| Day | Topic: Subtopic |
Reading (Main, Alternate, Deep) |
Due Dates |
|---|---|---|---|
| 1 Mon 3/28 |
Course Intro Unit Circle Trig Animation Complex Algebra Review Addition/Subtraction Multiplication/Division Complex Functions Exponentials Powers Trigonometric Functions Hyperbolic Trig. Functions |
Boas 2.1-2.5 RHB 3.1-3.2 Boas 2.9 RHB 3.3 Boas 2.10 RHB 3.4 Boas 2.11 RHB 3.4 Boas 2.12 RHB 3.7 | |
| 2 Wed 3/30 |
Multiple-valued Functions Roots Logarithms |
Boas 2.14 RHB 3.5 Boas 2.13 | |
| 3 Fri 4/1 |
More Multiple-valued Functions Complex Powers Inverse Trig. Functions |
Boas 2.14 Boas 2.15 |
Quiz 1 |
| 4 Mon 4/4 |
Derivatives Definitions Analyticity Theorems |
Boas 6.1 RHB 24.1 Boas 6.2 |
HW 1 (solutions) |
| 5 Wed 4/6 |
Cauchy-Riemann Equations Harmonic Functions. |
Boas 6.2 RHB 24.2 | |
| 6 Fri 4/8 |
Singularities & Zeros Branch cuts & Riemann sheets |
Boas 14.7, 14.9 RHB 24.5 |
Quiz 2 |
| 7 Mon 4/11 |
Analytic Continuation Gamma Functions Maple Real Graph Real Part Imaginary Part Properties Beta Functions Example: Period of Pendulum |
Boas 11.1-11.5 RHB 18.12.1 Boas 11.2-11.10 RHB 18.12.2 |
HW 2 (solutions) |
| 8 Wed 4/13 |
Complex-valued Series Theorems |
Boas 2.6-2.7 RHB 24.3 | |
| 9 Fri 4/15 |
Laurent Series Theorems Partial Fractions |
|
Quiz 3 |
| 10 Mon 4/18 |
Multipole Expansions |
|
HW 3 (solutions) |
| 11 Wed 4/20 |
ODE Intro Definitions Review of Differentials First Order ODE's Theorems Separable ODEs |
Boas 8.1 RHB 14 Intro Boas 8.2 | |
| 12 Fri 4/22 |
Exact Differentials Integrating Factors |
Boas 4.3 Boas 8.3 |
Quiz 4 |
| 13 Mon 4/25 |
Review/Catch-up Chain Rule Change of Variables |
|
HW 4 (solutions) |
| 14 Wed 4/27 |
Midterm (tentative) |
| |
| 15 Fri 4/29 |
Linear ODE Theorems Uniqeness Superposition Wronskians General Solutions |
RHB 15 Intro |
No Quiz |
| 16 Mon 5/2 |
Constant Coefficients Homogeneous |
Boas 8.5 RHB 15.1.1 |
HW 5 (solutions) |
| 17 Wed 5/4 |
Constant Coefficients Inhomogeneous Resonance |
Boas 8.6 RHB 15.1.2 | |
| 18 Fri 5/6 |
Series Solutions w/o Singularities Example: Quantum Harmonic Oscillator |
Boas 12 RHB 16.2 |
Quiz 5 |
| 19 Mon 5/9 |
More Series Solutions |
|
HW 6 (solutions) |
| 20 Wed 5/11 |
More Series Solutions |
| |
| 21 Fri 5/13 |
Separation of Variables Rectangular Coordinates Example: Quantum Harmonic Oscillator |
McIntyre 7.4, RHB 21.1 |
Quiz 6 |
| 22 Mon 5/16 |
Eigenfunction Expansions (Basics) Fourier Review |
|
HW 7 (solutions) |
| 23 Wed 5/18 |
Change of Dependent Variable Change of Independent Variable Example: Quantum Harmonic Oscillator |
Boas 4.11 RHB 5.6 | |
| 24 Fri 5/20 |
Legendre Polynomials Graphs Maple: Guessing Coefficients Orthogonal Polynomials Graphs Rodrigues' Formula Recurrence Relations Orthonormality More Multipole Expansions Generating Functions |
RHB 18 Boas 12.3-12.4, 12.22 Boas 12.22 Boas 12.6-12.8 Boas 12.5, 12.22 | |
| 25 Mon 5/23 |
Superposition of solutions Maple: Finding Coefficients Hermite Polynomial Series Example: Quantum Harmonic Oscillator Notes from Board |
Boas 12.9, 12.22 |
Quiz 7 |
| 26 Wed 5/25 |
Vector Spaces Definitions Eigenfunction Expansions (Theory) Sturm-Liouville Theory |
RHB 17 |
HW 8 (solutions) |
| 27 Fri 5/27 |
Partial Differential Equations PDE Definitions Special PDE's in Physics Classification of PDE's |
RHB 20.1 Boas 13.1 | |
| 28 Mon 5/30 |
Separation of Variables Curvilinear Coordinates Partial Differential Equations Boundary Conditions. Box vs. Infinite Classification Example: Laplace's eqn. in 1d & 2d |
McIntyre 7.4, RHB 21.1 |
|
| 29 Wed 6/1 |
PDE Superpositions |
RHB 21.2 |
Quiz 8 |
| 30 Fri 6/3 |
Classification of Singularities Theorems |
RHB 16.1 |
HW 9 |
| 31 Mon 6/6 |
Series Solutions with Singularities Example: Bessel Functions |
Boas 12.11 RHB 16.3 |
(solutions) |
| 32 Wed 6/8 |
MEMORIAL DAY |
| |
| 33 Fri 6/10 |
More complicated examples HW Example: Diffusion in a Cylinder |
| |
| 34 Mon 6/13 |
Partial Differential Equations Example: Method of Images Review |
RHB 21.5.3 |
HW 10 (solutions) |
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