Math 20D (Introduction to Differential Equations)

Course Topics: Ordinary Differential Equations
Instructor: TBA

Textbook(s):

• Boyce and Diprima, Elementary Differential Equations, 8th Edition, John Wiley and Sons, 2004, Chapters 1-7.

CATALOG DESCRIPTION: 20D. Introduction to Differential Equations (4)
Ordinary differential equations: exact, separable, and linear; constant coefficients, undetermined coefficients, variations of parameters. Systems. Series solutions. Laplace transforms. Computing symbolic and graphical solutions using Matlab. Formerly numbered Math. 21D. May be taken as repeat credit for Math. 21D. Prerequisite: Math 20C (or Math 21C) with a grade of C- or better.

LECTURES:

 Lecture Section(s) Topics Covered 1 1.1-1.3 Introduction: Mathematical modeling with ODE, Classification of ODE and PDE 2 2.1 Linear equations; Method of Integrating Factors 3 2.2 Separable Equations 4 2.3,2.4 Modeling with First Order Equations; Differences Between Linear and Nonlinear Equations 5 2.5 Autonomous Equations and Population Dynamics 6 2.6 Exact Equations and Integrating Factors 7 3.1,3.2 Second Order Linear Equations: Fundamental Solutions of Linear Homogeneous Equations 8 3.3 Linear Independence and the Wronskian 9 3.4 Complex Roots of the Characteristic Equation 10 3.5 Repeated Roots; Reduction of Order Week 4 Midterm 1 TOPICS COVERED: Boyce and DiPrima 1.1-3.4. 11 3.6 Nonhomogeneous Equations; Method of Undetermined Coefficients 12 3.7 Variation of Parameters 13 7.1,7.2 Systems of First Order Linear Equations: Introduction, Review of Matrices 14 7.3 Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors 15 7.4 Basic Theory of Systems of First Order Linear Equations 16 7.5 Homogeneous Linear Systems with Constant Coefficients 17 7.6 Complex Eigenvalues 18 7.7,7.8 Fundamental Matrices, Repeated Eigenvalues 19 7.9 Nonhomogeneous Linear Systems 20 5.1 Review of Power Series; Using Power Series to Solve ODEs Week 8 Midterm 2 TOPICS COVERED: Boyce and DiPrima 3.5-3.7,7.1-7.9. 21 5.2,5.3 Series Solutions Near an Ordinary Point 22 6.1 The Laplace Transform: Definition of the Laplace Transform 23 6.2 Solution of Initial Value Problems 24 6.3,6.4 Step Functions; Differential Equations with Discontinuous Forcing Functions 25 6.5 Impulse Functions. Week 10 Review REVIEW for Final Exam Week 11 Final Exam TOPICS COVERED: Boyce and DiPrima 1.1-7.9.