MATH 432/532 - Basic Analysis II
Spring 2013

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
 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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