Syllabus: Click here for details in a PDF file Course: Math 415, Ordinary and Partial Differential Equations, MWF 11:30am Texts: (1) Elementary Differential Equations & Boundary Value Problems (7th Ed) by Boyce and Diprima Topics: Solutions to first order, second order and higher order ordinary differential equations and partial differential equations; Phase plane analysis; Fourier series; Boundary value problems. Office Hours: MWF 10:30-11:30am @MW410  and by appointment Grading: first midterm (Fri. Oct 5, 20%), second midterm (Fri. Nov. 2, 25%), final exam( Mon. Dec 3 11:30am, 30%), class participation (5%), and homework (20%). The letter grade will be with an approximately 90(A)-80(B)-70(C)-60(D) scale. Policy: NO make-up exams without doctor's excuse. Late Homework will be no credit. Tentative Schedule: updated regularly

The HW problems need to be turned in. HW due every Wednesday in class. It includes all assignments given in the previous week (Mon, Wed, Fri).

 Monday Wednesday Friday Sept 17 Sept 19 (Autumn Classes Begin) Chapter 1:Introduction HW: 1.1 (11), 1.2(11),1.3(13,28) Sept 21 Chapter 2.1 & 2.2 Linear Equation: Method of Integrating Factors Separable Equations HW: 2.1 (6,10,15,18,28) Sept 24Chapter 2.2,2.3 Separable Equations Modeling with First Order Equations 2.2(4,11,25,33) Sept 26 Chapter 2.3,2.4 HW:2.3(4,9,16,21,24) Differences Between Linear and Nonlinear Equations Sept 28 Chapter 2.4, 2.5 HW:2.4(11,17,22,28) Autonomous Equations and Population Dynamics Oct 1 Chapter 2.5 HW:2.5(3,7,9,17) Oct 3 Chapter 2.6 HW2.6(7,9,19,26,27) Oct 5 Chapter 2.6 Oct 8 Chapter 2.7 Numerical Approximations and Population Dynamics HW2.7(3,15,18(too much computation, I decide not to give this question as HW)) Oct 10 First Exam Oct 12 2.8 The Existence and Uniqueness Theorem HW 2.8(4,7,11) Oct 15 Chapter 3.1 Homogeneous Equations with Constant Coefficients Fundamental Solutions of Linear Homogeneous Equations HW: 3.1 (6 13 19 20) Oct 17 Chapter 3.2 Linear Independence and the Wronskian HW: 3.2 (2,8,11,13,23) Oct 19 Chapter 3.3 Oct 22 Chapter 3.4, 3.5 HW: 3.3 (2,3,4,15,16,20) HW 3.4 (2,3,21) Complex Roots of the Characteristic Equation Oct 24 Chapter 3.5 HW: 3.5 (3,11,12,20,25,30) Repeated Roots; Reduction of Order Oct 26 3.6,3.7 HW 3.6 (3,8,14,24), HW 3.7(2,5,14,17) Nonhomogeneous Equations: Method of Undetermined Coefficients Variation of Parameters Oct 29 3.8,3.9 Mechanical and Electrical Vibrations HW 3.8 (2,6,9,13), HW 3.9(5,7,10) Oct 31 Supplement Material: Systems of ODEs HW 3.2 supplement (11(a),16,19 Click here for a PDF file of supplement material Nov 2 Supplement Material: 3.3 Homogeneus Linear Systems with constant coefficient HW 3.3 supplement (3,14 without drawing the direction field and phase portrait) Nov 5 Supplement Material: Stability Nov 7 Second Exam Nov 9 Supplement: Chapter 3.4 Complex eigenvalues HW:Solve (1)y''+9y=0 and (2) 16y''-8y'+145y=0 y(0) = -2 and y'(0)=1 by reformulating (a) and (b) to first order system equations and draw the phase portrait Nov 12 (Veteran's Day. No Classes) Nov 14 Chapter 10.1,Two-Point Boundary Value Problems HW 10.1: 2,3,4,11,13 Chapter 10.2Fourier Series Nov 16 Chapter 10.2, Fourier Series HW 10.2: 3,4,15,18 Nov 19 Chapter 10.3 The Fourier Convergence Theorem HW 10.3: 2,3 Chapter 10.4 Even and Odd Functions Nov 21 Chapter 10.4 Even and Odd Functions HW 10.4: 3,6,7,15,18,35 Chapter 10.5 Separation of Variables; Heat Conduction in a Rod Nov 23 (Columbus Day. No Classes) Chapter 10.5,10.6 Other Heat Conduction Problems HW 10.5: 3,5,8,10 HW 10.6: 2,3,9(a) Nov 28 Chapter 10.7: 1(a),6(a) The Wave Equation : Vibrations of an Elastic String Nov 30 Chapter 10.8: 1(a,b),2,5 Laplace's Equation Dec 3Final Exams Week Dec 5Final Exams Week Dec 7Final Exams Week