Classes are on M W F 11:00 AM - 11:50 AM in Lewis Room 109
Past classes:
- 01/24/2011 - Preliminary test
- 01/26/2011 - Vectors in Classical Physics. Scalar product and basis rotation. [Textbook sections 1.1-1.4]
- 01/28/2011 - Vectors in Classical Physics. Vector product and gradient. [Textbook sections 1.5, 1.7]
- 01/31/2011 - Vectors in Classical Physics. Curl, Laplacian. Physical examples. [Textbook section 1.7]
- 02/02/2011 - Groups. Fields. Vector spaces. Isomorphisms. Examples. [Textbook sections 3.1-3.4]
- 02/04/2011 - More on isomorphisms. An example.
- 02/07/2011 - Linear transformations and matrices. [Textbook sections 3.5-3.7]
- 02/09/2011 - Matrices, determinants, and similarity transformations. [Textbook sections 3.5-3.7]
- 02/11/2011 - Eigenvalues and eigenvectors. [Textbook section 3.10]
- 02/14/2011 - A physical example. The quantum harmonic oscillator. [Textbook section 3.10]
- 02/16/2011 - Exercises.
- 02/18/2011 - Inner product. Orthogonality and completeness. [Textbook sections 4.1,4.2]
- 02/21/2011 - Theorems on normed spaces. Schwarz's inequality. [Textbook section 4.2]
- 02/23/2011 - Gram-Schmidt orthogonalization. Adjoint transformations. [Textbook sections 4.2-4.4]
- 02/25/2011 - In-class test.
- 02/28/2011 - Self-adjoint and Hermitian operators. [Textbook sections 4.2-4.4]
- 03/02/2011 - Application of Schwarz's inequality: Heisenberg uncertainty principle.
- 03/04/2011 - Isometries. Unitary transformations. [Textbook sections 4.5-4.6]
- 03/07/2011 - Diagonalization of Hermitian operators. Commutating operators. Function space. [Textbook sections 4.7, 5.1]
- 03/09/2011 - Hilbert space. Lebesgue integration. Complete orthonormal sets of functions.
[Textbook sections 5.1-5.2]
- 03/11/2011 - More on complete orthonormal sets of functions. Properties of Dirac delta function. [Textbook
sections 5.2, 5.3]
- 03/21/2011 - Legendre Polynomials. Fourier Series. [Textbook sections 5.5, 5.6]
- 03/23/2011 - More on Fourier series. Extension to arbitrary invervals. Fourier transforms. [Textbook sections 5.6, 5.7]
- 03/25/2011 - Exercises on Fourier series and Legendre Polynomials.
- 03/28/2011 - Exercise on Fourier transforms. A last look at orthogonal polynomials.
- 03/30/2011 - Analytic functions. Cauchy-Riemann conditions. The exponential function. [Textbook sections 6.1, 6.2]
- 04/04/2011 - The square root and the logarithm functions. [Textbook section 6.2]
- 04/06/2011 - Complex integration. Cauchy and Cauchy-Goursat theorems. [Textbook section 6.3]
- 04/08/2011 - Cauchy integral formula. Derivatives of analytic functions. [Textbook section 6.4]
- 04/11/2011 - In-class test.
- 04/13/2011 - Exercises on complex integration.
- 04/18/2011 - Cauchy principal value of a complex integral. [Textbook section 6.5]
- 04/20/2011 - Examples of Cauchy principal values of complex integrals. [Textbook section 6.5]
- 04/25/2011 - Expansion of an analytic function in power series. Laurent and Taylor expansions. [Textbook section 6.7]
- 04/27/2011 - Exercises on power series expansions.
- 04/29/2011 - Residue theory and applications to real integrals. [Textbook section 6.8]
- 05/02/2011 - Jordan's Lemma and more integrals.
- 05/04/2011 - Generating functions for Bessel functions and Legendre polynomials.
- 05/06/2011 - Exercises.
Next class:
05/09/2011 - Final exam (12:00-2:00pm). Solutions
