### Math 4100: Differential Equations

#### Prerequisite:

Math 2300 (Calculus 3)

#### Course Topics and Core Homework Problems

The following information is provided for illustrative purposes. Details are subject to change.

#### Textbook

Elementary Differential Equations with Boundary Value Problems by William Boyce, Richard DiPrima, and Douglas Meade, eleventh edition.
The text is available electronically and enrolled students will be billed automatically. Please see your instructor’s syllabus for details.

#### Supplementary Notes

The supplementary planar systems notes linked below are also (optionally) available at the bookstore: ask for the 4100 course packet.

 Elementary Differential Equations with Boundary Value Problems (Boyce, DiPrima, Meade, 11th edition) Section Topic Homework 2.1 Linear Equations; Method of Integrating Factors 2c, 4c, 6c, 9, 12, 14(b,c), 21 2.2 Separable Differential Equations 2, 3, 5, 10(a,c), 14(a,c), 18 2.3 Modeling with First-Order Differential Equations 1, 2, 5, 17(a,b),18(a,b) 2.6 Exact Equations and Integrating Factors 1, 2, 4, 7, 11, 15, 19, 20 (see problem 17) 3.1 Homogeneous Differential Equations with Constant Coefficients 3, 6, 10, 13, 15, 17 3.2 Solutions of Linear Homogeous Equations; the Wronskian 3, 7, 9, 10, 12, 13, 14, 15, 18, 19, 21, 24, 25, 27, 28 3.3 Complex Roots of the Characteristic Equation 1, 6, 11, 12, 13, 15, 19 3.4 Repeated Roots; Redution of Order 1, 2, 6, 10, 13, 19, 20 3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients 1, 2, 5, 12, 14 3.6 Variation of Parameters 4, 6, 9, 10, 13 3.7 Mechanical  Vibrations 1, 4, 5, 8, 17, 18(a,b) 3.8 Forced Periodic Vibrations 4, 5, 7, 8 6.1 Definition of the Laplace Transform 1-3, 4(a,c), 6, 10, 12, 16 6.2 Solution of Initial Value Problems 3, 6, 7, 11, 15, 16, 17 6.3 Step Functions 1, 2, 5, 7, 9, 10, 14, 15, 16, 30 6.4 Differential Equations with Discontinuous forcing functions 1-4, 9, 11(a,b) 6.5 Impulse Functions 1, 3, 4, 6, 10(a,b) 6.6 The Convolution Integral 1(a), 4, 5, 7, 9, 11, 12 2.7 Numerical Approrixmations: Euler's Method 1,2,4 8.1 The Euler or Tangent Line Method 4, 5, 8, 22 Planar systems of Differential Equations (supplementary notes) 1 Introduction 1.1, 1.2 2 Some Concepts from Matrix Theory and Linear Algebra 2.1, 2.2(1,4,6,7,8), 2.3(1),2.4(3),2.5(1,2,3) 3 General Theory of Linear 2x2 Systems 3.1, 3.3, 3.4 4 Case 1 (homogeneous, linear, constant coefficient) 4.1, 4.2, 4.4, 4.5 5 Case 2 5.1, 5.2, 5.3 6 Case 3 6.1, 6.2, 6.4, 6.5 7 Solutions of Nonhomegeous systems 2.6(1,3), 7.1, 7.3, 7.4 8 Qualitative Methods 8.1, 8.2, 8.3 9 Linearization of Nonlinear Systems at Isolated Rest Points (as time permits) 9.1, 9.4, 9.5, 9.7