Class Hours: TR 12:30 - 1:45 in Memorial 114.
Text:
Introduction to Real Analysis
4TH Edition, John Wiley and Sons, Inc.
by
Robert G. Bartle and Donald R. Sherbert
ISBN-13: 978-0471433316;
ISBN-10: 0471433314
Additional reading:
Foundations of Analysis
by Joseph L. Taylor
Advanced Calculus
by Patrick M. Fitzpatrick, American Mathematical Society,
2nd Revised edition edition (January 13, 2009)
Introduction to Real Analysis
by William Trench,
available online
Principles of Mathematical Analysis
by Walter Rudin, McGraw-Hill; 3rd edition (January 1, 1976) - QA300. R8 1976
Mathematical Analysis
by Tom M. Apostol, Reading, Mass., Addison-Wesley Pub. Co., 1974 - QA300. A573 1974
Description:
MTH433
Advanced Calculus is a one semester
proof oriented Advanced Calculus course introducing the set of real numbers,
the concepts of continuity, differentiability and integrability, and the convergence
of sequences and series of functions. It can be taken either as a terminal
course for a Major in mathematics - check requirements on the
undergraduate degree requirements page
-
or can be continued with the Masters level sequence
MTH533 - MTH534 Introduction to Real Analysis.
MTH 630-631 develops the subject at the Ph.D. level.
Consult with your academic advisor.
Prerequisites:
MTH 211 (or 310) and 230.
Grading policy:
Homework (20%), Exam 1 (20%), Exam 2 (20%) and Final (40%).
General rules / information:
- check this page for updates.
- make sure that you have access to the UM listserv (email list via Blackboard) for this class
- you must show your work in order to obtain credit.
Homework 1 - due Thursday 9/3
Section 1.1: 4, 12, 14, 15, 16.
Section 1.2: 5, 8, 10, 15, 17.
Solutions Homework 1
Homework 2 - due Thursday 9/10
Section 1.3: 3, 9, 12, 13.
*Notice the change, only 1.3 is due. Some hints are included
in Solutions Homework 1 (above).
Homework 3 - due Thursday 9/17
Section 2.1: 2 a) b), 3 b), 6, 9, 19, 23.
Section 2.2: 10, 12, 15, 18.
Solutions Homework 3
Homework 4 - due Thursday 9/24
Section 2.3: 4, 5, 6, 9, 14.
Section 2.4: 2, 8, 16, 19.
Section 2.5: *TBA if time permits* 7, 8, 9, 12, 14.
Solutions Homework 4
Homework 5 - due Thursday 10/1
Section 3.1: 5, 8, 10, 14, 17.
Section 3.2: 6, 13, 15, 21, 22.
Section 3.3: 2, 3, 4, 7, 10, 12, 14.
Solutions Homework 5
Further reading:
Appendix A and B and lecture notes
The real numbers as a commutative field
Equivalence and order relations
Completeness of the real numbers
Existence of the square root
Equivalent definition of the supremum
Midterm 1, in class, Tuesday 10/6
Solutions Midterm 1
Includes all sections covered.
Homework 6 - due Thursday 10/22
Section 3.4: 4, 10, 11, 12, 14, 19.
Section 3.6: 3, 6, 8, 10.
Section 3.5: 2, 5, 10, 12.
Solutions Homework 6
Homework 7 - due Thursday 10/29
Section 3.7: 3 b), 4, 10, 11, 17.
Solutions Homework 7
Homework 8 - due Thursday 11/5
Section 4.1: 6, 7, 12, 15.
Section 4.2: 2, 4, 9, 12.
Section 4.3: 5, 8, 11.
Solutions Homework 8
Homework 9 - due Tuesday 11/17
Section 5.1: 4, 11, 13.
Section 5.2: 1, 8, 14.
Section 5.3: 3, 4, 5, 8, 11, 13, 17.
Section 5.6: 3, 4.
Solutions Homework 9
Midterm 2, Thursday 11/19
Solutions Midterm 2
Includes all sections covered after Midterm 1.
Same format as Midterm 1.
Grade scale:
A, A-: 90-100; B, B+: 80-89; B-: 70-79; C, C+: 60-69; C-: 50-59; D, F: 0-49
Homework 10 - due Thursday 12/3
Section 6.1: 1, 5, 10, 14.
Section 6.2: 2, 4, 9, 13, 14, 15.
Solutions Homework 10
Homework 11 - due Tuesday 12/8
Section 6.3: 7, 11.
Section 6.4: 2, 8, 12, 14.
Solutions Homework 11
Homework 12. In class
Section 7.1: 8, 14.
Section 7.2: 9, 11, 15, 21.
Solutions Homework 12
Review before Final
Final Thursday 12/10, 2:00 - 4:30 PM in MM114 (same room)
Includes all sections listed under homework, including homework not collected.
Total 10 problems. Partial credit will be given.
***The Honor Code is strictly enforced. Cellphones should be off and not used during the exam.