Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 185A: Complex Analysis
Approved: 2003-10-01 (revised 2013-03-01, )

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Basic Complex Analysis, 3rd Edition by Marsden & Hoffman; W. H. Freeman Publisher; $122.
Search by ISBN on Amazon: 978-0716728771

Prerequisites:

Completion of courses MAT 67 and MAT 125A.

Suggested Schedule:

Lecture(s)

Sections

Comments/Topics

1-2

1.1-1.3

Complex number system

3-4

1.4

Review continuous functions

5-6

1.5

Basic properties of analytic functions

7

1.6

Differentiation of elementary functions

8

2.1

Contour Integrals

9-10

2.2-2.3

Cauchy’s Theorem

11-12

2.4

Cauchy’s Integral Formula

13-14

2.5

Maximum Modulus Principle and harmonic functions

15

3.1

Convergent series of analytic functions

16-17

3.2

Power series and Taylor’s Thm

18-19

3.3

Laurent series and classification of singularities

20-21

4.1

Calculation of residues

22-23

4.2

Residue Thm

24-25

4.3

Evaluation of definite integrals

26-27

4.4

Evaluation of infinite series

Learning Goals:

This is an introductory course on the basic concepts and theory of functions of complex variables and their applications. Students will learn how to apply ideas and techniques from Calculus to formulate the definition of a complex analytic function and to study special properties of complex analytic functions. These functions give rise to a very rich and beautiful mathematical theory with numerous applications in mathematics and beyond.

Complex analysis appears in many areas of the natural sciences and has wide applications. Students will be challenged to improve their problem solving skills within the broad context of Calculus. Mastery of this course also supports the development of clear analytical thinking.

Assessment:

To assess the learning outcome for this course, the course will be graded through regular homework, midterm examinations, and a comprehensive final exam.