Mathematical Physics Lecture Coverage

Week 1

• Monday, August 24, Vector spaces and bases.
• Wednesday, August 26, Inner product. Orthonormality. Gram-Schmidt process. Schwarz and triangle inequalities.
• Wednesday, August 26, 2nd hour, Examples. Linear transformations.
• Friday, August 28, Linear functionals (bra and ket vectors). Functions of operators.

Week 2

• Monday, August 31, Operator conjugates. Hermitian and unitary operators.
• Wednesday, Sept. 2, Examples: Infinitesimal unitary transformation. Projection onto vector.
• Wednesday, Sept. 2, 2nd hour, HW discussion. Matrix representation of operators. Change of basis.
• Friday, Sept. 4, No class, Prof. out of town.

Week 3

• Monday, Sept. 7, No class, Labor day
• Wednesday, Sept. 9, Invariant subspaces and block diagonalization.
• Wednesday, Sept. 9, 2nd hour, HW discussion, eigenvalues and eigenvectors.
• Friday, Sept. 11, Spectral decomposition.

Week 4

• Monday, Sept. 14, Diagonalization of operators. Gaussian integration. Simultaneous diagonalization of operators.
• Wednesday, Sept. 16, Infinite dimensional vector space. Hilbert space.
• Wednesday, Sept. 16, 2nd hour, HW discussion, Hilbert space continued. Continuous index.
• Friday, Sept. 18, Delta function, generalized functions.

Week 5

• Monday, Sept. 21, Multidimensional delta functions.
• Wednesday, Sept. 23, HW discussion, Exam review
• Wednesday, Sept. 23, No 2nd hour
• Friday, Sept. 25, Midterm #1

Week 6

• Monday, Sept. 28, Orthogonal polynomials, least-squares, recursion relations.
• Wednesday, Sept. 30, Other properties of orthogonal polynomials.
• Wednesday, Sept. 30, No 2nd hour
• Friday, Oct. 2, Classical orthogonal polynomials, Rodriguez formula and differential equations.

Week 7

• Monday, Oct. 5, Fourier series.
• Wednesday, Oct. 7, Fourier series examples, Poisson summation formula.
• Wednesday, Oct. 7, Multidimensional Fourier series. Bragg diffraction. Fourier transform.
• Friday, Oct. 9, Fourier transform examples: Gaussian; Yukawa potential. Derivatives of Fourier transform.

Week 8

• Monday, Oct. 12, Fourier transform of distributions. Convolution theorem.
• Wednesday, Oct. 14, Parseval relation.
• Wednesday, Oct. 14, 2nd hour, exam review.
• Friday, Oct. 16, No class, Midsemester Break.

Week 9

• Monday, Monday, Oct. 19, Midterm #2
• Wednesday, Oct. 21, Complex analytic functions
• Wednesday, Oct. 21, 2nd hour, Conformal mappings
• Friday, Oct. 23, Complex integration

Week 10

• Monday, Oct. 26, Taylor series
• Wednesday, Oct. 28, Laurent series
• Wednesday, Oct. 28, 2nd hour, HW discussion, examples, residues
• Friday, Oct. 30, Jordan Lemma, evaluation of definite integrals, Principal value integrals

Week 11

• Monday, Nov. 2, No class, Prof. out of town
• Wednesday, Nov. 4, Hilber transforms, Kramers-Kronig relation
• Wednesday, Nov. 4, no 2nd hour
• Friday, Nov. 6, Steepest descents/saddle point integration

Week 12

• Monday, Nov. 9, First and second order ODE's
• Wednesday, Nov. 11, Wronskians and linear independence of solutions
• Wednesday, Nov. 11, 2nd hour, HW discussion and exam review
• Friday, Nov. 13, Midterm #3

Week 13

• Monday, Nov. 16, Wronskians and separation theorem. Inhomogeneous equations
• Wednesday, Nov. 18, Green's functions
• Wednesday, Nov. 18, 2nd hour, Power series solutions. Nonlinear ODE's
• Friday, Nov. 20, Constant coefficients

Week 14

• Monday, Nov. 23, Sturm-Liouville equations.
• Wednesday, Nov. 25, No class, Thanksgiving
• Friday, Nov. 27, No class, Thanksgiving

Week 15

• Monday, Nov. 30, Separation of variables in Cartesian coordinates. Space-time separation.
• Wednesday, Dec. 2, Separation in cylindrical coordinates
• Friday, Dec. 4, Separation in spherical coordinates

Final Exam Monday, Dec. 7, 1:00-4:00PM, Wean 8427