SMS 2411: Advanced Mathematical Methods
Sem 2 2014/2015
MAIN REFERENCE:
Nagle et al. (2012). Fundamentals of differential equations and boundary value problems. Boston: Pearson.
TUTORIALS:
(courtesy of Dr. Pah Chin Hee)
Preliminaries, Definition and Properties of Laplace Transform
Preliminaries on matrices,
Introduction of system of DEs, Linear Systems in Normal Form
Preliminaries on 2nd order ODE, Method of Separation Variables, One Dimensional Heat Flow Problem, Vibrating String Problem
Laplace Equation, Laplace Equation in Polar form, Dirichlet problem
|
Laplace transform using table, Partial fraction, Inverse Laplace Transform, Solving IVPs
Homogeneous Linear System with Constant Coefficients, Complex Eigenvalues
Even and Odd Function, Fourier Series
|
Solve IVPs using Laplace Transform, Integrating factor, Transform of Discontinuous Functions
Nonhomogeneous Linear Systems, The Matrix Exponential Function
Heat Equation, Wave Equation
|
MISCELLANEOUS:
- Download installer of Maxima (with GUI) here:
http://andrejv.github.io/wxmaxima/download.html - Download installer of Maxima (without GUI) here:
http://maxima.sourceforge.net/download.html - Maxima by Example: Ch. 3, Ordinary Differential Equation Tools by Edwin L. Woollett:
http://web.csulb.edu/~woollett/mbe3ode1.pdf - Examples of solutions to ordinary differential equations (ODes) using Maxima:
http://www.neng.usu.edu/cee/faculty/gurro/Software_Calculators/Maxima_Docs/MyMaximaBook/MaximaBookChapter9.pdf - Reporting guidelines
reporting_guidelines.docx |