MATH 244: Linear Analysis I (Sections 2 & 8)

Welcome to the course webpage for Math 244! This course is the first part of the Linear Analysis sequence (Math 244-Math 344) covering foundational methods and techniques primarily used for (linear) ordinary differential equations (ODEs) and systems thereof. In particular, we will discuss about first-order ODEs, modeling problems with first-order ODEs, fundamental linear algebra notions (such as vectors spaces as well as eigenvalues and eigenvectors) that will be used later in systems of ODEs, as well as ODEs of order n and systems of ODEs. In this web page and associated links, you will find information about Math 244 including (but not limited to) syllabus, tentative schedule, homework problems, and important dates, among others. Please visit the Canvas page for this course for more information and announcements.

Course Instructor: Dr. Stathis Charalampidis

SC's Office Hours: TR 11:15am-12:00pm & 2:15-3:00pm, or by appointment.
Class Meetings:

  • Section 2 (TR) 9:10-11:00am (38-148)
  • Section 8 (TR) 12:10-2:00pm (38-219)
Required Textbook:
  • Differential Equations and Linear Algebra, Authors: Stephen Goode and Scott Annin, Publisher: Pearson.

Class Material by Topic:

  • First-order ODEs.
  • Matrices and systems of linear (algebraic) equations.
  • Vector spaces, determinants, eigenvalues and eigenvectors.
  • Higher-order linear ODEs and systems of ODEs.
Syllabus and Tentative Schedule:

Please click here for the complete course syllabus. Make sure you make copies of the syllabus bring it with you in class. A very tentative schedule is as follows:

  • Week of 4/1: Basic ideas and notions of first-order ODEs. Separable ODEs (1.1-1.4).
  • Week of 4/8: Modeling with first-order ODEs (1.6-1.7); Introduction to matrices (2.1-2.2).
  • Week of 4/15: Matrix algebra, systems of linear equations and Gaussian elimination (2.3-2.6).
  • Week of 4/22: Determinants (3.4), vector spaces (4.1 & 4.3-4.4), and bases (4.5-4.6); The eigenvalue problem (7.1).
  • Week of 4/29: Diagonalization (7.2 & 7.3); General theory for linear ODEs and constant coefficients ODEs (8.1-8.2).
  • Week of 5/6: Method of undetermined coefficients (8.3); Oscillations of mechanicals systems (8.5).
  • Week of 5/13: RLC circuits and the variation of parameters method (8.6-8.7; if time permits)
  • Week of 5/20: ODEs with non-constant coefficients and the method of reduction of order (8.8-8.9; if time permits); First-order linear systems of ODEs (9.1).
  • Week of 5/27: Vector formulation, general results for systems of first-order linear ODEs (9.2-9.3).
  • Week of 6/3: Vector DEs: defective/non-defective matrix (9.4-9.5); Matrix exponential and phase plane (9.8-9.9) if time permits.
Homework Assignments:

Please visit the Canvas page for the course for a complete list of homework assignments.

Academic Calendar:

For your convenience, links for the academic calendar are included in this section: