UNIVERSITY OF HOUSTON-CLEAR LAKE
SYLLABUS – Fall 2018
PHYS 5531 Mathematical Methods in Physics 1
W 04:00 – 06:50PM STEM 3133
PHYS 5511 Recitation for Mathematical Methods in Physics 1
M 04:00 – 04:50PM STEM 3133
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: STEM 2252
EMAIL: garrison@uhcl.edu (best way to contact me)
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... This is a flipped class. You will be responsible for watching the video of the week on our Course Blackboard site before the class meets face-2-face on Wednesdays. Recitations will be used for feedback and clarification of that week’s materials.
Prerequisites: PHYS 3311 and PHYS 3312 or equivalent
Textbooks: Mathematical Methods for Physicists (7th Ed), Arfken, Weber and Harris
Recommended: Mathematical Methods of Physics, Mathews and Walker
Classical Electrodynamics (3rd Ed), John David Jackson
Any book of mathematical formulas and integration tables,
Example - Schaum’s Outlines: Mathematical Handbook of Formulas and Tables
Policies:
1. Office Hours: MR 2:00-4:00 pm and by appointment
2. Measurements: Two in-class exams & classroom participation
Date Percent
Group Problem Sets 30
Mid-term Oct. 10 30
Final Dec. 12 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 “+” or “-“, 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. All work that you turn in will be your own and not copied from any other sources.
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. Deadlines: Hard and soft problem set deadlines will be posted on the Blackboard site. Assignments turned in after the hard deadlines will not be accepted.
7. 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.
8. Incomplete: A final grade of “I” is given only in cases of documented emergency or special circumstances late in the semester, provided you have been making satisfactory progress. Both the student and the instructor must complete a grade contract.
9. Withdraw Policy: The last date for drop without academic penalty is listed on the Academic Records Calendar (November 13th 2017). You are responsible for independently verifying the drop date.
10. 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 |
AWH 7 |
|
2 |
Infinite Series |
AWH 1.1-1.6 |
|
3 |
Integrals |
AWH 1.10 |
|
4 |
Fourier Series and
Transforms |
AWH 19,20 |
|
5 |
Complex Variables |
AWH 1.8,11 |
|
6 |
Midterm Review |
|
|
7 |
Midterm Exam |
|
|
8 |
Linear Algebra |
AWH 1.7,2-3 |
|
9 |
Tensors |
AWH 4 |
|
10 |
Eigenvalue Problems |
AWH 6,10 |
|
11 |
Partial Differential
Equations |
AWH 9 |
|
12 |
Special Functions |
AWH 14,15 |
|
13 |
Thanksgiving Break –
No Class |
|
|
14 |
Probability |
AWH 23 |
|
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
· vector analysis
· linear algebra
· operators and matrices
· eigenspectrum analysis
• Curved
coordinates and tensors
· vector operators in curvilinear
coordinates
· tensor operations
· non-cartesian tensors
• Infinite
series
· convergence tests
· series of functions
· power series and Taylor's expansion
· infinite products
· Function of a complex variable
· Cauchy's integral formula
· analytic continuation
· conformal mapping
· calculus of residues
· method of steepest descents
• Partial
differential equations
· separation of variables
· eigenfuction expansion
· Sturm-Liouville theory
· Green's function
• Special
functions
· Bessel Functons
· Legendre functions
· other special functions
•
Boundary-value problems in electrostatics (Jackson)
· Green's theorem and Green's functions
· orthogonal functions and expansions
• Fourier
series and Fourier transform
· Fourier transform and inverse Fourier
transform
· convolution theorem
·
fast
Fourier transform
· applications
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