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 125B: Real Analysis
Approved: (revised 2007-04-24, Eric Rains)

ATTENTION:

Effective Winter 2010, the Department is in discussion about the use of a different textbook than what is noted on the suggested syllabus for this course. As always with any class, please consult with your instructor for more information.

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
William Wade, An Introduction to Analysis, 3rd Edition, Prentice Hall, ($120.00)
Search by ISBN on Amazon: 978-0131453333

Suggested Schedule:

Lecture(s)

Sections

Comments/Topics


Chapter 5

Riemann integration

2

1

Definition of Riemann integral

2

2

Riemann’s definition; properties

2

3

Fundamental theorem of calculus

2

4

Improper integrals


Chapter 11

Multivariate differentiation

2

1

Restricting to one variable


Chapter 8


1

2

Linear transformations


Chapter 11

Multivariate differentiation (continued)

2

2

Differentiability

1

3

Relations to univariate concepts

2

4

Chain rule

2

5

Multivariate MVT and Taylor’s theorem

2

6

Inverse function theorem


Chapter 12

Multivariate integration

2

1

Integrating indicator functions

2

2

Multivariate Riemann integral

2

3

Iterated integrals

2

4

Change of variables

Additional Notes:

Total number of lectures = 28.