MATH 432/532 - Basic Analysis II
Spring 2013

Homework & Reading Assignments

January
Monday
Tuesday
Wednesday
Friday
14
First Class Day
§6.1: Branching Processes

15
§6.2: Uniform Convergence of a Sequence of Functions
Exercises: 6.2.1, 6.2.2
16
§6.2: Uniform Convergence of a Sequence of Functions
Exercises: 6.2.4, 6.2.6, 6.2.7, 6.2.8, 6.2.11
18
§6.3: Uniform Convergence and Differentiation
Exercises: 6.3.1, 6.3.2, 6.3.3
21
MLK Day
22
§6.3: Uniform Convergence and Differentiation
Exercises: 6.3.4, 6.3.5 
23
§6.4: Series of Functions
Exercises: 6.4.1, 6.4.2, 6.4.3, 6.4.4
16
§6.5: Power Series
Exercises: 6.5.1, 6.5.2, 6.5.3
28
§6.5: Power Series
Exercises: 6.5.4, 6.5.5, 6.5.6, 6.5.7
29
§6.6: Taylor Series
Exercises: 6.6.2, 6.6.3, 6.6.4, 6.6.5, 6.6.6
30
§6.6: Taylor Series
Exercises: 6.6.7, 6.6.8
(prove Theorem 6.6.1 either way)


February
Monday
Tuesday
Wednesday
Friday



1
Chapter 6 Exam
4
§7.1: How Should Integration be Defined?
5
§7.2: The Definition of the Riemann Integral
Exercises: 7.2.1, 7.2.2, 7.2.3
6
§7.2: The Definition of the Riemann Integral
Exercises: 7.2.4, 7.2.5
8
§7.3: Integrating Functions with Discontinuities
Exercises: 7.2.6, 7.3.1, 7.3.2
11
§7.4: Properties of the Integral
Exercises: 7.4.3, 7.4.5
12
§7.5: The Fundamental Theorem of Calculus
Exercises: 7.5.1, 7.5.2, 7.5.3
13
§7.5: The Fundamental Theorem of Calculus
Exercises: 7.5.4, 7.5.6, 7.5.7
15
Integration in Rn
Exercises: 1, 2
18
Integration in Rn
Exercises: 3, 4
19
Fubini's Theorem
Exercises: 5
20
Fubini's Theorem
Chapter 7 Review
22
Chapter 7 Exam
Solutions
25
Smooth Manifolds
Exercises: 6
26
Smooth Manifolds
Exercises: 7, 8, 9
27
Differentiation in Several Variables
Exercises: 10, 11


March (tentative)
Monday
Tuesday
Wednesday
Friday



1
The Chain Rule
Exercises: 12, 13
4
The Jacobian
Exercises: 14, 15
5
Bump Functions
Exercises: 16, 17
6
Tangent Planes
Exercises: 18
8
Tangent Planes
Exercises: 19
11
Differentiation on Manifolds
Exercises: 20
12
Differentiation on Manifolds
13
Manifolds Review
15
Exam: Smooth Manifolds

18 - 22: Spring Break

25
Inverse Function Theorem
Preimage Theorem
Preview: Integration on Manifolds, Stokes Theorem, and where we're headed
26
Manifolds with Boundary
Orientation
Boundary Orientation
Exercises: 21
27
Tensors
Exercises: 22, 23, 24
29
Exterior Algebra
Exercises: 25, 26, 27, 28

April (tentative)
Monday
Tuesday
Wednesday
Friday
1
Determinant Theorem
Exercises: 29, 30, 31, 32
2
Differential Forms
Exercises: 33, 34
3
Differential Forms
Exercises: 35, 36
5
Partition of Unity
Integration on Manifolds
Exercises: 37, 38
8
Integration on Manifolds
Exercises: 39, 40
9
Exterior Derivative
Exercises: 41
10
Stokes Theorem
Exercises: 42, 43
12
Stokes Theorem
Exercises: 44, 45
15
Alees - Lebesgue Integral
16
Andrew - History of Functions
17
Stephenie - Cauchy Integral Formula
19
Josiah - Mechanics of Spinning Tops
22
Marki - Whitney Embedding Theorem
23
Kyndra - A Nonintegrable Derivative
24
Missy - Double Series
26
Jacob - Whitney Embedding Theorem
29
Diego - Hamiltonian Mechanics
30
Jeremiah - General Relativity



May (tentative)
Monday
Tuesday
Wednesday
Friday


1
Heidi - Taylor Series Solutions to the Schrödinger Equation 
3
Will - Gauss-Bonnet Theorem

                          

                         
8
Final paper due
1:30pm - 4:00pm




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