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

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

**Lectures:** MWF 9:10-10:00, Blocker 164

**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.

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

*Assignment #1* (due January 22): **7.1:** 1, 2, 3, 4; **7.2:** 1, 2, 3

*Assignment #2* (due January 29): **7.2:** 5, 7; **7.3:** 1(a,b,c), 2(a,c), 4, 5

*Assignment #3* (due February 5): **7.3:** 6; **7.4:** 1, 2(a,b,c), 3(a,b,c)

*Assignment #4* (due February 19): **8.1:** 1(a,b,c,d), 2(a,b), 4; **8.2:** 4, 5(b,c), 10

*Assignment #5* (due February 26): **8.3:** 1, 2, 3, 4, 7, 9; **8.4:** 1

*Assignment #6* (due March 5): **8.4:** 3, 4, 6, 7, 8, 11; **9.1:** 1

*Assignment #7* (due March 19): **9.1:** 2, 3(a), 4, 5(b), 8; **9.2:** 1, 4, 6

*Assignment #8* (not to be handed in): **9.2:** 7; **9.3:** 1(a,c), 2, 3, 5, 6, 7, 8(a,c,d)

*Assignment #9* (due April 2): **9.4:** 3, 4, 5, 6, 7, 8

*Assignment #10* (due April 9): **11.1:** 1, 2, 3, 4, 5(a,b); **11.2:** 1, 3

*Assignment #11* (due April 16): **11.2:** 5, 8, 9; **11.3:** 1(b,c), 2(a,c); **11.4:** 4, 5

*Assignment #12* (due April 23): **11.4:** 3, 6, 10, 11; **11.5:** 1(a,b), 4, 8

*Assignment #13* (not to be handed in): **11.5:** 6(a), 7, 9, 12(a,b); **11.6:** 1, 6

**Exams**

*In-class exam #1*: February 12, covers 7.1-7.4

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

Practice problems:
3, 9, and 10 from

Practice #1, and
4, 6(h), and 9 from

Practice #2
*In-class exam #2*: March 26, covers 8.1-8.4 and 9.1-9.3

*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 a limit for functions from **R**^{n} to **R**^{m}

*Final exam*: May 5, 8:00-10:00 am, covers 7.1-7.4, 8.1-8.4, 9.1-9.4, and 11.1-11.6 (but not the implicit function theorem)

*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},
Taylor's formula on **R**^{n}