Course Outline for Mathematics 4
Elementary Differential Equations

Effective: Fall 2018
SLO Rev: 12/06/2016

Catalog Description:

MTH 4 - Elementary Differential Equations

3.00 Units

Introduction to elementary differential equations, including first and second order equations, series solutions, Laplace transforms, and applications.
Prerequisite: MTH 2.
CB03: TOP Code 1701.00 - Mathematics, General
Course Grading: Letter Grade Only
Type Units Inside of Class Hours Outside of Class Hours Total Student Learning Hours
Lecture 3.00 54.00 108.00 162.00
Laboratory 0.00 18.00 0.00 18.00
Total 3.00 72.00 108.00 180.00

Measurable Objectives:

Upon completion of this course, the student should be able to:
  1. verify that a given solution satisfies a given differential equation and interpret it geometrically when appropriate;
  2. apply the existence and uniqueness theorems for ordinary differential equations;
  3. identify the type of a given differential equation and select and apply the appropriate analytical technique for finding the solution of first order and selected higher order ordinary differential equations;
  4. find power series solutions to ordinary differential equations;
  5. determine the Laplace Transform and inverse Laplace Transform of functions;
  6. solve Linear Systems of ordinary differential equations;
  7. create and analyze mathematical models using ordinary differential equations such as orthogonal trajectories, growth, decay, cooling, circuits, and mechanical vibrations.

Course Content:

  1. Introduction to Differential Equations, Notation and Terminology
    1. Classification and some origins of differential equations
    2. Geometrical interpretation of equations and solutions
    3. Definitions and examples of initial value problems, boundary value problems
    4. Existence and Uniqueness Theorem (for first order equations only)
  2. First Order Equations
    1. Separable equations
    2. Homogeneous equations
    3. Exact equations/integrating factors
    4. Linear equations
    5. Bernoulli equations
    6. Equations reducible to first order (substitution)
    7. Applications (orthogonal trajectories, growth, decay, cooling, circuits, etc.)
  3. Higher Order Linear Equations with constant coefficients
    1. Homogeneous equations
    2. Non homogeneous equations by:
      1. Undetermined coefficients
      2. Variation of parameters
    3. Application of second order linear equations
      1. Mechanical vibrations (undamped, damped, forced)
  4. Fundamental solutions, independence, Wronskian
  5. The Laplace Transform
  6. Systems of linear differential equation

Methods of Instruction:

  1. Lecture/Discussion
  2. Group Activities
  3. Handouts and rule interpretations.
  4. Distance Education
  5. Problem-solving

Assignments and Methods of Evaluating Student Progress:

1. Typical Assignments
  1. A mass of 1 slug is suspended from a spring whose characteristic spring constant is 9 pounds per foot. Initially the mass starts from a point 1 foot above the equilibrium position with an upward velocity of ? feet per second. Find the times for which the mass is heading downward at a velocity of 3 feet per second.
  2. Suppose a function y(t) has the properties that y(0) = 1 and y’(0) = -1. Find the Laplace transform of y’’ – 4y’ + 5y.
2. Methods of Evaluating Student Progress
  1. Exams/Tests
  2. Quizzes
  3. Homework
  4. Lab Activities
3. Student Learning Outcomes
Upon the completion of this course, the student should be able to:
  1. Critically analyze mathematical problems using a logical methodology.
  2. Communicate mathematical ideas, understand definitions, and interpret concepts.
  3. Increase confidence in understanding mathematical concepts, communicating ideas and thinking analytically.

Textbooks (Typical):

  1. Zill/Cullen (2013). Differential Equations with Boundary-Value Problems (8th). Cengage.
Additional Materials:
  • A calculator may be required.

Abbreviated Class Schedule Description:

Introduction to elementary differential equations, including first and second order equations, series solutions, Laplace transforms, and applications.
Prerequisite: MTH 2.

Discipline:
Mathematics*