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Applied Mathematics

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.