| Day | Topic: Subtopic |
Reading (Main, Alternate, Deep) |
Due Dates |
|---|---|---|---|
| 1 Mon 4/1 |
ODE Intro Definitions First Order ODE's Theorems Separable ODEs |
Boas 8.1 RHB 14 Intro Boas 8.2 | |
| 2 Wed 4/3 |
Change of Dependent Variable Change of Independent Variable Example: Quantum Harmonic Oscillator First Order ODE's Other Techniques |
Boas 4.11 RHB 5.6 Boas 8.4 RHB 14.2 | |
| 3 Fri 4/5 |
Review of Differentials Exact Differentials Integrating Factors |
Boas 4.3 Boas 8.3-8.4 |
Quiz 1 |
| 4 Mon 4/8 |
Linear ODE Theorems Uniqeness Superposition Wronskians General Solutions |
RHB 15 Intro |
HW 1 (solutions) |
| 5 Wed 4/10 |
Constant Coefficients Homogeneous |
Boas 8.5 RHB 15.1.1 | |
| 6 Fri 4/12 |
Constant Coefficients Inhomogeneous |
Boas 8.6 RHB 15.1.2 |
Quiz 2 |
| 7 Mon 4/15 |
Resonance Other 2nd Order |
Boas 8.7 |
HW 2 (solutions) |
| 8 Wed 4/17 |
Grad, Div, Curl (Review) Review of Spherical Coordinates Cylindrical Coordinates General Curvilinear Coordinates Laplacian Change of Variables Jacobian |
Boas 6.6-6.7 RHB 10.7-10.8 Boas 5.4 RHB 10.9 Boas 5.4 RHB 10.9 Boas 10.8-10.9 RHB 10.10 Boas 5.4 | |
| 9 Fri 4/19 |
Complex Algebra 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 |
Quiz 3 |
| 10 Mon 4/22 |
Multiple-valued Functions Roots Logarithms Complex Powers |
Boas 2.14 RHB 3.5 Boas 2.13 Boas 2.14 |
HW 3 (solutions) |
| 11 Wed 4/24 |
Inverse Trig. Functions |
Boas 2.15 | |
| 12 Fri 4/26 |
Branch cuts & Riemann sheets |
Boas 14.7, 14.9 RHB 24.5 |
Quiz 4 |
| 13 Mon 4/29 |
Derivatives Definitions Analyticity Theorems Cauchy-Riemann Equations Harmonic Functions. Singularities & Zeros |
Boas 6.1 RHB 24.1 Boas 6.2 Boas 6.2 RHB 24.2 |
HW 4 (solutions) |
| 14 Wed 5/1 |
Analytic Continuation Gamma Functions Maple Real Graph Real Part Imaginary Parg 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 | |
| 15 Fri 5/3 |
Complex-valued Series Theorems Laurent Series Theorems |
Boas 2.6-2.7 RHB 24.3 |
Quiz 5 |
| 16 Mon 5/6 |
Review |
|
HW 5 (solutions) |
| 17 Wed 5/8 |
Midterm (Tentative) |
| |
| 18 Fri 5/10 |
Series Solutions w/o Singularities Example: Quantum Harmonic Oscillator |
Boas 12 RHB 16.2 | |
| 19 Mon 5/13 |
Classification of Singularities Theorems Series Solutions with Singularities Example: Bessel Functions |
RHB 16.1 Boas 12.11 RHB 16.3 | |
| 20 Wed 5/15 |
Catch-up |
| |
| 21 Fri 5/17 |
Orthogonal Polynomials Graphs Rodrigues' Formula Recurrence Relations |
RHB 18 Boas 12.3-12.4, 12.22 Boas 12.22 |
Quiz 6 |
| 22 Mon 5/20 |
Eigenfunction Expansions (Theory) Sturm-Liouville Theory Orthonormality |
RHB 17 Boas 12.6-12.8 |
HW 6 (solutions) |
| 23 Wed 5/22 |
Superposition of solutions Hermite Polynomial Series Example: Quantum Harmonic Oscillator Notes from Board |
Boas 12.9, 12.22 | |
| 24 Fri 5/24 |
Multipole Expansions Generating Functions |
Boas 12.5, 12.22 |
Quiz 7 |
| 25 Mon 5/27 |
MEMORIAL DAY |
| |
| 26 Wed 5/29 |
Vector Spaces Definitions Partial Differential Equations PDE Definitions Special PDE's in Physics Classification of PDE's Partial Differential Equations Boundary Conditions. Box vs. Infinite Classification Example: Laplace's eqn. in 1d & 2d |
RHB 20.1 Boas 13.1 |
HW 7 (solutions) |
| 27 Fri 5/31 |
Partial Differential Equations Example: Method of Images |
RHB 21.5.3 |
Quiz 8 |
| 28 Mon 6/3 |
Separation of Variables Rectangular Coordinates Example: Quantum Harmonic Oscillator HW Example: Diffusion in a Cylinder |
McIntyre 7.4, RHB 21.1 |
HW 8 (solutions) |
| 29 Wed 6/5 |
PDE Superpositions Pics from Board Pics from Board Pics from Board |
RHB 21.2 | |
| 30 Fri 6/7 |
Review Pics from Board Pics from Board Pics from Board CAM's solutions |
|
Quiz 9 HW 9 (solutions) |
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