MATH 230: Differential Equations

Class Program
Degree Code
Symbolic or Quantitative Reasoning,
Math/Science Non-Laboratory
Credits 5 Lecture Hours 55
This course will introduce the student to the solution elementary differential equations and standard applications of differential equations in science. It will include the solution of first order linear differential equations with applications to exponential growth and decay problems, mixture problems, orthogonal trajectories, etc., solutions to second order differential equations with applications to harmonic motion, and the LaPlace transform.

Prerequisites

MATH& 163 or instructor permission
Quarters Offered
Spring
Course Outcomes

Upon successful completion of the course, students should be able to demonstrate the following knowledge or skills:

  1. Solve first order linear equations of all types
  2. Solve application problems using first order linear equations
  3. Solve higher order differential equations using various methods, such as variation of parameters, differential operators, etc.
  4. Apply the solution of higher order differential equations to harmonic motion problems
  5. Solve differential equations using Laplace Transforms
  6. Solve differential equations using series solutions
Institutional Outcomes
IO2 Quantitative Reasoning: Students will be able to reason mathematically.
Course Content Outline
  1. Introduction to differential equations
    Basic definitions and terminology
    Origins of differential equations
  2. First ordered differential equations
    Preliminary theory
    Separable equations
    Homogeneous equations
    Exact equations
    Linear equations
    Bernoulli equations
  3. Applications of differential equations
    Exponential growth and decay
    Newton’s Law of Cooling
    Mixture problems
    Chemical reactions
    Misc. Applications
  4. Linear equations of higher order
    Initial value and boundary value problems
    Linear dependence and Independence
    Solution to linear equations
    Finding a second solution from a known solution
    Homogeneous linear equations with constant coefficients
    Undetermined coefficients
    Differential operators
    Solving non-homogenous equations
    Variation of parameters
  5. Applications of second order equations
    Simple harmonic motion
    Damped motion
    Forced motion
  6. Differential equations with variable coefficients
    Cauchy Euler Equation
    Power series solutions around ordinary points
    Power series solutions around singular points
    Regular singular points
    Method of Frobenius
  7. Laplace Transforms
    The Laplace Transform
    The inverse transform
    Operational properties
    Translation theorems and derivatives of a transform
    Transforms of derivatives and integrals
Department Guidelines
In order to give the instructor the greatest flexibility in assigning a grade for the course, grades will be based on various instruments at the instructor’s discretion. However, to maintain instructional integrity there must be four class exams or three class exams and a project. A final exam will be given if there are less than four exams or a project may be substituted for the final exam if there are four in-class exams. At least 60% of the grade will be based on quantifiable work (exams, homework, quizzes, etc.). The remaining portion of the grade may be based on quantifiable work, attendance, projects, journal work, etc., at the instructor’s discretion. The following is a compilation of acceptable grading instruments: in class exams and a final, attendance, homework or quizzes, research paper, modeling projects on the calculator or computer. Other projects or assignments may be assigned as deemed appropriate at the instructor’s discretion.