Math 225 - Introduction to Differential Equations

Summer 2022 - Syllabus - Matthias K. Gobbert

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Basic Information

Course Description

Introduction to Differential Equations is a first introduction to the field of differential equations. Differential equations are equations, that involve both a function and one or more of its derivatives. The solution to a differential equation is a function of one or more variables. Differential equations arise in an extremely wide array of application areas and are vitally important in the sciences, engineering, and many other fields. This course will stress scalar first-order and second-order ordinary differential equations. We will also cover the solution by Laplace transforms and introduce systems of first-order ordinary differential equations. This course will develop both a proficiency with the terminology of differential equations and classical analytical solution techniques for ordinary differential equations, with a brief exposure to basic numerical techniques.
Additionally, I will show how to use the software package Matlab to help with some of tasks in this class. Matlab is the -- by far -- most popular mathematical software tool, used in fields ranging from mathematics, statistics, engineering, physical, natural, and life sciences, to economics and business. I use Matlab myself in my professional life, and the idea is to demonstrate how professionals use software tools effectively and appropriately.

Learning Goals

By the end of this course, you should:

Philosophical Underpinning

To provide some context of the more formal learning goals above, I am sharing some deeper thoughts how we fit into the grander scheme of things. The rationale of a state university is to provide a well-educated workforce to the companies in the State of Maryland as well as to the state and local governments themselves. On a fundamental level therefore, you need to able to learn new material as well as have demonstrated evidence of this ability. These are the fundamental purposes of university courses. This requires us to engage in the learning itself and its demonstration; I am trying to say that it is not the solution to a problem that we are after, and in broader thinking it is not even the solution process, but it is your active struggle to learn that we must encourage. This leads me to the following philosophical grade rubric: To earn a passing grade, you need to solve essentially all problems correctly. To earn a good grade, you need to solve essentially all problems correctly and demonstrate their correctness. To earn a very good grade, you need to do these in all cases and provide a professional presentation of your solutions. This rubric comes from the fact that neither you as customer would be willing to accept faulty solutions or unprofessional presentation, nor would the companies in the State be served by faulty solutions. These are some of the guiding principles behind my teaching.

Note on Recordings and Their Publication

This class is being audio-visually recorded so students who cannot attend a particular session and wish to review material can access the full content. This recording will include students' images, profile images, and spoken words, if their camera is engaged and their microphone is live. Students who do not consent to have their profile or video image recorded should keep their camera off and not use a profile image. Likewise, students who do not consent to have their voice recorded should keep their mute button activated and participate exclusively through alternative formats such as email or the chat feature (where available).

UMBC Statement of Values for Academic Integrity

Academic integrity is an important value at UMBC. By enrolling in this course, each student assumes the responsibilities of an active participant in UMBC's scholarly community in which everyone's academic work and behavior are held to the highest standards of honesty. Cheating, fabrication, plagiarism, and helping others to commit these acts are all forms of academic dishonesty, and they are wrong. Academic misconduct could result in disciplinary action that may include, but is not limited to, suspension or dismissal. Consult the the UMBC webpage on Academic Integrity at for the UMBC Undergraduate Student Academic Conduct Policy for undergraduate students and the UMBC Graduate School's Policy and Procedures for Student Academic Misconduct for graduate students.

Copyright © 1999-2022 by Matthias K. Gobbert. All Rights Reserved.
This page version 1.6, June 2022.