Instructor – Robert Philbin                                             Course Title: Differential Equations with Engineering App.s

Office:  Davis 238                                                                            Course Number: MAT 261

Phone:  846-5518                                                                              Credit Hours:  4

Email: robert dot philbin @ trinidad state (all one word) dot edu                 Clock Hours:   60

Semester:  Spring 2012                                                                       Assignments                Online Grade Review

Catalog Description:

Introduces ordinary differential equations. The content of this course includes all the topics of MAT 265 Differential Equations with an additional emphasis on applications and problem solving. A graphing calculator is required for this course

MAT265 Description: ntroduces ordinary differential equations.  Emphasizes techniques of problem solving and applications.  Topics include first, second, and higher order differential equations, series methods, approximations, systems of differential equations, and Laplace transforms, with an additional emphasis on applications and problem solving.  A graphing calculator is required for this course.

PREREQUISITE: MAT 202

Policies:

Attendance is expected. Missed tests cannot be made up. Cheating may result in reduction of grade or withdrawal from the course.  In all matters of student conduct, the Student Handbook shall apply.

OBJECTIVES: detail

  1.  Classify differential equations
  2. Demonstrate rudimentary knowledge of what solutions to initial value problems are. This includes geometric and numeric estimations of solutions.
  3. Demonstrate knowledge of a variety of analytical techniques used to find solutions to first order differential equations.
  4. Use a variety of mathematical models and numerical methods to analysis applications that involve first order equations.
  5. Demonstrate knowledge of the solution techniques of higher-order, linear differential equations.
  6. Use a variety of mathematical models and numerical methods to analysis applications that involve second order linear equations.
  7. Demonstrate knowledge of Laplace Transforms and/or Power Series.
  8. Demonstrate rudimentary knowledge of linear systems

 

Assessment Procedures and Grading:

  • 40% - Homework        (20% of problems in text)
  • 10% - Class participation and attendance - You are expected to ask questions, answer question, assist in solving problems, discuss, and learn how to use the software.
  • 35% - Chapter Tests and Section Tests
  • 15% - Final Exam
  • The grading cutoffs are 90, 80, 70, 60 for A, B, C, D, respectively.

Methods of conducting class

Class will be conducted by using lectures, recitation, and demonstrations of electronic methods. There is no lab component but the student is expected to do the electronic methods in the computer labs.

Required Supplies:

The student is expected to have a graphing calculator that can handle matrices and determinants as a minimum. The math lab has some available for your use when taking a test. If you have a computer and you intend to continue your mathematics program or engineering program might look into purchasing Maple for your computer.

Required Text: Elementary Differential Equations, 8th edition, by Boyce and DiPrima

Census date – Feb. 1 - The census date is thhe last date that the student can withdraw without having to pay for the course

Withdrawal Date – Apr 16 - The withdrawal date is the last date that the student can withdraw with a "W".

Integration of Critical Skills

Students will develop and demonstrate proficiency in reading technical material, computing (Excel spreadsheets, Maple programming, and Internet research), and problem solving, especially quantitative problems.

TSJC Mission Statement:

          Trinidad State Junior College enriches the academic, technical, and cultural life of our diverse community.  We are committed to offering traditional and alternate approaches to education, providing quality instruction, and promoting lifelong learning.

 

TOPICAL OUTLINE:

 

 I.      Classify differential equations and recognize solutions to differential equations.

         A.      Categorize differential equations (e.g. order, linear, ordinary, independent variable, etc.).

         B.      Verify explicit and implicit solutions to differential equations and initial value problems.

         C.      Discuss Existence and Uniqueness Theorem.

         D.      Use and apply directions fields.

         E.      Use and apply phase line (optional).

         F.      Use and apply Euler¿s approximation.

 II.     Develop techniques of finding solutions to first order differential equations and initial value problems.

         A.      Use the technique of separation of variables.

         B.      Solve first order linear equations.

         C.      Solve first order exact equations.

         D.      Solve first order equations using special integrating factors or substitution techniques (e.g. homogeneous, Bernoulli, linear coefficients, etc.).

 III.    Apply techniques of previous two sections to help solve applications that can be modeled with first order ordinary differential equations.

         A.      Discuss mathematical modeling and compartmental analysis.

         B.      Examine various applications including some of the following:

                 1.      Growth and Decay

                 2.      Newtonian Mechanics

                 3.      Mixture

                 4.      Heating and Cooling

         C.      Examine further numeric techniques ¿ Optional.

                 1.      Improved Euler¿s

                 2.      Runge-Kutta

 IV.     Develop techniques for solving higher-order, linear differential equations.

         A.      Utilize linear operators to facilitate understanding of linear ODEs.

         B.      Examine fundamental solution sets of Homogeneous Equations, linear independence, and the Wronskian.

         C.      Given one solution, solve for a second independent solution using reduction of order.

         D.      Examine homogeneous linear equations with constant coefficients.

         E.      Discuss Principle of Superpostion.

         F.      Examine nonhomogeneous equations

                 1.      Apply Method of Undetermined Coefficients.

                 2.      Apply Method of Variation of Parameters.

 V.      Introduce Linear Systems.

         A.      Examine modeling via systems.

         B.      Examine Elimination Method for systems.

 VI.     Apply techniques of previous two sections to help solve applications that can be modeled with second order ordinary differential equations.

         A.      Examine various applications including some of the following:

                 1.      Mass-spring oscillators and mechanical vibrations

                 2.      Interconnected Fluid Tanks

                 3.      Coupled Mass-spring systems

                 4.      Electrical Circuits

         B.      Introduce the Phase Plane (Optional)

 VII.    Develop the techniques of Laplace Transforms.

         A.      Know the definition and properties of Laplace Transforms.

         B.      Use tables to find Laplace Transform.

         C.      Use Inverse Laplace transforms and understand their properties.

         D.      Solve initial value problems using Laplace Transforms.

         E.      Examine Transforms of discontinuous and periodic functions (optional).

         F.      Examine Convolution Theorem (optional).

 VIII.   Develop the techniques of Power Series solutions.

         A.      Review Power Series and Analytic Functions.

         B.      Examine ordinary and singular points.

         C.      Find solutions near and ordinary point.