Applied Mathematics

A student who elects Applied Mathematics as a minor field wm be held responsible for the body of knowledge contained in a coherent croup or courses to be approved in advance by the Field Committee. The program must comprise at least 12 quarter units in J1ldulte work. Committee approval or any proposed course work group will depend on such factors as the student's major field interests, and the breadth of his or her prior mathematical course work record.

A student may satisfy the filed requirements by examination or achieving satisfactory grades in a group of courses selected as follows:

1. One course from the following list (offered by SEAS):

EE M208A/MAE M291A, EE M208B/MAE M291B, EE 208C, MAE 291C

2. Any two additional courses from 1, or Graduate courses offered by the Mathematics Department

Students formally enrolled in an approved program of courses u outlined above, and who achieve grades or B or better in all courses, and at least one A, will be deemed to have completed the minor field requirement.

A transfer student may petition the Field Committee for permission to list one course taken at another institution in his or her approved course group, provided the course was taken by the student in graduate status.

Examination for the Minor Field

See General Information Bulletin. EGS.32.

Syllabus for the Minor Field

I. Prerequisite Material (see “Outline of Normal Prerequisite Coverage" below).

II. Topics in Applied Mathematics corresponding to approved selections u described in “Minimum Preparation" above.

Outline of Normal Prerequisite Coverage

I. Linear Algebra

Fundamentals or linear algebra (including finite-dimensional vector space, linear transformations, matrices) as covered in contemporary Sophomore level calculus sequences (Mathematics 12A or 13BC).

II. Differential Equations

Ordinary differential equations and applications (vibrations, circuits, etc.), including transform methods of solutions for linear systems; some basic partial differential equations of engineering interest and simple boundary value problems, as covered in Junior and Senior level courses in Mathematics (presently 140 series of courses and in Engineering Mathematics 191A, 192 series).

III. Vector Calculus

Scalar and vector fields, gradient, divergence, curl, line integrals, surface integrals, integral theorems (as covered in Sophomore-level calculus sequences and undergraduate core-curriculum Engineering& courses, including E81ineerin& 1008).

IV. Functions of a Complex Variable

Analytic functions, series expansions, contour integrals, conformal mapping covered in part in Mathematics and Engineering courses in the undergraduate core-curriculum, and in Mathematics 132 (Introduction to Complex Analysis), and Engineering 191A.

V. Advanced Calculus (Introductory Real Analysis)

Functions, limits, derivatives, integrals, etc., emphasizing the axiomatic approach with complete proofs of theorems; e.g. Mathematics 131 (Analysis) or the equivalent.

References

Textbooks currently used in pertinent undergraduate Engineering and Mathematics courses.