**Lecturer:**Professor Randall J. Scalise**Meeting time and place:**11:00AM-12:20PM T,Th in 155 Fondren Science**Office hours:**after lecture MTWTh 12:30-2:30PM and by appointment in room 107.**Contact:**- Call or leave a message at 768-2504, or
- Leave a note in the Physics Department Office - 102 Fondren Science, or
- send me e-mail: <scalise@smu.edu>

**Exam Dates:**Open book, open notes, open Mathematica, closed internet.- Midterm - Thursday 8 March (before break) in lecture
- Final - Friday 11 May 2018, 11:30 AM-2:30 PM

**Old midterm exams**4321,7305.- Practice final exam
**Mathematica tutorial**PostScript 4 pages, 537511 bytes; PDF 4 pages, 32563 bytes**Grading:**- Homework - 60% (drop lowest)
- Midterm Examination - 20%
- Final Examination - 20%

**Texts**There is no course textbook, but any of the following may be useful. They are in the library and you can find them used (any edition) at abebooks.com- Mathematical Methods For Physicists by George B. Arfken and Hans J. Weber

# ISBN-10: 0120598760

# ISBN-13: 978-0120598762 - Mathematical Methods in the Physical Sciences by Mary L. Boas

# ISBN-10: 0471198269

# ISBN-13: 978-0471198260 - Advanced Engineering Mathematics by Erwin Kreyszig

# ISBN-10: 0471488852

# ISBN-13: 978-0471488859 - Advanced Engineering Mathematics by Peter V. O'Neil

# ISBN-10: 0534552080

# ISBN-13: 978-0534552084

- Mathematical Methods For Physicists by George B. Arfken and Hans J. Weber
**Lecture slides**- Fourier Series, Fourier Transform: 01, 02, 03, Peter Olver's notes. See also
- Generalized functions,Distributions: 04, 05
- Differential equations: 06, 07
- Numerical Approximations to Solutions of Differential Equations
- When I was your age, we programmed in BASIC. And we liked it. Not really.
- Mathematica notebook for the quantum harmonic oscillator.
- First-order (forward) Euler method for solving differential equations
- Runge-Kutta method

- Green functions (PDF format), Green functions (1/2), Green functions (2/2), Green function for heat equation
- Nonlinear Simple Pendulum
- Curvilinear Coordinates: 08, 09. See also Curvilinear coordinates, Orthogonal coordinates, Scale factors (h's).
- Divergence, gradient, curl, laplacian: 10, 11, 12.

**Lecture notes**- 26Jan16. Mathematica notebook, PDF file.
- 28Jan16. See also Aleph number, Georg Cantor's diagonalization.
- 04Feb16. See also Gaussian integrals.
- 09Feb16.
- 18Feb16. See also Green function example Mathematica notebook, PDF.
**Guest lecture**: Thursday 22 March 2019, Professor Stephen Sekula on Monte Carlo methods- 25Feb16. Second root to dD/dw=0; Green function homework solution.
- 01Mar16. Practice midterm solutions.
- 22Mar16. See also Visualizing Divergence and Curl.
- 24Mar16. See also Mixed partial derivatives.
- 29Mar16. See also Separation of variables.
- 31Mar16. See also Particle in a two-dimensional box.
- 05Apr16. See also Separation of variables 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 8/8.
- Bessel function (first kind) J
_{n}(complete, like sin and cos for cylindrical coord's), - Weber function, Neumann function, Bessel (second kind) Y
_{n}(infinite at s=0), - modified Bessel (first kind) I
_{n}(exponential growth for cylindrical coord's), - modified Bessel (second kind) K
_{n}(exponential decay for cylindrical coord's), - Legendre Polynomials - P
_{l}(cos θ) (complete in polar angle for spherical coord's) - Spherical harmonics - Y
_{lm}(θ, φ) (complete in polar and azimuthal angles for spherical coord's) - Spherical Bessel (first kind) j
_{n}(complete in radius r for spherical coord's) - Calculus of variations,
- The Chain Rule for Functions of Two Variables.

