**Instructor: **David Kerr
**Office:** Blocker 525L

**Office hours:** T 10:00-11:30 or by appointment

**Lectures:** MWF 10:20-11:10, BLOC 121

**Course description:**
Differential and integral calculus of functions defined on R

^{m}
including inverse and implicit function theorems and change of variable formulas for integration;
uniform convergence.

**Textbook:**
William R. Wade.

*An Introduction to Analysis*, fourth edition. Published by Prentice Hall.

Errata.

**Assignments** (due at the beginning of class)

*Assignment #1* (due January 25): **7.1:** 1, 2, 3, 4; **7.2:** 1, 2, 3

*Assignment #2* (due February 1): **7.3:** 1, 2(a,c), 3, 4, 5

*Assignment #3* (due February 8): **7.4:** 1(a,b), 2(a,b,c), 3(a,c); **8.1:** 1(a,b,c,d)

*Assignment #4* (due February 22): **8.2:** 4, 5(b,c), 10; **8.3:** 1, 2, 3, 4

*Assignment #5* (due March 1): **8.3:** 7, 9; **8.4:** 1, 3, 4, 6, 7, 11

*Assignment #6* (due March 8): **9.1:** 1(a), 2(a), 4, 8; **9.2:** 1, 4, 6, 7

*Assignment #7* (not to be handed in): **9.3:** 1(a,c), 2, 3, 5, 6, 7, 8(a,c,d); **9.4:** 3, 4, 5

*Assignment #8* (due March 29): **9.4:** 6, 7, 8; **11.1:** 1, 2, 3, 4, 5(a,b)

*Assignment #9* (due April 5): **11.2:** 1, 3, 4, 6; **11.3:** 1(b,c), 2(a,c)

*Assignment #10* (due April 12): **11.4:** 3, 4, 5, 6, 10; **11.5:** 1(a,b), 4

*Assignment #11* (due April 19): **11.5:** 6(a), 7, 9, 12(a,b); **11.6:** 1, 6

*Assignment #12* (due April 26): **12.1:** 2, 4, 5, 6; **12.2:** 3, 5

**Exams**

*In-class exam #1*: February 15, covers 7.1-7.4, 8.1

*Definitions you may be asked to state:* pointwise and uniform convergence for a sequence of functions

*In-class exam #2*: March 22, covers 8.2-8.4 and 9.1-9.4

*Definitions and theorems you may be asked to state:* interior, closure, and boundary of a subset of **R**^{n}, compactness,
the Heine-Borel theorem, the notion of continuity for functions from **R**^{n} to **R**^{m}

*Final exam*: May 8, 8:00-10:00 am

*Definitions and theorems you may be asked to state:* pointwise and uniform convergence for a sequence of functions, interior, closure, and boundary of a subset of **R**^{n}, compactness,
the Heine-Borel theorem, the notion of a limit for functions from **R**^{n} to **R**^{m}, differentiability and total derivative of a function from **R**^{n} to **R**^{m}, Jordan region,
Riemann integrability for a bounded function on a Jordan region