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Math 238 Intoduction to Differential Equations
INTRODUCTION TO DIFFERENTIAL EQUATIONS
COURSE GOALS/OBJECTIVES:
An introductory course for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study.
A graphing calculator is required.
Prerequisite: Math 201 or equivalent with a grade of "C" or better.
COURSE CONTENT:
2.1 Linear Equations; Method of Integrating Factors
2.2 Separable Equations
2.3 Modeling with First Order Equations
2.4 Differences Between Linear and Nonlinear Equations
2.5 Autonomous Equations and Population Dynamics
2.6 Exact Equations and Integrating Factors
2.8 The Existence and Uniqueness Theorem
EXAM 1
3.1 Homogeneous Equations with Constant Coefficients
3.2 Fundamental Solutions of Linear Homogeneous Equations
3.3 Linear Independence and the Wronskian
3.4 Complex Roots of the Characteristic Equation
3.5 Repeated Roots; Reduction of Order
3.6 Nonhomogeneous Equations; Method of Undetermined Coefficients
3.7 Variation of Parameters
3.8 Mechanical and Electrical Vibrations
3.9 Forced Vibrations
EXAM 2
4.1 General Theory of nth Order Linear Equations
4.2 Homogeneous Equations with Constant Coefficients
4.3 The Method of Undetermined Coefficients
4.4 The Method of Variation of Parameters
5.1 Review of Power Series
5.2 Series Solution Near an Ordinary Point
5.4 Regular Singular Points
5.5 Euler Equations
EXAM 3
6.1 Definition of the Laplace Transform
6.2 Solution of Initial Value Problems
6.3 Step Functions
EXAM 4
REQUIRED EVALUATION METHODS:
Written exams, quizzes, homework, class participation, group participation
TEXT BOOKS:
William E. Boyce and Richard C. DiPrima
Elementary Differential Equations, 8th Edition
John Wiley and Sons (2005)
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