Covers important concepts in applied mathematics, including complex analysis, vector calculus, Fourier Series, and integral transforms. Applications of the methods to various problems in science and engineering are discussed.
Covers fundamental topics in fluid dynamics: Euler and Lagrange descriptions of continuum dynamics; conservation laws for inviscid and viscous flows; potential flows; exact solutions of the Navier-Stokes equation; boundary layer theory; gravity waves. Students cannot receive credit for this course and AM 217. (AM 107 formerly AMS 107.)
Cross Listed Courses
PHYS 107
Teaches analytical methods for the solution of first- and second-order PDEs of two variables, including: the method of characteristics for first-order PDEs; separation of variables for the heat, wave, and Laplace’s equations in a finite or periodic Cartesian domain; homogeneous vs. forced problem; Sturm-Liouville theory; polar and spherical coordinate systems. Each method is illustrated by solving PDEs originating from real-life applications. Students cannot receive credit for this course and AM 212A.
Introduces continuous and discrete dynamical systems. Topics include: fixed points; stability; bifurcations; limit cycles; introduction to chaos. Examples are drawn from sciences and engineering. Familiarity with Matlab is preferred. Students cannot receive credit for this course and AM 214. (Formerly AMS 214.)
General Education Code
MF
Application of differential equations, probability, and stochastic processes to problems in cell, organismal, and population biology. Topics include systems biology, cellular processes, gene-regulation, and population biology. Students may not receive credit for this course and AM 215.
Covers fundamental aspects of scientific computing for research. Students are introduced to algorithmic development, programming (including the use of compilers, libraries, debugging, optimization, code publication), computational infrastructure, and data analysis tools, gaining hands-on experience through practical assignments. Basic programming experience is assumed.
Applications of computational methods to solving mathematical problems using Matlab. Topics include solution of nonlinear equations, linear systems, differential equations, sparse matrix solver, and eigenvalue problems. Students cannot receive credit for this course and MATH 148. (Formerly AMS 147.)
General Education Code
MF
This second course in scientific computing focuses on the use of parallel processing on GPUs with CUDA. Basic topics covered include the idea of parallelism and parallel architectures. The course then presents key parallel algorithms on GPUs such as scan, reduce, histogram and stencil, and compound algorithms. Applications to scientific computing are drawn from problems in linear algebra, curve fitting, FFTs, systems of ODEs and PDEs, and image processing. Finally, the course presents optimization strategies specific to GPUs. Basic knowledge of Unix, and C is assumed. (Formerly AMS 148.)
Introduction to scientific machine learning covering dimension reduction techniques for scientific data, modern methods in sparse regression and compressed sensing, deep neural networks for modeling real-life systems, and neural ordinary differential equations.
Introduction to mathematical modeling emphasizing model construction, tool selection, methods of solution, critical analysis of the results, and professional-level presentation of the results (written and oral). Focuses on problems that can be solved using only analytical tools, and simple Matlab routines. Applications are drawn from a variety of fields such as physics, biology, engineering, and economics.
Second course in mathematical modeling emphasizing the general process of scientific inquiry: model construction, tool selection, numerical methods of solution, critical analysis of the results, and professional-level presentation of the results (written and oral). Focuses on problems that must be solved using numerical tools. Applications are drawn from a variety of fields.
General Education Code
SI
Students submit petition to sponsoring agency.
Students submit petition to sponsoring agency.