# Math 23: Differential Equations

Winter 2013

Wake Vortex Study (NASA Langley Research Center)

Look here for more pictures and brief explanations

Please check the syllabus regularly as it is subject to change. Also, we will make frequent use of x-hours during the term. So, you shouldn't schedule events during our x-hours.

NOTE: If you are in Section 01 (Sutton), make sure you download the class notes before coming to class and look them over. We will be using these in class. You might want to print them out (2 or 4 pages per side) and take notes in the margins.

 Date Reading (Due Today) Topics Class Notes for Sec. 01 Mon., January 7 Chp. 1, 2.1 Course Overview; First Order ODEs Overview First Order ODEs, Part I Tues., Jan. 8 (x-hour) 2.1, 2.2 & 2.6 Linear & Separable Equations Wed., Jan. 9 2.3 & 2.6 Separable & Exact Equations Fri., Jan. 11 2.3-2.5 Existence & Uniqueness Theorem; linear vs. non-linear; First Order ODEs, Part II Mon., Jan. 14 2.5 & 2.7 Modeling w/ First Order ODes; Autonomous Equations & Geometric Methods; Intro. to Matrix Algebra Tues. Jan. 15 (x-hour) 2.1-2.7 Intro. to Matrix Algebra 2x2 Matrices Wed., Jan. 16 2.7, 3.1 & 3.2 Second Order linear Equations Second Order ODEs, Part I (revised 01-18-2013) Fri., Jan. 18 3.1-3.3 Second Order linear Equations: Wronskian & Complex Roots Mon., Jan. 21 MLK Day: No Class Tues., Jan. 22 (x-hour) 3.4-3.6 Second Order linear Equations:const. Coeff. w/ repeated roots; Non-homogenoeus Eqs.: Method of Undetermined Coefficients Second Order ODEs, Part II (revised 01-24-2013) Wed., Jan. 23 3.5 & 3.6 Method of Undetermined Coefficients & Variation of Parameters Fri., Jan. 25 3.6 - 3.8 Second-Order Linear Non-Hom.Eqs.: Variation of Parameters Mon., Jan. 28 3.7 & 3.8 Review of Techniques Tues., Jan. 29 (x-hour) Chp. 1-3, 5.1 & 5.2 Application: Spring-Mass System Power Series and POwer Series Solutions to ODEs Wed., Jan. 30 (Exam I is tonight at 6PM in 008 Kemeny!) 5.1- 5.3 Series Solutions near ordinary points Power Series Solutions (revised 02-05-2013) Fri., Feb. 1 5.1 - 5.4 Series Solutions near ordinary points; Euler's equation and Solutions Near Regular Singular Points Mon., Feb. 4 5.1 - 5.4 Series Solutions Near Ordinary Points Tues., Feb. 5 (x-hour) 5.1 - 5.4 Euler's equation and Solutions Near Regular Singular Points Wed., Feb. 6 7.1 - 7.4 Systems of First Order ODEs; Basic Theory: Existence & Uniqueness Systems of ODEs, Part I (revised 02-13-2013) Fri., Feb. 8 Winter Carnival: No Class Mon., Feb. 11 7.1 - 7.4 Linear Independence, Eigenvalues & Eigenvectors Tues., Feb. 12 (x-hour) No Class Wed., Feb. 13 7.4 & 7.5 The Eigenvalue Problem and the connection with Systems of Linear ODEs Fri., Feb. 15 7.5 & 7.6 Basic Theory: Superposition & the Wronskian; Systems with Constant Coefficients: Real Distinct Roots Systems of ODEs, Part II (revised 02-19-2013) Mon., Feb. 18 7.7 & 7.8 Systems with Constant Coefficients: Complex & Repeated Eigenvalues Tues., Feb. 19 (x-hour) 7.1-7.9 Systems with Constant Coefficients: Complex & Repeated Eigenvalues; Non-Homogeneous Linear Systems Wed., Feb. 20 7.1-7.9 Non-Homogeneous Linear Systems; Linear Systems Wrap-up Fri., Feb. 22 5.1 - 5.4 & 7.1-7.9 Review Mon., Feb. 25 (Exam II is Tonight at 6PM in 008 Kemeny!) 10.1 Two-Point Boundary Value Problems Tues., Feb. 26 (x-hour) No Class Wed., Feb. 27 10.2 Inner Products and Fourier Coefficients Fri., March 1 10.3 & 10.4 Fourier Series and the Fourier Convergence Theorem Mon., March 4 10.5 & 10.6 Heat Equation Tues., March 5 (x-hour) 10.5 & 10.6 Heat Equation Wed., March 6 10.7 Wave Equation Fri., March 8 10.7 Wave Equation & Wrap-up Tues., March 12 3-6PM Final Exam Location 008 Kemeny Hall

Last Updated 1 March, 2013