# Physics 227 - Elementary Mathematical Physics - Winter 2001

## Tentative Syllabus:

Text:  Mathematical Methods in the Physical Sciences, Mary L. Boas, second edition, Wiley 1983.

Jan 3-10              Ch. 1, Infinite Series, Power Series.
Motivation, convergence tests, Maclaurin and Taylor series, other useful series, examples of use.

Jan 12 - 24          Ch. 2, Complex Numbers.
Cartesian and polar form, power series definition of functions of a complex variable, powers roots
and logarithms of complex numbers.  Applications to interference, damped and driven oscillators,
resonance, electric circuits, complex impedance.

Mon Jan 15          Martin Luther King holiday.

Fri Jan 26       First midterm exam (open book, calculators allowed).  Solutions and scores  here .

Jan 29 - Feb 14    Ch. 3, Linear Equations, Vectors, Matrices  and Determinants.
Ch. 10,  sections 1-5,  Coordinate transformation; tensor analysis.
Elementary matrix operations.  Matrices as linear operations on a vector space.  Real and unitary
transformations. Determinants and the existence of an inverse. Eigenvalues and eigenvectors, matrix
diagonalization.  Applications to coordinate transformations, coupled oscillators.

Feb 16 - 28          Ch. 7, Fourier Series.
Motivation,  solution of wave equation as a Fourier series, derivation of expansion, complex Fourier
expansion. Relation between Fourier expansions of a function and expansion of a vector in terms of
particular basis vectors.

Mon Feb 19         Presidents' Day holiday.

Fri Feb 23        Second midterm exam, in class. Open book, no calculators. Solutions and scores  here .

Mar 2 - 9            Ch. 15, sections 4-5, Integral Transforms.
Fourier transforms, analogy with unitary transformations of complex vectors, Parseval's theorem,
Dirac delta function.

Wed Mar 14      Final exam  2:30-4:20 PM, Smith 205.   ! NOTE ROOM CHANGE !
Open book. No calculators allowed on this exam.

General Information
Assignments and Solutions
Mathematica