- Bessel function (first kind) J
- 07Apr16. See also Variational Calculus, 1/2, 2/2
- Evolutionary computation (Genetic Algorithms)
- "Evolving Inventions" by John R. Koza, Martin A. Keane and Matthew J. Streeter, Scientific American February 2003 p53
- War of the Weasels An Evolutionary Algorithm Beats Intelligent Design by Dave Thomas in Skeptical Inquirer, Vol 34, No 3.
- 15 Real-World Uses of Genetic Algorithms from Brainz.org

- 12Apr16. Complex functions of a complex variable 1/2. See also
- 14Apr16. Complex functions of a complex variable 2/2. See also Cauchy's integral theorem.
- 19Apr16. See also Residue.
- Linear Algebra, Matrix Operations: 1/3, 2/3, 3/3. See also LU Decomposition.
- Group Theory:
1/2,2/2
See also
- Klein four-group a.k.a. Z
_{2}xZ_{2}a.k.a Vierergruppe - Group
- Group Theory
- Finite Group
- Lie Group

- Klein four-group a.k.a. Z

- Dirac Belt Trick
- Knot Theory Rope Trick
- Paperclip trick
- Pages 1 - 10 (PDF format)
- Pages 11 - 20 (PDF format)
- Pages 21 - 29 (PDF format)
- Green functions (PDF format), Green functions (1/2), Green functions (2/2)
- Nonlinear Simple Pendulum
- Pages 30 - 40 (PDF format)
- Pages 41 - 50 (PDF format)
- Pages 51 - 55 (PDF format)
- Pages 56 - 66 (PDF format) Separation of variables 1/6, 2/6, 3/6, 4/6, 5/6, 6/6.
- Vibrating Rectangular Membrane - solutions to the wave equation in 2 dimensions
- 2D Vibrations of a Membrane
- Pages 67 - 77 (PDF format)
- Pages 78 - 88 (PDF format)
- Variational Calculus, 1/2, 2/2, Feynman Lectures: Principle of Least Action
- Complex Numbers; Complex Variables and Functions; Conformal Mapping; Contour Integration and Residues; Laurent Expansion; Laurent Series Examples; Residue Examples; Lecture slides: 1/2, 2/2
- Group Theory: 1/2,2/2
- 26Apr16. See also
- Introduction to the general theory of relativity,
- General relativity,
- Is Middle Earth flat?,
- Curved Space - Feynman lecture II-42 audio,
- Relativistic rocket I,
- Relativistic rocket II,
- Tests of general relativity,
- What Do You Mean, The Universe Is Flat? (Part I),
- What Do You Mean, the Universe Is Flat? Part II: In Which We Actually Answer the Question,
- metric tensor and Christoffel symbols for a sphere,
- Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe,
- The Universe Never Expands Faster Than the Speed of Light by Sean Carroll,
- Covariance and contravariance of vectors.

- Breit-Wigner links
**Homework**Due dates are strictly enforced. 50% if late; 0% once the solutions are posted. You may work together, but the work that you turn in should be unique. Identical work will receive a grade that is divided among all parties. It is possible to find answers to some homework problems on the internet; do not do this. The point, after all, is not to fool me into thinking that you have learned physics, but rather actually to learn some physics.- homework #1 (PDF format) - due Wednesday 31 Jan 2018 at 11:00:00AM

(Mathematica example notebook PDF format, Fourier.nb) - homework #2 (PDF format) - due Wednesday 7 Feb 2018 at 11:00:00AM
- homework #3 (PDF format) - due Wednesday 14 Feb 2018 at 11:00:00AM
- homework #4 (PDF format) - due Wednesday 21 Feb 2018 at 11:00:00AM
- homework #5 (PDF format) - due Wednesday 28 Feb 2018 at 11:00:00AM
- No homework due on 7 Mar 2018 because of the midterm exam on Thursday 8 Mar 2018.
- No homework due on 14 Mar 2018 because of Spring Break.
- homework #6 (PDF format) - due Wednesday 21 Mar 2018 at 11:00:00AM
- homework #7 (PDF format) - due Wednesday 28 Mar 2018 at 11:00:00AM
- homework #8 (PDF format) - due Wednesday 4 Apr 2018 at 11:00:00AM
- homework #9 (PDF format) - pseudocode for Monte Carlo assignment #12 due Wednesday 11 Apr 2018 at 11:00:00AM
- homework #10 (PDF format) - due Wednesday 18 Apr 2018 at 11:00:00AM
- homework #11 (PDF format) - due Wednesday 25 Apr 2018 at 11:00:00AM
- homework #12 (PDF format) - due Wednesday 2 May 2018 at 11:00:00AM

You may find the discussion of Olbers' Paradox in chapter 2 of Barbara Ryden's Introduction to Cosmology useful. Be careful to use "flat" variables.

- homework #1 (PDF format) - due Wednesday 31 Jan 2018 at 11:00:00AM
**Homework Solutions****Disability Accommodations, Religious and Excused Absences****Official University Calendar**- Links:
- Mathematics for Physics by Michael Stone and Paul Goldbart
- Mandelbrot Set Explorer
- Robust Op Amp Realization of Chua's Circuit by Michael Peter Kennedy
- The Chaos Game (Triangle) Mathematica notebook
- The Chaos Game (Square) Mathematica notebook
- Hennon Map Mathematica notebook

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