MATH 344: Linear Analysis II (Section 1)

Welcome to the course webpage for Math 344! This course is the second part of the Linear Analysis sequence (Math 244-Math 344) covering foundational methods and techniques primarily used for (linear) ordinary differential equations (ODEs) and partial differential equations (PDEs). In particular, we will discuss upon the Laplace transform, power series methods, Fourier series techniques as well as orthogonality of functions and Sturm-Liouville theory. In this web page and associated links, you will find information about Math 344 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-12:45pm, or by appointment
Class Meetings:

  • TR (Section 1) 9:10-11:00am (38-148)
Suggested Textbooks:
  • Elementary Differential Equations and Boundary Value Problems, Authors: William E. Boyce and Richard C. DiPrima, Publisher: John Wiley & Sons.
  • Differential Equations and Linear Algebra, Authors: Stephen Goode and Scott Annin, Publisher: Pearson.

Class Material by Topic:

  • Laplace transform methods
  • Power series methods
  • Fourier series methods and their extensions
  • Orthogonality of functions and Sturm-Liouville theory (if time permits)
Syllabus and Tentative Schedule:

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

  • Week of 9/18: Laplace Transform Part I (Properties).
  • Week of 9/25: Laplace Transform Part I (Inverse transform and IVPs).
  • Week of 10/2: Laplace Transform Part II (Shifting theorems; convolution).
  • Week of 10/9: Series solutions of ODEs Part I (review of series; applications).
  • Week of 10/16: Series solutions of ODEs Part II (Regular singular points and Frobenius series).
  • Week of 10/23: Projections and orthogonal functions Part I (Gram-Schmidt orthogonalization).
  • Week of 10/30: Projections and orthogonal functions Part II (Normal equation and least-squares solution).
  • Week of 11/6: Fourier Series Part I (Definitions, theorems and properties).
  • Week of 11/13: Fourier Series Part II (Heat equation and BVPs).
  • Week of 11/27: Fourier Series Part III (Sturm-Liouville BVPs and special functions).
  • Week of 12/4: Fourier Series Part IV (cont'ed: Special functions).
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: