
Instructor: Dr. Natalia Dushkina
Office: CAPUTO Hall, Room 237
Phone: 8723424
Email: Natalia.Dushkina@millersville.edu
Office hours: Mon/Wed/Fri 9:00 – 11:00 a.m.
I. COURSE ORIENTATION
Course: 
Physics 395 – Techniques in Mathematical Physics 
Credit: 
3 credits 
Lectures: 
Mon., Wed., Fri. 8:00 – 8:50 a.m., RODDY 256 
Required Text: 
Mathematical Methods in the Physical Sciences, 3rd ed., by Mary L. Boas, John Wiley & Sons, Inc., 2006,
(ISBN 0471198269) 
Prerequisite: 
PHYS 233 and MATH 365 
Course Description: 
This course is aimed at physics students. It deals with treatment of advanced mathematical techniques such as complex analysis, matrices, Fourier series, calculus of variations, special functions and integral transforms applied to selected areas of physics. 
Course Goal: 
 To review and reinforce material learned in undergraduate mathematics classes.
 To make you familiar and secure with basic advanced mathematical techniques and their application to selected areas and problems of physics.
 To prepare you for graduate classes in mechanics, quantum mechanics, electricity and magnetism.

Course Objectives: 
After finishing this course, you will
 Become more comfortable, confident, and accurate in using mathematical tools in physics;
 Perform and apply correctly calculations with vectors, matrices, series and special functions to physics problems in classical Mechanics, Optics, Electricity and Magnetism.
 Pushed to more depth and breadth in understanding mathematical tools already learned in undergraduate mathematics courses.
 Understand and explore in details special functions and Fourier Transforms;
 Be able to solve physical problems using series solutions of differential equations, Fourier Transforms using delta functions, partial differential equations.
 Be more competent in using computer methods for graphics or numerical solutions when solving matrix equations, in series and integral transforms calculations.

Testing & Grades: 
5 Exams of Equal Weight (75% of final grade)
Problem Sets (25% of final grade)
 Assigned problem sets will be collected and all the problems will be graded.
 The student will be allowed access to his/her lecture notes during exams.
 Makeup exams will be granted only of the student has a legitimate reason.

II. COURSE CONTENT
Introduction: Matrices, and Determinants. Solving linear equations by using matrices. Matrices in Optics.
Topic 1: Infinite series. Geometric progression. Convergent and divergent series. Power series
(Ch. 1).
Topic 2: Complex Variables; Complex algebra; Powers and roots of complex numbers; Logarithms (Ch. 2).
Topic 3: Fourier Series; Complex form of Fourier series (Ch. 7)
Topic 4: Ordinary Differential equations: The Laplace Transform; The Dirac Delta Function (Ch. 8)
Topic 5: Special Functions; Gamma and beta functions (Ch. 11).
Topic 6: Legendre Polynomials; Legendre Series; Bessel’s Functions (Ch. 12).
Topic 7: Some Partial Differential Equations in Physics; Poisson’s Equation (Ch. 13).
Topic 8: Matrices in Classical and Quantum Mechanics; Tensors (Ch. 10 – Sec. 15).
Topic 9: Calculus of Variation; The Euler Equation; Lagranges’s Equations (Ch. 9).
Topic 10: Complex Variables (Ch. 14).
No classes On:
March 12, 14, 16: Spring Break
April 11: Possible Weather Makeup day
May 4: Reading Day
III. EXAM SCHEDULE
EXAM I: February 5, Monday, Topics 1, 2.
EXAM II: February 26, Monday, Topics 3, 4.
EXAM III: March 26, Monday, Topics 5, 6.
EXAM IV: April 16, Monday, Topics 7, 8.
FINAL EXAM: May 10, Thursday, 2:45 – 4:45 p.m., Roddy 256, Topics 9, 10.
IV. ADDITIONAL REFERENCES
 Abramowitz, M. and Stegun, I.: “Handbook of Mathematical Functions”, (9th ed., 1970, Dover Publications, Inc.).
 Arfken, G.: “Mathematical Methods for Physicists”, (4th ed., 1995 and 2nd ed., 1970, Academic Press).
 Lea, S. M.: “Mathematics for Physicists”, (2004, Thomson Brooks/Cole)
 Lea, S. M.: Student solutions Manual for “Mathematics for Physicists”, (2004, Thomson Brooks/Cole)
 Mathews, J. and Walker, R. L.: “Mathematical Methods for Physics”, (2nd ed., 1970, W. A. Benjamin, Inc.).
