Markus Schmidmeier
Florida Atlantic University

Differential Equations I

Fall 2020

Hi, here is some information about my course Differential Equations I (CRN: 11894, MAP 2302-002, 3 credits). We meet Tuesdays and Thursdays 9:30 - 10:50 a.m. The course will be taught Online-Live on Zoom.

Course Description

A differential equation is an equation that defines a relation between a function and its derivatives. In this course we learn how to solve the simplest differential equations by elementary methods.

Solving differential equations is at the core of mathematical modeling --- which is one of the most important and powerful tools for studying phenomena which occur in our universe. In modeling, one first collects equations, often differential equations, which describe the phenomenon. The second step, and the one we deal with mostly in this course, is to understand and solve those equations. Here we focus on equations where the unknown is a function in one real variable. The third step then is to go back to the original problem and apply the knowledge gained in the study of the equations.

Course Prerequisites

Calculus II with a minimum grade of C.

Textbook

Christian Constanda, Differential Equations. Second Edition, Springer 2017, ISBN-13: 978-3-319-50223-6.

Topics

We will follow the textbook and aim to cover in full or in part the following chapters:

• First-Order Equations and Mathematical Models (Chapters 2 and 3, 4 weeks)
  We will cover in detail three types of first-order equations: separable, linear and Riccati-type equations. In modeling, we will deal with exponential and logistic growth.
• Linear Second-Order Equations and Mathematical Models (Chapters 4 and 5, 4 weeks)
  In second order, we will focus on linear equations, in particular on those with constant coefficients. The method of undetermined coefficients is used to deal with the non-homogeneous case. In modeling we will study oszillations.
• Higher-Order Linear Equations and Systems of Differential Equations (Chapters 6 and 7, 5 weeks)
  We will review some algebra (the fundamental theorem and methods from matrix theory) to generalize results from the previous chapters to higher order equations and to linear systems.
• The Laplace Transform (Chapter 8, as time permits)

Tutoring

There is free math tutoring at the Math Learning Center.
Online tutoring is available through zoom. Click here for available times.
In-person tutoring is appointment based. Click here to search for availablitites.

Credit

• I will assign homework problems every week, you can find the assignments here:
  Homework problems
  Please try to have nice solutions to several of the problems, then send me your work via e-mail, for example by scanning in handwritten work. Submit a single pdf-file, the file name should indicate your name. Together, the 11 best homework sets will count for 50% of the grade.
• One presentation of at most 10 minutes is expected before November 19. The topic is a problem from the textbook which you may suggest (old homework problems won't do). The presentation counts for 10% of the grade.
• The final exam will take place on Thursday, December 10, 7:45 - 10:15 a.m. It will count for 40% of the grade. The first part consists of solutions to three problems from our textbook: (A) One about modeling (Ch. 3 or 5); (B) one about systems of ODEs or higher order ODEs (Ch. 7 or 6); (C) and one problem of your choice. No homework assignments, examples from class, or problems presented before. Please send me the solutions and a scanned copy of a picture ID by e-mail by Tuesday, November 24 (Tuesday, December 1 at the latest). Then I'll pick one of the problems for your talk. The second part is a presentation on Zoom during the time of the final exam. At the beginning of your talk please introduce yourself and turn your webcam on.

Further Information

For the Disability Policy, the Make-Up Policy, the Code of Academic Integrity, Religious Accommodation, my Grading Scale and Financial Assistance Opportunities please visit Infos for all my courses.

Contact Me

Office hours:  TR 3-5 p.m. online via zoom : Meeting ID: 395 037 9152, Password: Markus3to5, from the waiting room please call me by telephone; or by appointment

Course page:  http://math.fau.edu/markus/courses/diffeq20.html

Phone:  561-459-1975 (home)

E-mail:  markus@math.fau.edu.

---

Last modified:  by Markus Schmidmeier