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# Math 220: Differential Equations

### Course Prerequisites

Grade of C or better in MATH 210 (Calculus III)

### Course Description

The course covers techniques and applications of differential equations, first and second order equations, Laplace transforms, series solutions, graphical and numerical methods, and partial differential equations.

3 hours

### Course Materials

#### Textbook

Nagle, Saff, and Snider, Fundamentals of Differential Equations, 9th edition, with MyLab Math (printed textbook is optional).

#### MyLab Math

MyLab Math access for this title is required and must be purchased through Blackboard. MyLab Math already includes an electronic version of the textbook, so buying a printed copy is optional.

The following textbook sections/topics are covered in Math 220
Section Topic(s)
1.1 Background: Introduction to ODEs
1.2 Solutions and IVPs
1.3 Direction Fields
1.4 Euler's Method
2.1 Introduction: Falling body
2.2 Separable Equations
2.3 First Order Linear Equations
2.4 Exact Equations
3.2 Mixing Problems and Population Models
3.4 Newtonian Mechanics
3.5, 5.7 (optional) RLC Circuits
3.6-3.7 (optional) Numerical Methods
4.1 The Mass-spring oscillator
4.2 Homogeneous Linear Equations
4.3 Auxiliary Equations with Complex Roots
4.4 Method of Undetermined Coefficients
4.5 The Superposition Principle and Undetermined Coefficients Revisited
4.6 Variation of Parameters
4.7 Cauchy-Euler Equations and Reduction of Order
4.9-4.10 (optional) Mechanical Vibrations
5.2 Differential Operators, Method of Elimination for Systems
5.4 (optional) Phase Plane
7.2 Laplace Transform
7.3 Properties of Laplace Transforms
7.4 Inverse Laplace Transform
7.5 Solving Initial Value Problems by Laplace Transforms
7.6 Transforms of Discontinuous Functions
7.9 Dirac Delta Function
10.1 Introduction to Partial Differential Equations
10.2 Separation of Variables, Boundary Value Problems, and Eigenvalue Problems
10.3 Fourier Series
10.4 Fourier Sine and Cosine Series
10.5 Heat Equation
10.6 Wave Equation