Upper-Division

AM 100 Mathematical Methods for Engineers

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.

Credits

5

Instructor

Hongyun The Staff

Requirements

Prerequisite(s): AM 20 and AM 30, or by permission of instructor.

Quarter offered

Fall

AM 107 Introduction to Fluid Dynamics

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.)

Credits

5

Cross Listed Courses

PHYS 107

Instructor

The Staff, Nicholas Brummell

Requirements

Prerequisite(s): AM 112 or MATH 107 or PHYS 116C or EART 111.

Quarter offered

Fall

AM 112 Introduction to Partial Differential Equations

Focuses on analytical methods for partial differential equations (PDEs) of two variables, including: the method of characteristics for first-order PDEs; classification of second-order PDEs; separation of variables; Sturm-Liouville theory; and Green's functions. Illustrates each method using applications taken from examples in physics. Students cannot receive credit for this course and AM 212A.

Credits

5

Instructor

Marcella Gomez

Requirements

Prerequisite(s): AM 100 or by permission of the instructor. Enrollment is restricted to juniors and seniors.

Quarter offered

Winter

AM 114 Introduction to Dynamical Systems

Introduces continuous and discrete dynamical systems. Topics include: fixed points; stability; limit cycles; bifurcations; transition to and characterization of chaos; fractals. Examples are drawn from sciences and engineering. Students cannot receive credit for this course and course 214. (Formerly AMS 114.)

Credits

5

Instructor

Pascale Garaud, Qi Gong, Dejan Milutinovic, Daniele Venturi

Requirements

Prerequisite(s): AM 20; or MATH 21 and MATH 24; or PHYS 116A. Enrollment is restricted to sophomores, juniors and seniors.

General Education Code

MF

Quarter offered

Fall

AM 115 Stochastic Modeling in Biology

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 course 215.

Credits

5

Instructor

Marcella Gomez

Requirements

Prerequisite(s): STAT 131 and AM 20; a university-level course in biology, and operational knowledge of a programming language; or consent of instructor.

Quarter offered

Spring

AM 129 Foundations of Scientific Computing for Scientists and Engineers

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. (Formerly AMS 129.)

Credits

5

Instructor

The Staff, Dongwook Lee

Quarter offered

Fall

AM 147 Computational Methods and Applications

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.)

Credits

5

Instructor

Hongyun Wang, Daniele Venturi, Abhishek Halder

Requirements

Prerequisite(s): AM 10 or MATH 21. Knowledge of differential equations (AM 20 or MATH 24) is recommended.

General Education Code

MF

Quarter offered

Winter

AM 148 GPU Programming for Scientific Computations

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.)

Credits

5

Instructor

Pascale Garaud

Requirements

Prerequisite(s): AM 147 or MATH 148 or PHYS 115. Enrollment is restricted to juniors and seniors.

AM 170A Mathematical Modeling 1

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.

Credits

5

Instructor

Pascale Garaud

Requirements

Prerequisite(s): Satisfaction of the Entry Level Writing and Composition requirements. AM 30, and AM 114 or AM 214, and STAT 131 or CSE 107, or by permission of the instructor. Enrollment is restricted to juniors and seniors; graduate students may apply by permission of the instructor.

Quarter offered

Spring

AM 170B Mathematical Modeling 2

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.

Credits

5

Requirements

Prerequisites: AM 129 or AM 209, AM 147, and AM 170A. AM 170A may be taken concurrently with 170B on an exceptional basis by permission of the instructor. Enrollment is restricted to seniors. Graduate students may apply with permission of the instructor.

General Education Code

SI

AM 198 Independent Study or Research

Students submit petition to sponsoring agency.

Credits

5

Repeatable for credit

Yes

Quarter offered

Fall, Winter, Spring

AM 198F Independent Study or Research

Students submit petition to sponsoring agency.

Credits

2

Repeatable for credit

Yes

Quarter offered

Fall, Winter, Spring