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  1. Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODEs) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especial...more

  2. Introduction to the Dirac Delta Function.

  3. Introduction to the Epsilon Delta Definition of a Limit.

  4. Using the epsilon delta definition to prove a limit.

  5. Introduction to the Kawa Development Environment: Evaluation of Expressions, Loading Function Definitions From a .Scm File, Mapping Arbitrary Unary Functions Over Lists in Scheme Using the Map Operation, Mapping List Functions (Car, Cdr) Over Lists of Lists, Using Mapping Functions with More than One Input by Passing Multiple Lists into Map, Implementing the Unary Version of Map Using Recursion, Apply, Which Allows You to Specify a Functio...more

  6. Figuring out the Laplace Transform of the Dirac Delta Function.

  7. Note: This course is being offered this summer by Stanford as an online course for credit. It can be taken individually, or as part of a master’s degree or graduate certificate earned online through the Stanford Center for Professional Development. The goals for the course are to gain a facility with using the Fourier transform, both specific techniques and general principles, and learning to recognize when, why, and how it is used. To...more