Differential Equation

Math308

Class time: MW: 4:10 - 5:25 PM Room: Bloc 128

Helpsessions: Will soon be announced

Prerequisite: Math 251 or equivalent; knowledge of Matlab or Maple would be helpful.

Textbook: Elementary Differential Equations, Boyce and DiPrima

Course Description: Ordinary differential equations, solutions in series, solu- tions using Laplace transforms, systems of differential equations.

Grading.Your grade will be based on homework, two in-class tests which will be within one class day of (October 10 & November 21) and a final exam (Tuesday, December 13, Tuesday,3:30-5:30 p.m.). The homework will count for 20%, each in-class test for 25% and the final for 30%. Your letter grade will be assigned this way: 90-100%, A; 80-89%, B; 70-79%, C; 60-69%, D; 59% or less, F.

Important Note: Because of recent budgetcuts, the Department of Mathematics cannot provide any paper for tests and the final. Test and final problems will be written on single pages, so there will not be any room on the copies for solutions.
Also: these syllabus will Not be handed out in class.

Homework: Click here:

Make-up policy: Make-ups for missed quizzes and exams will only be allowed for a university approved excuse in writing. Wherever possible, students should inform the instructor before an exam or quiz is missed. Consistent with University Student Rules, students are required to notify an instructor by the end of the next working day after missing an exam or quiz. Otherwise, they forfeit their rights to a make-up.

Scholastic dishonesty: Copying work done by others, either in-class or out of class, is an act of scholastic dishonesty and will be prosecuted to the full extent allowed by University policy. Collaboration on assignments, either in-class or out-of-class, is forbidden unless permission to do so is granted by your instructor. For more information on university policies regarding scholastic dishonesty, see University Student Rules .

Copyright policy: All printed materials disseminated in class or on the web are protected by Copyright laws. One xerox copy (or download from the web) is allowed for personal use. Multiple copies or sale of any of these materials is strictly prohibited.

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Textbook: Calculus Early Vectors , Stewart

Temptative Schedule: This is a projected roadmap of the course. Modifications necessitated by circumstances are inevitable. Whilst most of the sections below will be covered in lecture, some might be assigned for reading.

• Chapter 1: 1 week
  • Section 1.1. Some Basic Mathematical Models; Direction Fields
  • Section 1.2. Solutions of Some Differential Equations
  • Section 1.3. Classification of Differential Equations

• Chapter 2: 2 weeks
  • Section 2.1. Linear Equations; Method of Integrating Factors
  • Section 2.2. Seperable Equations
  • Section 2.3. Modeling with First Order Equations
  • Section 2.4. Differences Between Linear and Nonlinear Equations
  • Section 2.5. Autonomous Equations and Population Dynamics
  • Section 2.6. Exact Equations and Integrating Factors
• Chapter 3: 3 weeks
  • Section 3.1. Homogeneous Equations with Constant Coefficients
  • Section 3.2. Solutions of Linear Homogeneous Equations; the Wronskian
  • Section 3.3. Complex Roots of the Characteristic Equation
  • Section 3.4. Repeated Roots; Reduction of Order
  • Section 3.5. Nonhomogeneous Equations; Method of Undetermined Coefficients
  • Section 3.6. Variation of Parameters
  • Section 3.7. Mechanical and Electrical Vibrations
  • Section 3.8. Forced Vibrations
  
  

  Exam I October 10
  

  Preparation Sheet for Exam I :
  

• Chapter 6: 1.5 weeks
  • Section 6.1. Definition of the Laplace Transform
  • Section 6.2. Solution of Initial Value Problems
  • Section 6.3. Step Functions
  • Section 6.4. Differential Equations with Discontinuous Forcing Functions
  • Section 6.5. Impulse Functions
  • Section 6.6. The Convolution Integral
• Chapter 7: 3 weeks
  • Section 7.1,7.2 Introduction and Review of Matrices
  • Section 7.3. Linear Algebraic Equations: Linear Independence, eigenvalues, Eigenvectors
  • Section 7.4. Basic Theory of Systems of first Order Linear Equations
  • Section 7.5. Homogeneous Linear systems with Constant Coefficients
  • Section 7.6. Complex Eigenvalues
  • Section 7.7. Fundamental Matrices
  • Section 7.8. Repeated Eigenvalues
  • Section 7.9. Nonhomogeneous Linear Systems
• Chapter 5: 2 weeks
  • Section 5.1. Review of Power Series
  • Section 5.2. Series Solutions near an Ordinary Point, Part I
  • Section 5.3. Series Solutions near an Ordinary Point, Part II
  • Section 5.4. Euler Equations; Regular Singular Points
  
  

  Exam II, November 21
  

  Preparation Sheet for Exam II : This sheet will be added to the test:
  

  • Section 5.5. Series Solution near a Regular Singular Point, Part I
  • Section 5.6. Series Solution near a Regular Singular Point, Part II

The remaining lectures may come from either Chapter 8 (Numerical Methods) or Chapter 9 (Nonlinear Systems).

Final: December 13, 3:30 - 5:30 (usual class room) Preparation Sheet for Final

Extra Office hours for Final Thursday, Decemder 8, 1:30 - 5:00 pm.