Math 15  Differential Equations
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Course Details 


Description 

This course is an introduction to Ordinary Differential Equations. Topics include first order equations, linear equations, reduction of order, variation of parameters, spring motion and other applications, CauchyEuler equations, power series solutions, Laplace transform, and systems of linear differential equations. 

Prerequisites 

Math 8 

How It Transfers 

UC, CSU IGETC AREA 2 (Mathematical Concepts) 

Textbook 

Zill, A First Course in Differential Equations, Classic 5th Ed., Brooks/Cole, 2001 

Mathematics Skills Associated With This Course 

Entry Level Skills 

Skills the instructor assumes you know prior to enrollment in this course
 Perform integration using separation of variables
 Perform integration using integration by parts
 Perform integration using partial fractions
 Perform implicit differentiation
 Compute and manipulate power and Taylor series and determine intervals of convergence
 Evaluate improper integrals and resolve indeterminate forms using L'Hopital's Rule


Course Objectives 

Skills to be learned during this course
 Identify and solve separable, homogeneous, exact, linear, Bernoulli, Ricatti and Clairaut firstorder differential equations.
 Sketch solution curves of first order differential equations using direction fields.
 Solve linear differential equations with constant coefficients.
 Solve linear second order differential equations using reduction of order.
 Solve nonhomogeneous linear differential equations using variation of parameters.
 Solve applications including spring motion, mixing problems and falling with resistance.
 Solve CauchyEuler equations.
 Find series solutions to linear differential equations, and demonstrate the method of Frobenius.
 Find Laplace transforms and inverse Laplace transforms of functions.
 Solve differential equations using the Laplace transform.
 Solve systems of linear differential equations with constant coefficients.
