Applied & Engineering Physics (AEP) 4210 will be an introduction to some of the common mathematical tools used by scientists and engineers to solve real-world problems. There will be an emphasis on developing on the concepts and intuition required to use such tools ("the science") and how to detect when a problem might yield to an approach using such a tool ("the art"). We build upon a solid background in calculus and linear algebra, with no other formal prerequisites. Of course, physics courses or familiarity with domains where such mathematics is applied (e.g. signals processing) is useful for context and motivation. If you have any questions about whether it is appropriate for you to take this class, please feel free to contact me directly.

Topics covered will include vector and tensor algebra, curvilinear coordinate systems and parametrization in analysis, the Dirac delta function, an introduction to the theory of complex variables, Fourier Series, Fourier and Laplace transforms, some applications to ordinary differential equations, and the calculus of variations.

Textbooks

Mathematical Physics: Applied Mathematics for Scientists and Engineers (2nd ed., 2007) by Bruce Kusse and Erik Westwig

The text is the same as the first edition, the only addition in the second edition are a couple of pages of errata in the back. Please let me know if you find any other errors.

The part of the class on complex analysis (about the middle third of the course) is known to be a little tough going for those without previous exposure. I recommend consulting a complex analysis textbook as a supplement to Chapter VI, as it will have more examples and problems to work on; there are many possible options for those with different inclination (terse vs. verbose, geometric vs. formula-based, full of applications vs. none at all, etc.), so feel free to ask me about ones that you feel would best suit you.

Announcements

• The final exam will take place on Wednesday, December 18 at 7:00pm in 115 Rockefeller Hall (our usual classroom). It will cover all the material in the course (§1-9 of [KW]).
• Here are the solutions to Prelim II.
• There will not be Tuesday office hours on (11/26) due to the Thanksgiving break.
• Prelim II will take place on Tuesday, November 19 at 7:30pm in 165 McGraw Hall (same room as last time). It will cover all the material that we got to up to 11/07 (up to and including the entire chapter on complex analysis), with an emphasis on §5-6, the material since the first prelim and on which we've had homework assignments.
• Here are the solutions to Prelim I.
• (10/07) Due to the prelim, the office hours from Tuesday and Wednesday have been shifted to Monday afternoon: 2:30-3:30pm in Malott 581, 3:30-4:30 in Clark 218. Thursday office hours will take place at their usual time and place.
• Prelim I will take place on Tuesday, October 8 at 7:30pm in 165 McGraw Hall (by Libe Slope, on the west side of the Arts Quad). It will cover all material that we get to up to 10/03 (esssentially up to and including Dirac delta functions), with an emphasis on §1-4, on which we have had homework assignments. You should only bring a writing instrument (in particular, no notes, books, calculators, etc.); everything else will be provided to you on location.
• Here is the syllabus.
• Here is the questionnaire from the first day. If you were not present, please submit this to me as soon as you can.
• The first class takes place on Thursday, August 29.

Homeworks

Unless otherwise stated, homeworks are to be turned into the "AEP 4210" homework boxes on the second floor of Clark Hall by 12:20pm on the due date.

• Homework 1, due Friday, September 6. Solutions
• Homework 2, due Friday, September 13. Solutions, Graphs (.pptx)
• Homework 3, due Friday, September 20. Solutions
• Homework 4, due Friday, September 27. Solutions, Graph (.pptx)
• Homework 5, due Friday, October 4. Solutions
• Homework 6, due Friday, October 11. Solutions
• Homework 7, due Friday, October 18. Solutions, Graphs (.pptx)
• Homework 8, due Friday, October 25. Solutions
• Homework 9, due Friday, November 1. Solutions
• Homework 10, due Friday, November 8. Solutions
• Homework 11, due Friday, November 15. Solutions, Graphs (.pptx)
• Homework 12, due Friday, November 22. Solutions, Graphs (.pptx)
• Post-Prelim HW: re-do Prelim II problems as a homework assignment, due Monday, November 25 in class.
• Homework 13, due Friday, December 6. Solutions, Graphs (.pptx)

Topics covered

• Week 1 (08/29): Introduction to the course, Einstein summation notation (§1.1-1.2)
• Week 2 (09/03-09/05): Scalar and vector fields, integral and differential operators and their calculus (§2.1-2.3)
• Week 3 (09/09-09/12): Physical interpretations of grad, div, curl; Gauss's theorem, Green's theorem, Stokes's theorem, Helmholtz's theorem (§2.3-2.5)
• Week 4 (09/16-09/19): Curvilinear coordinate systems: general formalism, scaling factors, coordinate transformations, effect on operators (§3.1-3.5)
• Week 5 (09/23-09/26): Tensors, tensor transformations, tensor diagonalization (§4.1-4.5)
• Week 6 (09/30-10/03): Pseudo-objects, Dirac delta function and applications (§4.6, 5.1-5.7)
• Week 7 (10/07-10/10): Review, Exam (10/08), introduction to complex variables and their functions (§6.1-6.3)
• Week 8 (10/14-10/17): Analytic functions, integrating complex functions (§6.4-6.6).
• Week 9 (10/21-10/24): Complex power series, Taylor series, and Laurent series, Laurent series coefficients and singularities (§6.7-6.9)
• Week 10 (10/28-10/31): The residue formula, definite integrals and contour closure, Cauchy principal part, trigonometric integrals, harmonic functions, conformal mapping (§6.10-6.12)
• Week 11 (11/04-11/07): More on conformal mapping, Schwarz-Christoffel mapping (§6.11-6.12),
• Week 12 (11/11-11/14): Fourier series, exponential form, convergence, discrete version (§7.1-7.4)
• Week 13 (11/18-11/21): Review, Exam (11/19), the Fourier transform and its properties, convolution (§8.1-8.6)
• Week 14 (11/25-11/26): Fourier transforms of periodic functions, the multiplication/convolution dichotomy across the Fourier transform, the sampling theorem (§8.6-8.7)
• Week 15 (12/02-12/05): Limits of Fourier transforms, Laplace transforms, properties and applications (§9.1-9.7)
• Week 16 (12/09-12/10): Review of semester and looking ahead.

Back to Brian Hwang's home page.