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8/20/2015 4:44 PM

Ph 385 Syllabus (Fall 2015)

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Phys 385: Introduction to Theoretical Physics I  MWF 9:10-10:00, TH 425. This is a course for junior physics and astronomy majors, covering the vector calculus needed for the upper-division E&M course. We will also cover vectors, matrices, groups, tensor notation, special relativity, the wave equation, Fourier series and transforms and the Dirac delta function.

Prerequisites: Lower-division physics, differential equations (via Ph 330 co-requisite). Co-requisite: Ph 330 (upper-division mechanics).

Instructor: Roger Bland - office/lab Th 204, phone 338-2433 / 338-1888; cell phone 415-321-9758. Office hours MW 8:10, M11:10, or by email (rogerbland'at'gmail.com).

Text, first half of course:  Notes on Vector Spaces, available in print from PAC in TH 115 or in electronic form (see downloads).  Required Text, second half of course: div, grad, curl and all that, fourth edition, by H.M. Schey (Norton, N.Y., 2005, ISBN 9780393925166 0-393-92516-1 (paper)).  (NOTE:  there was a change of notation in spherical polar coordinates between version 3 and version 4 in Schey's text.)  Optional reference: Mathematical Techniques, third edition, by D.W. Jordan and P. Smith (Oxford, 2002, ISBN 0-19-924972-5 (paper)).

Topics to be Covered

Topic

Class Notes

div grad curl

Jordan and Smith

Vectors and Vector Spaces

Ch. 1

 

Ch. 9-11

Matrices, Rotations and Tensors

Ch. 2-6

 

Ch. 7, 8, 10

The Lorentz Transformation

Ch. 6a

 

 

The Wave Equation

Ch. 7.8

 

Ch. 20

Fourier Series and Fourier Transforms

Ch. 9,10

 

Ch. 26 and 27

Vector Calculus

 

All of it

Ch. 31-34

Learning Objectives

Vector Spaces

  • Understand the (magnitude, direction) and component representations of vectors, and the relation between the two representations.
  • Understand the properties of displacement vectors in space as they can be generalized to other classes of objects (vector spaces).  Learn to recognize a set of objects which has the general properties of a vector space.
  • Learn the standard properties of matrices and operations using matrices. 
  • Understand the use of the matrix inverse, and be able to calculate the inverse of a given matrix.
  • Learn to carry out calculations with vectors and matrices using the Einstein summation convention.
  • Learn the properties of the Kronecker delta symbol and the Levi-Civita totally anti-symmetric tensor, and be able to use them in calculations with vectors and matrices.
  • Learn the special properties of rotation matrices.
  • Learn how to transform space and time coordinates and electromagnetic fields between rest frames in relative motion.
  • Learn the basic properties of the permutation and rotation groups.
  • Understand the wave equation for transverse displacements of a stretched string.
  • Understand the general solution for waves on a string.
  • Learn the properties of sinusoidal solutions to the wave equation.
  • Understand how to use the Fourier series to describe a wave on a string with general initial conditions.
  • Understand why functions satisfying the wave equation for a string form a vector space, and why the functions in the Fourier expansion form an orthonormal basis for this vector space.
  • Learn the basic properties of the Dirac delta function.
  • Be able to calculate the Fourier transform of a function.

Vector Calculus

  • Understand the definition of a vector field, and be able to calculate its partial derivatives.
  • Be able to plot vector fields in two dimensions.
  • Understand the definition of line, surface and volume integrals, and become skilful at evaluating them for a given function.
  • Learn the definitions of the divergence, curl and gradient in terms of limits involving volume, surface and line integrals, respectively.
  • Learn the definitions of divergence, curl and gradient in terms of partial derivatives, and be able to evaluate them for a given function.
  • Learn the relation between Cartesian, cylindrical and spherical coordinates.  Be able to carry out integrals and evaluate derivatives in all three coordinate systems.
  • Understand Gauss’s theorem and Stokes’ theorem.

Homework: There will be homework due every week. The assignments are given on the course schedule. The homework is very important. It counts as part of the final grade, and it will be hard to do well on the tests without having done the homework. Here are a few suggestions for doing homework.

  • Always start the problem by drawing a diagram, if at all relevant.
  • Explain your solution to the problem in words. This is just as important as the calculations.
  • Try to find someone to work with on the homework. Whether you end up getting help or giving help to some one else, you will be better off.

Exams: There will be three midterms and a 2-1/2 hour comprehensive final. In addition, there will be frequent short quizzes.

Grading: The grade will be based on the homework and exam grades as indicated below.

 
        Final Exam               30%
        Midterms                 30%
        Quizzes (drop 2)         20%
        Homework (drop 2)        20%

My grading is based roughly on a curve, with an average grade of about 3.0 (B).

Dropping and Withdrawal:  You may drop yourself from the course at any time up through September 8.  Withdrawal after this date is permitted only for "serious and compelling reasons."  You will only be allowed to register twice for a course; if you withdraw from or fail a course twice, you will not be allowed to register a third time.  See the Physics and Astronomy Department policy on withdrawal at http://physics.sfsu.edu under Department Policies.

Plagiarism:  Representing work done by others as your own work is expressly forbidden.  See the Physics and Astronomy  Department policy on plagiarism at http://physics.sfsu.edu under Department Policies.

Accessibility:  Students with disabilities who need reasonable accommodations are encouraged to contact the instructor.  The Disability Programs and Resource Center (DPRC) is available to facilitate the reasonable accommodations process.  The DPRC is located in the Student Service Building and can be reached by telephone (voice/TTY 415-338-2472) or by email (dprc 'at' sfsu.edu).

PROGRAM/Degree:  BA Physics                                                              COLLEGE:  Science and Engineering         DATE:  January 7,2010

Program Mission: This program is designed to educate students who need knowledge and skills in the fundamentals of physics in order to pursue careers as technicians, high school teachers, technical sales people, or technical writers, high-school teachers, technical writers, aerospace business people, or to possibly continue to a professional program in law, business, or medicine, or to continue in a graduate program in astronomy or physics.. Graduates should have the fundamental mathematical, scientific, and learning skills to enable them to be lifelong learners who can rapidly learn and master new scientific and technical developments and who can present these ideas to others.

 This objectives of this course are aligned with the outcomes of the degree mission statements in the following ways.  This course combines education in the fundamentals of physics with advanced coursework in theoretical physics.  It helps to provide the mathematical, scientific, and learning skills to enable graduates to be lifelong learners who can rapidly learn and master new scientific and technical developments and who can present these ideas to others.  The skills taught in this course prepare students for careers in science and engineering, education, and other fields (business, for example) where quantitative abilities are valued.