AM-Applied Mathematics

Case-study-based, first-quarter introduction to single-variable calculus, with computing labs/discussion sections featuring contemporary symbolic, numerical, and graphical computing tools. Case studies drawn from biology, environmental sciences, health sciences, and psychology. Includes functions, mathematical modeling, limits, continuity, tangents, velocity, derivatives, the chain rule, implicit differentiation, higher derivatives, exponential and logarithmic functions and their derivatives, differentiating inverse functions, the mean value theorem, concavity, inflection points, function optimization, and curve-sketching. Students cannot receive credit for this course and AM 11A or ECON 11A or MATH 11A or MATH 19A. (Formerly AMS 15A.)

Case-study based, second-quarter introduction to single-variable calculus, with computing labs/discussion sections featuring symbolic numerical, and graphical computing tools. Case studies are drawn from biology, environmental science, health science, and psychology. Includes indefinite and definite integrals of functions of a single variable; the fundamental theorem of calculus; integration by parts and other techniques for evaluating integrals; infinite series; Taylor series, polynomial approximations. Students cannot receive credit for this course and AM 11B or ECON 11B or MATH 11B or MATH 19B. (Formerly AMS 15B.)

Covers the fundamental aspects of scientific computing for research. Introduces algorithmic development; programming (including the use of compilers, libraries, debugging, optimization, and code publication); computational infrastructure; and data-analysis tools. Students gain hands-on experience through practical assignments. Basic programming experience will be assumed. May be taught in conjunction with AM 129 some quarters. (Formerly AMS 209.)

Teaches basic numerical methods for numerical linear algebra and, thus, the solution of ordinary differential equations (ODEs) and partial differential equations (PDEs). Covers LU, Cholesky, and QR decompositions; eigenvalue search methods (QR algorithm); singular value decomposition; conjugate gradient method; Runge-Kutta methods; error estimation and error control; finite differences for PDEs; stability, consistency, and convergence. Basic knowledge of computer programming is needed. (Formerly AMS 213.)

Focuses on applications of mathematical and computational methods with particular emphasis on advanced methods applying to organismal biology or resource management. Students read current literature, prepare critiques, and conduct projects.