Florida Atlantic University • Fall 2024• Markus Schmidmeier

## Differential Equations

Hi, welcome to my course Differential Equations (MAP 2302-001, CRN 11925, 3 credits). We meet Mondays and Wednesdays, 4:00 - 5:20 p.m. in Physical Sciences 111.

Course DescriptionA 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.

PrerequisiteCalculus 2 with a minimum grade of C.

TextbookChristian Constanda,

Differential Equations,second edition, Springer 2017, ISBN-13: 978-3319843506 (paper back).

TopicsWe aim to cover in full or in part the following chapters:

- First-Order Equations and Mathematical Models (Chapters 2 and 3, 5 weeks) We will cover in detail three types of first-order equations: separable, linear and Bernoulli-type equations. In modeling, we will deal with exponential and logistic growth.
- Linear Second-Order Equations and Mathematical Models (Chapters 4 and 5, 6 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. we will review some algebra (the fundamental theorem and methods from matrix theory) to generalize results from the previous chapters.
- As time permits, we either get started with systems of several linear differential equations (Chapter 7) or else learn about the Laplace transformation --- which not only is a quite different approach to differential equations but also allows dealing with non-continuous forcing

Computer AlgebraDuring the course, we may use computer algebra (Mathematica) for visualization and solution of differential equations.

TutoringThe Math Learning Center in GS 211 offers in-person tutoring M-R 10-5 and F 10-4. Also, small group tutoring is available. For details please visit MLC or e-mail mlc@sci.fau.edu.

For online tutoring via zoom, please see ONLINE for available days and times.

Credit

I will assign homework problems every week, they will be posted on CANVAS. The problems will not be graded, but some may show up on a quiz.Homework:We will have a quiz every week onQuizzes:Wednesday.The quiz is based on the homework assignments. The best twelve quizzes count for50 %of the grade.One presentation during class about a problem from our textbook will count forPresentation:10 %of the grade. The presentation needs to be given before November 6. Unless there are volunteers, I will assign presentations for the next class meeting at random among all registered students.The final exam is comprehensive and will count forFinal Exam:40 %of your grade. It is scheduled for Monday, December 9, 4:00 - 6:30 p.m. in our classroom. Please bring a picture id (Owl card or drivers licence)!

Further InformationFor the Disability Policy, the Make-Up Policy, the Code of Academic Integrity, Religious Accommodation, my Grading Scale, the FAU Attendance Policy Statement, Financial Assistance Opportunities and the FAU Covid Statement please visit Infos for all my courses.

Contact Me

MW 10:00 - 11:20 a.m. in SE 272.Office hours:561-297-0275 (office)Phone:E-mail:mschmidm@fau.eduMarkusWeb Site:

Last modified:by Markus Schmidmeier