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SMC|Academic Programs|Mathematics|Math 15 - Differential Equations

Math 15 - Differential Equations

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, Cauchy-Euler 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 Cauchy-Euler 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.