UNIVERSITY OF HOUSTON-CLEAR LAKE

 

SYLLABUS – Fall 2010

 

 

PHYS 5531                 Mathematical Methods in Physics 1

                                    T 07:00 – 09:50PM Bayou 2104

 

PHYS 5511                Recitation for Mathematical Methods in Physics 1

                                    W 08:00 – 08:50PM Bayou 3326

 

Co-requisite requirement: PHYS 5531 and 5511 must be taken together. If you drop one of these courses during the semester you must also drop the other. If at the end of the semester your name does not appear on the rosters for both courses, you will receive a grade of F in the course for which you are still registered.

 

INSTRUCTOR:          David Garrison

OFFICE:                     BAYOU 3531-2         

EMAIL:                       garrison@uhcl.edu

TELEPHONE:            281-283-3796

 

Course Description:    A review of essential mathematics required to solve graduate level physics problems: differential equations, complex math, linear algebra, infinite series, etc...

 

Prerequisites:               PHYS 4131 and PHYS 4132 or equivalent

 

Textbooks:                  Mathematical Methods of Physics, Mathews and Walker

                                    Mathematical Methods for Physicists, Arfken and Weber

 

Recommended:            Classical Electrodynamics (3rd Ed), John David Jackson

Any book of mathematical formulas and integration tables,

Example SchaumÕs Outlines: Mathematical Handbook of Formulas and Tables

 

Policies:

 

1.   Office Hours:      T R 2:30-5:30 pm and by appointment

 

2.   Measurements:    Two in-class exams & take-home problem sets

 

Date                 Percent

                                    Problem Sets                                                      30

Mid-term                                 Sept. 29              30                

Final                                        Dec. 8                 40

 

3.   Grading:              The lower grade boundaries will be:

 

A – 85%

B – 70%

C – 55%

D – 40%

F –  Below 40%

 

Refined letter grade system, including Ò+Ó or Ò-Ò, will be used

This course will utilize a group learning approach to problem sets.

 

4.   Honesty Code:     I will be honest in all my academic activities and will not tolerate dishonesty.

 

5.   Make-ups:           Make-up exams are not recommended.  If you know ahead of time that you will be unable to attend an exam, please let me know in advance so that we can make other arrangements.

 

6.   Disability Accommodation Statement:     If you are certified as disabled and are entitled to accommodation under the ADA Act., sec 503, please see the instructor as soon as possible.  If you are not currently certified and believe that you may qualify, please contact the Coordinator of Disabled Services, at 283-2627, in Health and Disability Services.

 

7.   Learning Objectives: Upon completion of this course, students should be able to solve problems in the areas listed below.

 

Week

Topic

Chapter(s)

1

Ordinary Differential Equations

MW1

2

Infinite Series

MW2 AW5

3

Integrals

MW3

4

Fourier Series and Transforms

MW4 AW14,15

5

Midterm Review

 

6

Midterm Exam

 

7

Complex Variables

MW5 AW6,7

8

Linear Algebra

MW6 AW1-3

9

Tensors

MW15 AW2

10

Eigenvalue Problems

MW9,10

11-12

Partial Differential Equations and Special Functions

MW8 AW9

13

Probability

MW14 AW19

14

Thanksgiving Break

 

15

Final Review

 

16

Final Exam

 

 

Students in the Collaborative Physics Ph.D. Program are responsible for understanding the following topics whether or not they are covered in the class

 

Methods of Mathematical Physics I

 

¥ Review

á     vector analysis

á     linear algebra

á     operators and matrices

á     eigenspectrum analysis

¥ Curved coordinates and tensors

á     vector operators in curvilinear coordinates

á     tensor operations

á     non-cartesian tensors

¥ Infinite series

á     convergence tests

á     series of functions

á     power series and Taylor's expansion

á     infinite products

á  Function of a complex variable

á     Cauchy's integral formula

á     analytic continuation

á     conformal mapping

á     calculus of residues

á     method of steepest descents

¥ Partial differential equations

á     separation of variables

á     eigenfuction expansion

á     Sturm-Liouville theory

á     Green's function

¥ Special functions

á     Bessel Functons

á     Legendre functions

á     other special functions

¥ Boundary-value problems in electrostatics (Jackson)

á     Green's theorem and Green's functions

á     orthogonal functions and expansions

¥ Fourier series and Fourier transform

á     Fourier transform and inverse Fourier transform

á     convolution theorem

á          fast Fourier transform

á          applications

¥ Variational calculations

á          calculus of variations

á    variational approaches in electrostatics and elsewhere

 

Textbooks typically used for graduate-level Mathematical Methods courses are:

 

1)             Mathematical Methods for Physicists by Arfken and Weber

2)             Mathematical Methods of Physics by Mathews and Walker

3)             Classical Electrodynamics by Jackson

4)             Mathematical Methods of Physics and Engineering by Riley, Hobson and Bence

5)             Mathematical Physics by Hassani

6)             A Course of Mathematical Analysis by Whittaker and Watson

7)             Mathematics of Classical and Quantum Physics by Bryon and Fuller

8)             Mathematical Physics by Butkov

9)             Mathematical Methods for Scientists and Engineers by McQuarrie

10)          Mathematical Methods in the Physical Sciences by Boas

11)          Introduction to Solid State Physics by Kittel

12)          Methods of Theoretical Physics I and II by Morse and Feshbach

13)          Methods of Theoretical Physics I and II by Courant and Hilbert

14)          Principles of Advanced Mathematical Physics I and II by Richtmayer