MATH 308 Differential Equations (3)

Catalog Description:

First and second order linear differential equations. LaPlace transforms, systems of differential equations with applications. (Offered every semester.)


Prerequisites:

 

MATH 211 Calculus III: MATH 211 may be taken concurrently with MATH 308.

  1. Understand and use the fundamental theorem of calculus.
  2. Familiarity with integration by parts and partial fractions.
  3. Understand the concept of a vector field.
  4. Familiarity with power series and regions of convergence.
  5. Ability to use a computer algebra system or graphics calculator.
  6. Ability to analyze functions and their graphs.
  7. Understand partial differentiation.

Required Course Materials:

Dennis G. Zill, A First Course in Differential Equations, 10th edition, Brooks/Cole Publishing Company Boston, 2013 (ISBN: 9781133804062) This will include the online homework tool WebAssign.


Course Coordinator:

Douglas C. Phillippy, Ph.D., Associate Professor of Mathematics


Course Audience:

Students majoring in mathematics, information science, or engineering.


Course Objectives:

  1. To develop the ability to solve an ordinary differential equation of first or second order.
  2. To develop the ability to model certain physical phenomenon using ordinary differential equations.
  3. To develop an ability to analyze a differential equation by using numerical or graphical techniques.
  4. To enhance learning by examining geometric, numerical, and algebraic aspects of each problem.
  5. To acquire an understanding of the breadth of mathematics by introducing applications in a wide variety of scientific fields.
  6. To enhance the ability to communicate mathematical concepts through a series of written laboratory assignments and classroom discussions.
  7. To select and use technology when appropriate in problem solving.
  8. To develop the process of making appropriate conjectures, finding suitable means to test those conjectures, and drawing conclusions about their validity.

Topics:

  1. First-order differential equations: a) separable variables, b) homogeneous equations, c) exact equations, d) linear equations, e) integrating factors, f) Bernoulli equations.
  2. Second-order differential equations: a) reduction of order, b) undetermined coefficients, c) variation of parameters.
  3. Homogeneous differential equations: a) linear independence, b) differential operators, c) annihilator approach.
  4. Laplace transforms and their applications to solving differential equations.
  5. Numerical and graphical methods: a) orthogonal trajectories, b) direction fields, c) Euler's method.
  6. Applications: a) simple harmonic motion, b) damped and forced motion, c) electrical systems, d) mixture problems, e) population growth, f) radioactive decay.
  7. Power series solutions.
  8. Existence and uniqueness of solutions.

 

Revised: September 2011

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