MATH 3243

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MATH 3243
Differential Equations I

Lecture Notes

The following are lecture notes designed for the Differential Equations I class at ATU. These notes have been improved and will continue to be. Please feel free to browse through them.

To Students: BEWARE! The notes posted here are those that I write for myself to bring to class so that if you miss class, you can see approximately what we covered. I will NOT be posting notes as they would appear in class. There will be many missing examples and explanations. This is not a replacement for coming to class and taking notes yourself.

§ 1.2 Basic Terminology
§ 1.3 Graphical Method of Solution: Direction Field of y' = f(t,y)
§ 2.1 Existence and Uniqueness of Solutions to First Order Linear IVP
§ 2.2 Solving First Order Linear Differential Equations
§ 2.3 Modeling with First Order Linear Differential Equations: Mixing Problems and Cooling Problems
§ 2.4 Additional Applications: Population Dynamics and Radioactive Decay
§ 2.5 Existence and Uniqueness of Solutions to First Order Nonlinear IVP
§ 2.6 Separable Differential Equations
§ 2.7 Exact Differential Equations
§ 2.8 Applications of First Order Nonlinear Equations: The Logistic Population Model
§ 2.9 Applications of First Order Differential Equations to Mechanics.
§ 2.10 Numerical Solutions: Euler's Method.
§ 3.1 Second Order Linear Differential Equations: Existence and Uniqueness Results
§ 3.2 The General Solution of Homogeneous Equations
§ 3.3 Second Order Linear Homogeneous Equations with Constant Coefficients
§ 3.4 Characteristic Equations with Repeated Roots
§ 3.5 Characteristic Equations with Complex Roots
§ 3.6 Applications of Homogeneous Equations: Unforced Mechanical Vibrations
§ 3.7 The Structure of the General Solution to a Nonhomogeneous Equation
§ 3.8 The Method of Undetermined Coefficients
§ 3.9 The Method of Variation of Parameters
§ 3.10 Applications of Nonhomogeneous Equations: Forced Mechanical Vibrations and Electrical Circuits

MATH 3243 Differential Equations I

Lecture Notes

MATH 3243
Differential Equations I