DifferentialEq: Laplace

This module reviews the basic principles of mathematics covered in the FE Exam. We first review the equations and characteristics of straight lines, then classify polynomial equations, define quadric surfaces and conics, and trigonometric identities and areas. In algebra we define complex numbers and logarithms, and show how to manipulate matrices and determinants. Basic properties of vectors with their manipulations and identities are presented. The discussion of series includes arithmetic and geometric progressions and Taylor and Maclaurin series. Calculus begins with definitions of derivatives and gives some standard forms and computation of critical points of curves, then presents grad, del and curl operators on scalar and vector functions. Differential equations are calcified and to methods to solve linear, homogenous equations are presented. Fourier series and transforms are defined along with standard forms, and finally Laplace transforms and their inverse are discussed. In all cases, basic ideas and equations are presented along with sample problems that illustrate the major ideas and provide practice on expected exam questions.Time: Approximately 4.5 hours | Difficulty Level: Medium

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