mathematics and Statistics
3M1: Mathematical Methods (MATH3341, 530.341) The lecturer for the unit is Professor Andrew Bassom (Room 1.31 (entry via 1.29),
[email protected]). References There is no one prescribed set text book. There is no single book that covers all the material in the unit to an appropriate depth and so to read around the topics you will need to consult a number of sources. The extent of the course is best ascertained by attending the lecures but if you want further examples or a more leisurely development of the material I recommend the following references. Boyce, W.E. & DiPrima, R.C. 2005 Elementary differential equations and boundary value problems. Wiley, 790pp. Bronson, R. 1993 Schaum’s outline of theory and problems of differential equations. McGrawHill, New York, 358pp. DuChateau, P. & Zachmann, D.W. 1986 Schaum’s outline of theory and problems of partial differential equations. McGrawHill, New York, 241pp. Spiegel, M.R. 1974 Schaum’s outline of theory and problems of Fourier analysis with applications to boundary value problems. McGrawHill, New York, 191pp. Bender, C.M. & Orszag, S.A. 1978 Advanced mathematical methods for scientists and engineers. McGrawHill, New York, 593pp. Lectures and Practical Classes Three lectures per week. There will also be occasional laboratory sessions, but these will not occur all weeks and their timing will be advised as the unit proceeds. Lecture times: Monday 9am and Thursday 8-10am. All classes will be held in lecture room G.11 of Civil & Mechanical Engineering. In weeks when the practical class runs, it will be held in the Mathematics Computing Laboratory at 11am on Friday. Assignments Assignments will be set every two or three weeks. Questions will be distributed in class and placed on the Web (see the 3M1 page referenced below). Outline solutions will be made available in due course.
Assessment One three-hour exam at the end of semester will be worth 70 % of the total marks. Marks from the four assignments will make up the other 30 % of the final assessment. The penalty for late submission of assessment will be 20% per day. Notices and course information Visit the 3M1 Web page http://www.maths.uwa.edu.au/Units/math3341-s1-2009-crawley/view
Objectives The primary objective is to introduce the methods, both exact and approximate, used to solve ordinary and partial differential equations that arise frequently in engineering and science/ when modelling real world phenomena. The archetype equations of mathematical physics will be discussed, and the behaviour of solutions described. Outcomes Students should gain knowledge of the archetype equations of mathematical physics, their properties, characteristics of their solutions and some appreciation of the types of engineering and science problems which lead to these equations. Students will acquire skills in solving these equations using analytical methods of separation of variables, integral transforms, asymptotics and numerical techniques.
Unit Outline Introduction [1] Ordinary Differential Equations [18] Summary of exact techniques, including algebraic packages. Series solutions. Singularities (5). Two-point boundary value problems. Sturm-Liouville Theory (4). Asymptotic Methods (2). Regular and singular perturbations for integrals and ODEs (7). Partial Differential Equations [18] The archetype Equations (heat, wave, Laplace); derivation and properties (3). Separation of variables, Fourier series, convergence, singularity extraction (4). Spherical and cylindrical geometry problems (3). Finite and integral transforms (8). Summary/revision [2] Faculty policies on: Calculators http://ecm.uwa.edu.au/studentnet/exams/calculators Plagiarism http://ecm.uwa.edu.au/studentnet/exams/dishonesty Appeals http://ecm.uwa.edu.au/studentnet/exams are applied.
