PHYSICS 227-8 

Autumn 2008, Winter 2009

 

 Instructor: Prof. Stephen D. Ellis

Office: B401 (PAB)
Telephone: 5-2396

Email: sdellis@u.washington.edu

 

 

Text: Mathematical Methods in the Sciences, by Mary L. Boas, John Wiley & Sons Press, Third Edition, 2006.

Note that the text includes solutions to some of the problems at the back of the book (and that there is a companion volume to the previous edition with worked out solutions to approximately 25 % of the exercises, many of which are the same). More detailed solutions to the practice problems can be found in the various Appendix B to the Lectures (see below).

Other texts that may prove useful are:
Classical Mechanics, Tom W.B. Kibble and Frank H. Berkshire, Imperial College Press; (2004) (text for Phys 229);
Classical Dynamics, Stephen T. Thornton and Jerry B. Marion, Thomson Brooks/Cole; 5th edition (2004) . 

 

 

Computers: Basic use of a computer mathematics program such as Mathematica is now an integral part of this course (the computational part) and its discussion will be included in the lectures (see the Mma notebooks linked below).

A
Hands-On Introduction to Mathematica (from the folks at Wolfram) is available here. You can watch with a web browser. The recommended approach is to work along with the demo in a running version of the Mathematica.

 

 

Physics 227 (Autumn 2008)

 

Lectures:

 

Lecture 1 (9/24/08) Introduction: The Big Picture

Lecture 2 (9/26/08, 9/29/08, 10/1/08) Infinite Series (Mma nb, pdf)

Lecture 2 Appendix B (9/26/08) Some worked examples (Mma nb)

Lecture 3 (10/1/08, 10/3/08,10/6/08) Power Series (Mma nb, pdf)
Lecture 3
Appendix B (10/1/08) Some worked examples (Mma nb, pdf)

Lecture 4 (10/6/08, 10/7/08, 10/8/08, 10/10/08) Complex Numbers (Mma nb, pdf)
Lecture 4
Appendix B (10/6/08) Some worked examples (Mma nb, pdf)

Lecture 5 (10/13/08, 10/14/08, 10/15/08, 10/17/08) Complex Variables II (Mma nb, pdf)

Lecture 5 Appendix B (10/13/08) Some worked examples (Mma nb, pdf)

Lecture 6 (10/20/08, 10/21/08) Vectors I (Mma nb, pdf)

Lecture 6 Appendix B (10/20/08) Some worked examples (Mma nb, pdf)

Lecture 7 (10/22/08, 10/27/08, 10/28/08) Vectors and Matrices II (Mma nb, pdf)

Lecture 7 Appendix A Dirac Notation

Lecture 7 Appendix B (10/22/08) Some worked examples (Mma nb, pdf)

Lecture 8 (10/29/08, 10/31/08, 11/3/08) Vectors and Matrices III (Mma nb, pdf)
Lecture 8
Appendix B (10/29/08) Some worked examples (Mma nb, pdf)

Lecture 9 (11/3/08, 11/4/08, 11/5/08, 11/7/08) Eigenvectors and Eigenvalues
An Example
(Mma nb, pdf)

Lecture 9 Appendix A (11/3/08) Newton and the Pendulum

Lecture 9 Appendix B (11/3/08) Some worked examples (Mma nb, pdf)

Lecture 10 (11/10/08, 11/12/08) Intro to Group Theory (Mma nb, pdf)

Lecture 10 Appendix B (11/10/08) Some worked examples

Lecture 11 (11/14/08,11/17/08) Partial Differentiation (Mma nb, pdf)
Lecture 11
Appendix B (11/14/08) Some worked examples (Mma nb, pdf)

Lecture 12 (11/18/08,11/19/08, 11/21/08) Vector Analysis I (Mma nb, pdf)

Lecture 12 Appendix B (11/18/08) Some worked examples (Mma nb, pdf)

Lecture 13 (11/21/08, 11/24/08, 11/25/08) Vector Analysis II (Integrations) (Mma nb, pdf)

Lecture 13 Appendix A (11/21/08) Divergences in Curvilinear Coordinates

Lecture 13 Appendix B (11/21/08) Some worked examples (Mma nb, pdf)

Lecture 14 (12/1/08) Differential Equations (Mma nb, pdf)
Lecture 14
Appendix B (12/1/08) Some worked examples (Mma nb, pdf)

 

 

Physics 228 (Winter 2009)

 

Lectures:

 

Lecture 14 (1/6/09, 1/7/09, 1/8/09) Differential Equations (Mma nb, pdf)
Lecture 14
Appendix B (1/6/09) Some worked examples (Mma nb, pdf)
Lecture 15 (1/12/09, 1/13/09, 1/14/09) Fourier Series Expansion (Mma nb, pdf)

Lecture 15 Appendix B (1/12/09) Some worked examples (Mma nb, pdf)
Lecture 16 (1/15/09, 1/19/09, 1/20/09) Fourier Integral Expansion (Mma nb, pdf)
Lecture 16
Appendix B (1/14/09) Some worked examples (Mma nb, pdf)

Lecture 17 (1/21/09, 1/22/09, 1/26/09,1/27/09) Analytic Function and Integrals (Mma nb, pdf)Lecture 17 Appendix B (1/21/09) Some worked examples (Mma nb, pdf)

Lecture 18 (1/28/09, 1/29/09, 2/3/09) Laplace Transforms (Mma nb, pdf)
Lecture 18
Appendix B (1/29/09) Some worked examples (Mma nb, pdf)

Lecture 19 (2/4/09, 2/9/09,2/10/09) Green Function Techniques (Mma nb, pdf)
Lecture 19
Appendix B (2/4/09) Some worked examples (Mma nb, pdf)

Lecture 20 (2/11/09, 2/12/09, 2/16/09) Calculus of Variations (Mma nb, pdf)

Lecture 20 Appendix A (2/11/09) Coupled oscillators (Mma nb, pdf, note the animation at the end which is a handy way to visualize the motion)
Lecture 20
Appendix B (2/11/09) Some worked examples (Mma nb, pdf)

Lecture 21 (2/17/09, 2/18/09, 2/19/09, 2/23/09) Legendre Polynomials I (Mma nb, pdf)

Lecture 21 Appendix B (2/17/09) Some worked examples (Mma nb, pdf)

Lecture 22 (2/24/09, 2/25/09, 2/26/09) Legendre Polynomials II (Mma nb, pdf)

Lecture 22 Appendix B (2/24/09) Some worked examples (Mma nb, pdf)

Lecture 23 (3/2/09, 3/3/09, 3/5/09) Frobenius, Bessel and cylindrical coordinates (Mma nb, pdf)

Lecture 23 Appendix B (3/2/09) Some worked examples (Mma nb, pdf)

Lecture 24 (3/5/09, 3/9/09) 2nd Order Partial Differential Equations I (No Time Dependence)
(Mma nb, pdf)

Lecture 24 Appendix B (3/9/09) Some worked examples (Mma nb, pdf)

Lecture 25 (3/11/09, 3/12/09) 2nd Order Partial Differential Equations II (Time Dependence)
(Mma nb, pdf)

Lecture 25 Appendix B (3/11/09) Some worked examples

Lecture 25 Appendix C (3/11/09) Some more worked examples

Lecture 26 () Poissons Equation (Sources)