Markus Schmidmeier
Florida Atlantic University

Engineering Mathematics I

Fall 2018

Hi, here is some information about my course Engineering Mathematics I (CRN: 11886, MAP 3305-003, 3 credits). We meet Monday, Wednesday and Friday 12:00-12:50 p.m. in PS 113.

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)

Excursion

We will explore how computer algebra (Sage) can be used for visualization and solution of Differential Equations.

Tutoring

The Math Learning Center in GS 211 has drop-in tutoring M-R 9-6, F 9-4, U 1-5. For questions, please e-mail mlc@sci.fau.edu.

Credit

• I will assign homework problems every week. The problems will not be graded, but some may show up on a quiz:   Homework problems.
• We will have a quiz every Friday of about 20 minutes each; the twelve best quizzes count for 60 % of the grade. No calculators can be used during the quiz.
• The Final Exam on Sunday, December 9, 6:45 - 9:15 p.m. in SO 250 is comprehensive and will count for 40 % of your grade. Please bring a picture id (Owl card or drivers licence)!

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:  Monday 2:00 - 4:00 p.m. and Wednesday 3:30 - 5:00 p.m. in SE 272.

Course page:  http://math.fau.edu/markus/courses/emath18f.html

Phone:  561-297-0275

E-mail:  markus@math.fau.edu.

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Last modified:  by Markus Schmidmeier