Boyce and Diprima,
Elementary Differential Equations,
8th Edition, John Wiley and Sons, 2004, Chapters 1-7.
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.
Introduction: Mathematical modeling with ODE, Classification
of ODE and PDE
Linear equations; Method of Integrating Factors
Modeling with First Order Equations; Differences
Between Linear and Nonlinear Equations
Autonomous Equations and Population Dynamics
Exact Equations and Integrating Factors
Second Order Linear Equations:
Fundamental Solutions of Linear Homogeneous Equations
Linear Independence and the Wronskian
Complex Roots of the Characteristic Equation
Repeated Roots; Reduction of Order
TOPICS COVERED: Boyce and DiPrima 1.1-3.4.
Method of Undetermined Coefficients
Variation of Parameters
Systems of First Order Linear Equations: Introduction,
Review of Matrices
Linear Algebraic Equations; Linear Independence,
Basic Theory of Systems of First Order Linear Equations
Homogeneous Linear Systems with Constant Coefficients
Fundamental Matrices, Repeated Eigenvalues
Nonhomogeneous Linear Systems
Review of Power Series;
Using Power Series to Solve ODEs
TOPICS COVERED: Boyce and DiPrima 3.5-3.7,7.1-7.9.
Series Solutions Near an Ordinary Point
The Laplace Transform: Definition of the Laplace Transform
Solution of Initial Value Problems
Step Functions; Differential Equations with
Discontinuous Forcing Functions