Math 2260
Ordinary Differential Equations I

Fall, 2026

Text Book:

Prerequisites: Math 2000

Course Contents:

• Introduction (Chapter 1)
  • Some Basic Mathematical Models; Direction Fields (Section 1.1)
  • Solutions of Some Differential Equations (Section 1.2)
  • Classification of Differential Equations (Section 1.3)
• First Order Differential Equations (Chapter 2)
  • Linear Equations; Method of Integrating Factors (Section 2.1)
  • Separable Equations (Section 2.2)
  • Modeling with First Order Equations (Section 2.3)
  • Differences Between Linear and Nonlinear Equations (Section 2.4)
  • Autonomous Equations and Population Dynamics (Section 2.5)
  • Exact Equations and Integrating Factors (Section 2.6)
• Second Order Linear Equations (Chapter 3)
  • Homogeneous Equations with Constant Coefficients (Section 3.1)
  • Solutions of Linear Homogeneous Equations; the Wronskian (Section 3.2)
  • Complex Roots of the Characteristic Equation (Section 3.3)
  • Repeated Roots; Reduction of Order (Section 3.4)
  • Nonhomogeneous Equations; Method of Undetermined Coefficients (Section 3.5)
  • Variation of Parameters (Section 3.6)
  • Mechanical and Electrical Vibrations (Section 3.7)
• The Laplace Transform (Chapter 6)
  • Definition of the Laplace Transform (Section 6.1)
  • Solution of Initial Value Problems (Section 6.2)
  • Step Functions (Section 6.3)
• Systems of First Order Linear Equations (Chapter 7)
  • Preliminaries (Sections 7.1-7.3)
  • Basic Theory of Systems of First Order Linear Equations (Section 7.4)
  • Homogeneous Linear Systems with Constant Coefficients (Section 7.5)

Evaluation:

Leture Notes:

Assignments: Please drop your finished assignments in the mail box 41 beside the departmental general office before and on the due date.

Assignment 1, Due time: 6:00pm, Wednesday, Sept. 23

Midterm Test (in class): Wednesday, Oct. 14, 2026

Final Exam: (to be annouced)

Note that this syllabus is tentative and should not be considered definite. The instructor reserves the right to modify it (including the dates of tests) to meet the needs of the class. It is the student responsibility to attend class regularly and to make note of any change.