This course schedule will evolve as the semester progresses. All indicated sections are from the Greenberg text, unless otherwise indicated. Students are strongly encouraged to cover the material in the text prior to each lecture, where Sections of the text are indicated here ahead of time, so that class time can be used to work problems and explore important details of each topic during lecture.
January 12, Meet & Greet
Today's discussion was an attempt to figure out the backgrounds of class attendees, so as to best tweak the existing course plan to make it most beneficial for all. In particular, as a result of this discussion, we are going to include more material from Chapter 16 at the beginning of the course and more material from Chapters 4 & 7 in the last third of the course.
January 14: Start Chapter 16
Gradient, divergence & curl, covering roughly and quickly through 16.5.
January 19: 16.6
In addition to covering the material in 16.6, we will introduce some standard tensor analysis notation in Cartesian coordinates.
January 21: Finish 16.6 & 16.7
Additional examples of combinations of del operators, using tensor notation. The del operator in other coordinate systems.
January 26: 16.8 & 16.10
Conservative vector fields and their integrals & the divergence theorem.
January 28: 16.9
Stokes' Theorem, and an opportunity to discuss the connections between the different theorems and vector Calculus identities.
February 2: Wave Equations
The first-order wave equation in one space dimension. Introduction to the second-order wave equation.
February 4: No Lecture
February 9: Exam #1
The first exam will be on Chapter 16 and the related material covered in the course.
February 11: Sections 19.2 & 19.3
The second-order wave equation in one and two space dimensions.
February 16: Sections 19.4 & 20.2
Emphasis on big picture in separation of variables solutions. D'Alembert's solution. Laplace equation in Cartesian coordinates.
February 18: Sections 20.2 (cont'd) & 20.4 (sort of)
Continued discussion of Laplace equation. Discussion of Fourier perspective of the different PDEs we've considered.
February 23: Sections 20.3
Laplace equation in plane polar coordinates.
February 25: Finished Section 20.3
Discussion of solutions in cylindrical and spherical coordinates.
March 2: Dive into Chapter 21
Essentials of complex numbers and complex algebra, from Sections 21.2 & 21.3
March 4: Exam #2
March 16: Sections 21.4 & 21.5
Polar representation, branch cuts, Cauchy-Riemann conditions.
March 18: Finish 21.5, Section 23.2
Examples, Cauchy-Riemann in polar representation, harmonic functions, complex integration.
March 23: Sections 23.3 & 23.4
Cauchy's Theorem. Fundamental Theorem.
March 25: Section 23.5
Cauchy Integral Formula, Generalized Cauchy Integral Formula.
March 30: Section 24.2
Essential review of Taylor series, extending understanding to behavior in the complex plane.
April 1: Section 24.3
Laurent series.
April 6: Finish 24.3 & Start 24.4
Undetermined coefficient expansions. Classification of singularities.
April 8: Sections 24.4 & 24.5
Non-isolated singularities. Residues.
April 13: Exam #3
The third exam covers Chapters 21, 23, and 24.1-3
April 15: Finish Section 24.5
Inverse Laplace transform examples.
April 20: Section 4.2
Power series solutions.
April 22: Start Section 4.3
Frobenius series, identifying the exponent of the lowest-order term.
April 27: Finish Section 4.3
Finish our discussion of Frobenius series. Selected examples about irregular singular points.
