# Math 4512: Partial Differential Equations for Science and Engineering (Instructor: Sergei Chmutov)

## Summer 2012. Tentative Daily Schedule

 06/18 (Mo) Homogeneous Equations with Constant Coefficients. (sec. 3.1) 06/19 (Tu) Complex Roots of the Characteristic Equation. (sec. 3.4) 06/20 (We) Definition of the Laplace Transform. (sec. 6.1) 06/21 (Th) Solution of Initial Value Problems. (sec. 6.2) 06/22 (Fr) Step Functions. (sec. 6.3) 06/25 (Mo) Differential Equations with Discontinuous Forcing Functions. (sec. 6.4) 06/26 (Tu) Impulse Functions. (sec. 6.5) 06/27 (We) Convolution Integral. (sec. 6.6) 06/28 (Th) Euler's Equation; Regular Singular Points. (sec. 5.5) 06/29 (Fr) Series Solution Near a Singular Point. I. (sec. 5.6) 07/02 (Mo) Series Solution Near a Singular Point. II. (sec. 5.7) 07/03 (Tu) Bessel's Equation. (sec. 5.8) 07/04 (We) NO CLASSES 07/05 (Th) Review for midterm. 07/06 (Fr) MIDTERM 1. 07/09 (Mo) The Two-Point Boundary Value Problem. (sec. 10.1) 07/10 (Tu) Fourier Series. (sec. 10.2) 07/11 (We) Fourier Convergence Theorem. (sec. 10.3) 07/12 (Th) Even and Odd Functions. Separation of Variables. (sec. 10.4, 10.5) 07/13 (Fr) Separation of Variables; Heat Conduction in a Rod. (sec. 10.5) 07/16 (Mo) Heat Conduction Eq'n: Motivation via Derivation . (sec. 10.8A) 07/17 (Tu) Other Heat Conduction Prob's: Nonhomogeneous, Neuman, Mixed Boundary Cond'ns. (sec. 10.6) 07/18 (We) Wave Equation: Motivation via Derivation; Vibrations of an Elastic String. (sec. 10.8B,10.7) 07/19 (Th) Vibrations of an Elastic String. (sec. 10.7) 07/20 (Fr) Laplace's Equation: Separation in Cartesian Coordsinates Dirichelet vs Neuman Boundary Conditions. (sec. 10.8) 07/23 (Mo) Separation and Solution in Polar and Cylindrical Coordinates. (sec. 10.8) 07/24 (Tu) Review for midterm. 07/25 (We) MIDTERM 2. 07/26 (Th) Two-point Boundary Value Problems. (sec. 11.1) 07/27 (Fr) Sturm-Liouville Boundary Value Problems I. (sec. 11.2) 07/30 (Mo) Sturm-Liouville Boundary Value Problems II. (sec. 11.2) 07/31 (Tu) Nonhomogeneous Boundary Value Problems . (sec. 11.3) 08/01 (We) Singular Sturm-Liouville Problems. (sec. 11.4) 08/02 (Th) Bessel Series Expansion: Vibrating Drum. (sec. 11.5) 08/03 (Fr) Review for final.