General Information
Kevin Crosby
DSC 204 x5855
kcrosby@carthage.edu
http://personal.carthage.edu/kcrosby
Office Hours: MW: 9-10, TR: 3-4
Course Prerequisites
PHYS 203, MATH 112, 113
Textbooks and other supplies
Required Texts:
- Mathematical Methods in the Physical Sciences, M. L. Boas (Wiley, 3rd Ed., 2006)
- Div Grad Curl and all that, H. M. Schey (W.W. Norton, 4th Ed., 2005)
- Mathematical Methods Using Mathematica, S. Hassani, (Springer-Verlag, 1st Ed., 2003)
Software Used in the Course:
- Mathematica
- Interactive Physics
- Excel
Course Description
This is a course in the mathematical tools that underlie much of fundamental scientific inquiry including data analysis, modeling, and simulation of physical phenomena. The course will be in project-format. There will be five group or individual project to complete, the mathematical skills for which are developed through daily homework assignments.
Course Objectives
The goal of the course is to develop the mathematical skills and techniques that are most widely used in upper-level physics courses and by practicing scientists.
Requirements
Projects
Projects will comprise a major portion of your course grade and time investment. Approximately every two weeks there will be a challenging computational physics project to complete: each will be a direct application of methods learned in this course. There are 5 projects scheduled, each will require at least 2 hours of work every day outside of class. Project reports will be word-processed with appropriate figures and diagrams. They should be written in “Journal Format” (details to be provided). The Projects are due in class two weeks after they are assigned.
Homework
I will collect assigned homework each week. Your write-ups should reflect a considerable investment of your time in crafting detailed and complete solutions. Solutions should consist of sufficient explanatory detail to make it clear that you understand the mathematics and concepts. USE WORDS TO DESCRIBE YOUR LOGIC. Equations alone are usually not sufficient to convey meaning. The mathematics should be logically developed in a clear and complete sequence of steps. Problem assignments are on the course schedule. Late homework is not accepted so that solutions may be made available in a timely manner. While collaboration is encouraged, each student should submit homework write-ups that reflect their own understanding of the problems.
Exams
There will be two midterm exams and a final exam (comprehensive). The exams will be based on the homework assignments and the projects. The text and your own hand-written notes are allowed.
Computers
We will make regular use of computer tools and physics simulations. Many of the homework problems and projects will require the use of Mathematicaâ, Excel, and Interactive Physics (these are available on the physics laptops in class and the CVL). Let the instructor know if you are not comfortable with use of the computers or software: some help can be provided there.
Blackboard
http://blackboard.carthage.edu
You will be required to enroll in this Physics course on Blackboard: Math Methods in the Physical Sciences. You can find it in Blackboard's Course Catalog in the Physics folder. There, you will find announcements, supplementary course materials, and communication capability with the instructor and fellow students.
Grading and Policies
- Homework 25%
- Projects 45 %
- Hour Exams (2) 20%
- Final Exam 10%
Academic Honesty
Students are bound by the terms of the Carthage College Academic Honesty Contract in the Student Handbook. Any act of academic dishonesty is sufficient cause for failure of the course.
Course Calendar
Necesary revisions will be distributed in class.
Date |
Topic |
Project/Activity |
Homework |
Readings |
| Feb 8 | Vectors, dot & cross products, vector fields, pt. charge electric field, coordinate systems | Using Mathematica to plot fields |
105: 12,13,18,19 I: 1,2,3 |
100-105, DG: 1-8 UM: 1-19, 50-53 |
| 13 | Multiple integrals, surface area, volume, center-of-mass, moment of inertia |
|
247: 1,6,25,37 256: 3,9 |
242-255 UM: 86-89 |
| 15 | Spherical & cylindrical coordinates, change of variable, physical applications of integrals |
Project 1 – Planet Peanut |
267: 1,4,5 269: 24 |
258-266,DG: 11-21 |
| 20 | Partial derivatives, normal to surface, surface integrals, flux |
|
272: 1,3 II: 1,2,10 |
270-272,DG: 21-41 |
| 22 | Divergence, |
Using Mathematica in integration |
II: 8,14,23 |
314-320 DG: 42-52 |
| 27 | divergence theorem, volume integrals, |
|
||
Mar 1 |
Gauss’ Law |
Project 2 – Gravity Mapping |
DGC II: 1,2,8,10 |
|
6 |
Line integrals, work, curl, Stokes’ Theorem |
|
307: 5 III: 3 |
299-304,DG: 63-82 UM: 107-110 |
8 |
Gradients, potential, conservative forces, Laplacian |
Project 2 Due |
308: 17 III: 15 |
DG: 82-103 |
Spring Break |
||||
| 20 | Linear Systems of Equations, Determinants |
Exam I Circuit diagrams |
95: 1,2 |
82-94 UM: 66-70 |
| 22 | Matrices, Matrix Math, Inverse, Rotations
|
Using Mathematica to solve linear systems |
122: 7,9,16,21 |
114-121 |
| 27 | Eigenvalues, eigenvectors, Normal Modes |
|
158: 12,15,17 |
148-152 UM: 70-78 |
| 29 | Eigensystems, coupled systems |
Project 3 – 1D Crystal Interactive Physics |
172: 15,23 |
165-171 |
| Apr 3 | Fourier Series, periodic signals |
|
354: 1 |
340-346, 350-354 UM: 146-150 |
| 5 | Fourier Series (cont’d), harmonic decomposition, FFTs |
Using Mathematica to decompose signals |
374: 3 |
372-377 |
| 10 | Ordinary Differential Equations: Separable Equations |
Terminal velocity, drag |
398: 4 399: 21,27,29 |
390-396 UM: 177-185 |
| 12 | Linear ODEs |
Exam II – FFT System response |
403: 1,15 |
401-403 |
| 17 | Series solutions to ODEs: pendulum problem |
Using Mathematica to solve ODEs |
|
|
| 19 | Numerical Integration of ODEs |
|
|
UM: 155-162 |
| 24 | Euler’s method for first-order ODEs |
Project 4 – Solar Sail |
|
UM: 162-170 |
| 26 | More numerical methods: Runge-Kutta method |
|
|
|
| May 1 | Partial Differential Equations: Laplace Equation |
|
626: 2,8 |
619-626
|
| 3 | Partial Differential Equations: Diffusion Equation |
Project 5 - TBA |
632: 2,8 |
628-632 |
| 8 | Partial Differential Equations: Wave Equation |
637: 1,3, |
633-637 |
|
| 10 | Probability and Statistics |
734: 3-6,9 |
722-734 |
|
| 14 | Methods of Counting |
|
742: 1,4,11 |
736-742 |
| 17 | Review |
|
|
|
| 22 | Final Exam: 3:45 pm - 5:45 pm |
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