SUNY-Geneseo/Physics & Astronomy
Spring 2024
Mathematical Methods
in Physics
(Phys 228)
MW 12:30 - 1:20, ISC 229

 

   Dr. Pogo  (pogo at geneseo.edu)
   Where's Pogo?
   Office: ISC 228D
   Discord Office Hours
   
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Equation Sheet for Final Exam
  
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What am I doing here? At the end of this course, your skill with a variety of commonly used mathematical and numerical methods in physics in engineering (as listed below) will be substantially increased. You should already have some prior exposure to most of these techniques through you calculus and differential equations courses. We will focus on the practical rather than the theoretical aspects of each technique, but there will naturally be some theory involved. The topics include derivatives and partial derivatives, infinite series (including Fourier series and Taylor series), vector calculus, complex numbers, linear algebra, tensors, differential equations, and probability. There will also be some examination of commonly used numerical techniques.

What do I have to read? The textbook is: Mathematical Methods in the Physical Sciences, by Mary Boas (3rd edition, Wiley). This book is very readable.

 image of 3D Gaussian  
How will I be graded? Your grade will be determined by:  
      Weekly Assignments & Quizzes:
      Participation in Office Hours
      Exams (3 total)
 
  35%
    5%
  60%
100%
 
 

Final Exam: The final exam will be held on Tuesday, May 14, 2024, from noon to 2:30 pm, and will be comprehensive.

Assignments: Homework will be done primarily on CAPA this semester. However, some assignments will also require submission of Mathematica documents, or other supporting written work. This work will be graded on clarity (a combination of neatness and completeness) and presentation quality. Be warned: an answer is not the same as a solution. Assignments that are too hard to understand are also too hard to grade, and will receive zeroes.

       Here are some tips for successful Mathematica submissions:
        • Use the correct filename, EXACTLY. Do not change or misplace a single character. Be aware
           that you may have already instructed your computer to lie to you (!) about your file names
           (most specifically, to hide the extensions from you). You will find that this practice is always
           and forever unacceptable for scientists. It is expected that you will correct this on your
           computer immediately upon reading this sentence for the first time.
        • In a text cell, put your name and the assignment number into the top of the worksheet. Also, label
          each individual problem with the corresponding problem number in a text cell.
        • Do the assignment correctly. Make sure your final solution is not just a “naked” number floating
          without sufficient context.
        • Choose reasonable and unique variable names.
        • Run your entire notebook as a whole before saving and submitting! ! ! !
        • Appearance counts: your work should be reasonably spaced and (* documented *).
        • Supplement your equations with text and/or diagrams when necessary. A third party who is not in
           the class should be able to determine both the question and the answer from your solution,
          without needing to even see the assignment itself.
        • Plots should have a sufficient and reasonable range for the independent variable. Contour
          and surface plots should have correct aspect ratios.
 
 
 
What is the course schedule? Here is the anticipated schedule:

Class

Date

Topic

1

Monday, January 22

Infinite Series [Ch. 1]

2

Wednesday, January 24

Series II; Taylor series and approximations of derivatives [Ch. 1]

3

Monday, January 29

Vector calculus I: dot, cross, del, and grad [Ch. 6]

4

Wednesday, January 31

Vector calculus II: divergence, curl, Laplacian [Ch. 6]

5

Monday, February 5

Numerics: Plotting with Mathematica

6

Wednesday, February 7

Derivatives/Chain rule [Review/Ch. 4]

7

Monday, February 12

Complex analysis I [Ch. 2]

8

Wednesday, February 14

Complex analysis II [Ch. 2]

9

Monday, February 19

Numerics: General computing with Mathematica

10

Wednesday, February 21

Linear algebra I [Ch. 3]

11

Monday, February 26

Exam #1 (covers classes 1-8)

12

Wednesday, February 28

Linear algebra II  [Ch. 3]

13

Monday, March 4

Numerics: Curve fitting

14

Wednesday, March 6

Eigenvalues & Eigenvectors  [Ch. 3]

 

 

No class: Spring Break

15

Monday, March 18

Tensors  [Ch. 10]

16

Wednesday, March 20

Coordinate Transformations  [Ch. 10]

17

Monday, March 25

Multi-variable integration review with Numerics [Review/Ch. 5]

18

Wednesday, March 27

1st order ordinary differential equations (separation of variables) [Ch. 8]

19

Monday, April 1

2nd order ordinary differential equations (constant coefficients) [Ch. 8]

20

Wednesday, April 3

Numerics: Differential equations (Mathematica DSolve, NDSolve)

 

Monday, April 8

No class: Eclipse

21

Wednesday, April 10

Exam #2 (covers classes 9-17)

22

Monday, April 15

Fourier series I [Ch.7]

23

Wednesday, April 17

Fourier series II & Fourier Transforms [Ch. 7]

24

Monday, April 22

Partial differential equations (heat equation) [Ch. 13]               

 

Wednesday, April 24

No class: GREAT Day

25

Monday, April 29

Partial differential equations (wave equation) [Ch. 13]

26

Wednesday, May 1

Probability: interpreting a pdf, counting, “choosing”  [Ch. 15]

27

Monday, May 6

Probability: common distributions (normal, binomial, Poisson)  [Ch. 15]

28

Wednesday, May 8

Statistics: standard deviation  [Ch. 15]

{29}

Tuesday, May 14

Final Exam (comprehensive): noon

Assignments are due every Thursday morning from February 1 through May 2 (except March 14).
Because “study day” is a Thursday this year, Assignment #14 is instead due on Friday, May 10.
 
What if I have trouble with the homework? Visit me during online office hours (see times listed above) and I’ll try to point you in the right direction. Also, I know that most of you will work in groups, and I won’t attempt to stop it. However, the learning is in the doing. Nobody on this planet learns from copying somebody else’s work, no matter how clear or correct it is. Every part of every problem that you let somebody else do for you is something that you are deciding that you just don’t want to learn. You will not have their help on exams! 
 
For this course, use of online homework solutions is considered academic dishonesty.  Students must not turn in homework problems that someone else has solved or copied solutions found online.  At best you will not receive credit for the homework; at worst you will be charged with academic dishonesty.

Learning Outcomes

 At the end of this course, students will:

  • Gain proficiency in taking derivatives and partial derivatives
  • Gain proficiency in the use of geometric series, power series, Fourier series, and Taylor series
  • Gain proficiency in the use of vectors and vector operators
  • Gain proficiency in the use of complex numbers
  • Gain proficiency in the use of linear algebra and tensors
  • Gain proficiency in the use of differential equations
  • Gain proficiency in basic probability and statistical analysis
  • Gain proficiency in some basic types of numerical analysis using tools in Mathematica and Excel
  • Learn multiple practical uses for each of the above topics.

Also, the college provides information at the following URL relating to a variety of topics: 

https://wiki.geneseo.edu/display/PROVOST/Syllabus+Resources+Related+to+Student+Success