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A University Level Introductory Course in Differential Equations
What you'll learn
• Classify differential equations according to their type and order.
• Solve first order differential equations that are separable, linear, homogeneous, exact, as well as other types that can be solved through different substitutions.
• Use first order differential equations to model different applications from science.
• Solve linear second order equations with constant coefficients (both homogenous and non-homogeneous) using the method of undetermined coefficients, variation of parameters, and Laplace transforms.
• Understand the theory of linear second order differential equations and how it relates to ideas from linear algebra.
• Use linear second order equations with constant coefficients (both homogenous and non-homogeneous) to model applications from science.
Requirements
• First year differential and integral calculus
Description
This course will teach everything that is usually taught in the first two semesters of a university/college course in differential equations. The topics we will consider in this course are
1. First Order Differential Equations
2. Linear Equations of Higher Order
3. Laplace Transform Methods
4. Linear Systems of Differential Equations
5. Power Series Methods
6. Partial Differential Equations
7. Fourier Series
8. Sturm Liouville Eigenvalue Problems
9. Nonlinear Systems of Differential Equations
10. Numerical Methods
Who this course is for:
• Students taking differential equations at college or university
• Students preparing to take differential equations at college or university
• Anyone who wants to learn about the subject of differential equations
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