This course introduces a wide variety of mathematical tools and methods to analyze phenomena in the physical, life and social sciences. Focus of this course will be on analytical tools (the ones involving use of pen and paper) rather then the computational tools (the ones involving use of computers). Though students are encouraged to learn numerical skills with packages from programming language like Python or Matlab or C++ (or whatever else a particular student prefers) and use them in their projects.
MATH 22 and MATH23, or permission of the instructor..
Dimensional Analysis, Scaling, Differential Equations and Two-Dimensional Dynamical Systems. Perturbation Methods: Regular perturbation, The Poincare-Lindstedt Method, Asymptotic analysis, Singular perturbation, Boundary layers and uniform approximations, Initial layers, The WKB approximation, Asymptotic expansion of integrals, Boundary value problem. Eigenvalue Problems, Integral Equations, and Green's Functions: Sturm-Liouville problems, Orthogonal functions, Fourier Series, Integral Equations, Volterra Equations, Fredholm equations with Degenerate Kernels, Green’s function, Green’s function via eigenfunctions. Partial Differential Equations: Conservation laws, Several dimensions, Green’s identities, Energy method for uniqueness, Laplace and Poission equation, Separation of variables. Discrete Models: Difference Equations, Stochastic Models, Probability-Based Models.
| Percentage of total grades | |
|---|---|
| One Midterm exam | 25 % |
| Homework | 20% |
| Class participation | 5% |
| Project | 20% |
| Final Exam | 30% |
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Students with diagnosed learning disability are encouraged to discuss with the instructor any appropriate accommodations that might be helpful. All discussions will remain confidential, although the Student Accessibility Services office may be consulted.
You are encouraged to work together on homework. However, the final writeup should be your own. On exams, all work should be entirely your own; no consultation of other persons, printed works, or online sources is allowed without the instructor's explicit permission.