ModelCourses/Ordinary Differential Equations

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General Description

• Sophomore or junior level course
• Pre-requisite: Calculus

Possible textbooks include, but are not limited to:

• Fundamentals of Differential Equations and Boundary Value Problems, by Nagle, Saff, and Snider, Addison-Wesley.
• Elementary Differential Equations and Boundary Value Problems by Boyce and DiPrima, Wiley.

Course Objectives

Upon successful completion of this course, students will be able to:

• Determine if a given function is a solution to a particular differential equation; apply the theorems for existence and uniqueness of solutions to differential equations appropriately;
• Distinguish between
  (a) linear and non-linear differential equations;
  (b) ordinary and partial differential equations;
  (c) homogeneous and non-homogeneous differential equations;
• Solve ordinary differential equations and systems of differential equations using:
  (a) Direct integration
  (b) Separation of variables
  (c) Reduction of order
  (d) Methods of undetermined coefficients and variation of parameters
  (e) Laplace transform methods
• Determine particular solutions to differential equations with given initial conditions.
• Analyze real-world problems such as motion of a falling body, compartmental analysis, free and forced vibrations, etc.; use analytic technique to develop a mathematical model, solve the mathematical model and interpret the mathematical results back into the context of the original problem.
• Apply matrix techniques to solve systems of linear ordinary differential equations with constant coefficients.
• Find the general solution for a first order, linear, constant coefficient, homogeneous system of differential equations; sketch and interpret phase plane diagrams for systems of differential equations.

Problem Sets

Use of Problem Sets

The problem sets were assembled to allow for personalization by individual faculty. The topics covered are fairly standard in a beginning statistics course, but faculty can rearrange the topics and delete any sections they do not wish to cover, or wish to assess by other means. The names of the problem sets are meant to be descriptive and the learning objectives will help you evaluate if the set should be included or not.

Download the problem sets

A copy of the course can be found at at the MAA website
The course can be downloaded here <insert link>.

To use the files remove the .txt from the end. The .tgz can be added. This file can now be directly uploaded into your own course:

• go to Filemanager
• Upload the file
• etc <provide enough detail to allow for easy installation by anyone>

Description of Problem Sets

• 0-Introduction_01-Solutions-and-Initial-Value-Problems
  Students will be able to:
  • Determine if a given function is a solution to a particular differential equation
  • Identify elements of a given solution to a differential equation
  • Model with differential equations

• 0-Introduction_02-Classification-of-Differential-Equations
  Students will be able to distinguish between:
  • linear and non-linear differential equations;
  • ordinary and partial differential equations;
  • homogeneous and non-homogeneous higher order differential equations

• 1-First-order-equations_01-Integrals-as-solutions
  Students will be able to:
  • Solve simple first order differential equations by direct integration
  • Solve simple differential equations using their knowledge from Calculus

• 1-First-order-equations 02-Existence-and-Uniqueness-Theorem
  

• 1-First-order-equations 03-Slope-fields-and-Equilibrium-Solutions
  

• 1-First-order-equations 04-Separable
  

• 1-First-order-equations 05-Linear-integrating-factor
  

• 1-First-order-equations 06-Exact-Equations
  

• 1-First-order-equations 07-Substitution-Techniques-and-Integrating-Factors
  

• 1-First-order-equations 08-Autonomous
  

• 1-First-order-equations 09-Eulers-method
  

• 1-First-order-equations 10-Applications
  

• 1-First-order-equations 11-Miscellaneous
  

• 2-Higher-order-equations 01-Introduction-to-Linear
  

• 2-Higher-order-equations 02-Linear-2nd-order-constant-coeff-homogeneous
  

• 2-Higher-order-equations 03-Linear-higher-order-constant-coeff-homogeneous
  

• 2-Higher-order-equations 04-Free-Mechanical-vibrations
  

• 2-Higher-order-equations 05-Nonhomogeneous-Undetermined-Coefficients
  

• 2-Higher-order-equations 06-Nonhomogeneous-Variation-Parameters
  

• 2-Higher-order-equations 07-Forcing-resonance
  

• 3-Linear-systems 01-Intro-to-systems
  

• 3-Linear-systems 02-Matrices
  

• 3-Linear-systems 03-Linear-systems
  

• 3-Linear-systems 04-Eigenvalue-method
  

• 3-Linear-systems 05-2D-systems-vector-fields
  

• 3-Linear-systems 06-Second-order-systems mass-spring-system-01
  

• 3-Linear-systems 07-Repeated-eigenvalues
  

• 3-Linear-systems 08-Complex-eigenvalues
  

• 3-Linear-systems 09-Nonhomogeneous-systems
  

• 4-Laplace-transforms 01-Laplace-transforms
  

• 4-Laplace-transforms 02-Shifts-and-IVPs
  

• 4-Laplace-transforms 03-Partial-fractions
  

• 4-Laplace-transforms 04-Periodic-functions
  

• 4-Laplace-transforms 06-Convolution
  

• 4-Laplace-transforms 07-Delta-function
  

WeBWorK Workshop, Ann Arbor Michigan June 2013