Math 450B
Advanced Calculus II

This course is theoretical in nature and may be thought of as a bridge from "recipe-oriented" undergraduate math class to the rigor and creativity of higher mathematics.  The goal is to put the calculus of several variables on a mathematically rigorous footing and to learn to understand and create proofs in this subject matter.  Topics include: Topology on Rn; continuity and differentiability of functions from domains in Rm to Rn; Taylors formula; inverse and implicit function theorems; integration of functions on Jordan regions; iterated integrals; change of variable theorem; curves and surfaces in Rn; theorems of Green, Gauss, and Stokes. Please expect to devote a generous amount of time to this course. 

Class Meetings              Tuesday & Thursdays, 3:30  to 4:45 p.m.

Math 450A

Plus (+) and minus (–) grades will be assigned for this course.  There will be two midterm exams, each worth 100 points, and a final exam worth 200 points. The dates of the midterms will be announced in class. Class participation is encouraged and will resolve borderline grades, with the possibility, for example, of a final B+ grade becoming an A-. 

Scheduled Time of Final Exam: Tuesday, May 18, 2021, 3:00 to 5:00 p.m.

Homework assignments will be posted on this webpage (below).  Because of the easy availability of solutions on the internet, homework will not be graded and generally not turned in, however, it is extremely important to attempt solutions to all problems on your own.  Occasionally you will be asked to turn in homework problems in order to informally assess your understanding.  Students are encouraged to work together on the homework. We will also devote class time to solutions to the assignments.

An Introduction to Analysis 4th edition, by William Wade.

Coverage: Parts or all of Chapters 8, 9, 11, 12, 13. The text and the lectures are designed to augment each other and are both important. 

Errata to Textbook:

Instructor Information
David Klein
Santa Susana Hall,  Room 127  
Phone: (818) 677-7792
email:, web page:
Office Hours: Tuesday, Thursday 3:00 to 3:30 p.m. & by Appointment

Exams and Homework Assignments

Read Chap 8,  Do problems: 8.2.9, 8.3.1a, 8.3.3, 8.3.6, 8.3.8a, 8.3.9, 8.4.2, 8.4.3, 8.4.9ab

Read Chap 9,  Do problems: 9.1.2, 9.1.5d, 9.1.7, 9.2.6, 9.3.4, 9.3.5, 9.3.6, 9,3,7, 9.3.8bcd, 9.4.3, 9.4.4, 9.4.5, 9.4.8

Read Chap 11, Do problems: 11.1.1, 11.1.2a, 11.1.4, 11.1.5ab, 11.1.6ab, 11.2.1, 11.2.3, 11.2.5, 11.2.8, 11.3.2, 11.3.5, 11.4.1, 11.4.6, 11.4.9, 11.5.1, 11.5.8, 11.6.1, 11.6.3, 11.6.4, 11.6.5, 11.6.6

Exam 1 (on material through Chapter 11) Tuesday, March 23

Read Chap 12, Do problems: 12.1.2, 12.1.5b, 12.1.6a, 12.1.8, 12.2.3, 12.2.4, 12.2.8, 12.2.9, 12.3.1, 12.3.2, 12.3.3, 12.3.4, 12.3.6, 12.4.1, 12.4.2, 12.4.4a, 12.4.5, 12.4.6, 12.4.9

Exam 2 (on material in Chapter 12) Thursday, April 15

Read Chap 13, Do problems: 13.1.3. 13.1.5ac, 13.1.6, 13.1.7a, 13.1.8, 13.1.11ab, 13.2.1, 13.2.2,13.2.3, 13.2.6, 13.3.1, 13.3.4ab, 13.3.5, 13.4.1, 13.4.2, 13.4.3, 13.4.4a, 13.5.1, 13.5.2c, 13.5.3ab, 13.5.4a, 13.5.5ab, 13.5.7, 13.5.8, 13.5.9, 13.5.10abcd, 13.6.1a, 13.6.2ab, 13.6.3ac, 13.6.4a, 13.6.5, 13.6.8, 13.6.11a

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Student behavior, academic dishonesty, university policies

Academic Dishonesty is covered in Appendix C of the CSUN catalog. Academic dishonesty will be reported to the Office of Student Affairs.  For information about CSUN's policy for academic dishonesty, see: Note also that according to CSUN policy, a grade that is sanctioned due to academic dishonesty cannot be replaced by subsequent course grades:

This syllabus is subject to change during the semester.  Any changes will be posted here and announced in class.