J.D. Mireles James
Mathematical Sciences
Florida Atlantic University

# Differential Equations 1

Spring 2018

What, where, and when?
(MAP 2302 001, 3 credits). We meet on Tuesdays and Thursdays from 9:30am-10:50am in the Physical Sciences Building - Room 113.

Contact Me

Office hours:  Tuesday and Thursday,4pm-5pm in SE 262.

Phone:  561-297-2490

E-mail:  jmirelesjames@fau.edu.

(Description) Differential equations appear throughout the sciences and engineering as mathematical models of physical systems. Solving the differential equation understanding or "predicting" what the physical system will do. We will start with the most basic kinds of differential equations --first order scalar equations -- and learn analytical, geometric, and numerical methods for studying or solving these equations. Then we will extend these techniques to more complicated problems like systems of linear and nonlinear equations. We will try to lean something about mathematical modeling as we go, but the main focus of this course is mathematical analysis of the equations themselves.

Prerequisite

MAC 2312 (Calculus II) with a minimum grade of C.

Textbook and Topics

Textbook: Differential Equations-- by Paul Blanchard, Robert Devaney, and Glen R. Hall

We will cover at least the following material:

 Chapter 1 First-Order Differential Equations Introduction to basic techniques for studying first order scalar equations. Chapter 2 First-Order Systems of Differential Equations Extend the basic techniques to systems of equations (or vector valued equations). Chapter 3 Linear Systems In depth study of linear systems of differential equations. Emphasis on eigenvalues and eigenvectors of constant coefficient systems. Chapter 4 Forcing and Resonance Study of systems subject to external driving. Chapter 5 Nonlinear Systems Introduction to the study of nonlinear problems.

Time permitting we may discuss some material form Chapters Six, Seven, and Eight.

Objectives

• Apply calculus I and II skills to find analytic solutions of some differential equations and systems of differential equations.
• Develop qualitative techniques for studying differential equations. These techniques are based on geometric understanding of slope fields and vector fields.
• Apply tools from linear algebra to solve linear systems of equations.
• Learn how to linearize nonlinear systems and study the resulting linear systems. Understand what this local information tells you about the original nonlinear system.
• Learn how to use numerical software to simulate solutions of differential equations. Learn how to plot and interpret the results.

Tutoring

Tutoring is available at the Math Learning Center (MLC), located at GS 211. For tutoring resources, visit MLC

FREE MATH TUTORING for FAU students: The MLC provides the following FREE academic support services for FAU students:

1. Drop-in tutoring in the SAM LAB (Succeed At Methods) in GS207 during all hours of operation
a. ALL METHODS TUTORING is done in the SAM Lab except on Sundays. On Sundays, please visit the MLC as the SAM Lab is closed.
b. Monday – Thursday: 9am – 5pm and Friday: 9am – 4pm

2. Drop-in tutoring in the MLC GS211 during all hours of operation
a. Monday – Thursday: 9am – 5pm, Friday: 9am – 4pm, and Sunday: 1pm – 5pm

3. Small group tutoring by appointment. Appointments can be made in TutorTrac. Go to www.fau.edu/tutoring and click on ‘Find a Tutor,’ then ‘Click Here to Make an Appointment.’ Login with your FAU ID and password and click on ‘Search for Availabilities.’ For Center, choose SAM Lab for Methods of Calculus and Math Learning Center for everything else. Choose your Section (Class) and click ‘Search.’ Choose your time and then click ‘Save.’ If there are no appointments listed for your course, please email bferoz@fau.edu and request an appointment.

Credit

Homework:  I will assign homework problems every day, or at least once a week. I will collect all the homework. Quizzes:  I will give some short pop-quizes during the semester. These may not be announced ahead of time. The quiz questions will be similar to assigned exercises, and will help you understand how ready you are for an exam situation. There will be two midterm exams and a final exam.

Final Exam:  Date, time and location of the final exam to be announced.

Item Homework/Quizzes Date Percentage Assigned/administered in class 30% (Range) Mid/Late Feb & early April 20% (each) Date and time to TBA 30%

 % letter grade 93-100 90-92 87-89 84-86 80-83 75-79 70-74 60-69 59 and below A A- B+ B B- C+ C D F

The instructor reserves the right to adjust the grading scale in the students favor. The grade of I (incomplete) will only be given for reasons specified on page 67 of the FAU Undergraduate Catalog.

Missed Exams and Quizzes

A missed midterm or final exam may be made up; however, it is the student’s responsibility to establish with documentation that the exam was missed for an allowable reason. The student cannot make up a missed midterm or final exam without such documentation. A missed quizz cannot be made up, but the two worst quiz grades will be dropped.

Attendance

Attending lectures is an important part of making progress in this course. You will find that if you don't come to class you will get behind very quickly. Any announcement made in class (quizz warnings, exam dates, and so on) are considered official course information. Also, I will assign homework in class. These assignemnts will not be posted online or anywhere else (if you must miss class you should try to check with a classmate about the assignment or any other important announcments). The instructor reserves the right to take attendance on any given course meeting. The following is quoted from FAU university wide policy: Students are expected to attend all of their scheduled University classes and to satisfy all academic objectives as outlined by the instructor. The effect of absences upon grades is determined by the instructor, and the University reserves the right to deal at any time with individual cases of non-attendance. Students are responsible for arranging to make up work missed because of legitimate class absence, such as illness, family emergencies, military obligation, court-imposed legal obligations or participation in Universityapproved activities. Examples of University-approved reasons for absences include participating on an athletic or scholastic team, musical and theatrical performances and debate activities. It is the student’s responsibility to give the instructor notice prior to any anticipated absences and within a reasonable amount of time after an unanticipated absence, ordinarily by the next scheduled class meeting. The instructor will allow each student who is absent for a University-approved reason the opportunity to make up work missed without any reduction in the student’s final course grade as a direct result of such absence.

Code of Academic Integrity policy statement

Students at Florida Atlantic University are expected to maintain the highest ethical standards. Academic dishonesty is considered a serious breach of these ethical standards, because it interferes with the university mission to provide a high quality education in which no student enjoys an unfair advantage over any other. Academic dishonesty is also destructive of the university community, which is grounded in a system of mutual trust and places high value on personal integrity and individual responsibility. Harsh penalties are associated with academic dishonesty. For more information, see University Regulation 4.001 at http://www.fau.edu/regulations/chapter4/4.001_Code_of_Academic_Integrity.pdf

Students with Disabilities

In compliance with the Americans with Disabilities Act (ADA), students who require special accommodation due to a disability to properly execute coursework must register with Student Accessibility Services (SAS) and follow all SAS procedures. SAS has offices across three of FAU’s campuses – Boca Raton, Davie and Jupiter – however disability services are available for students on all campuses.

Contact: Office for Students with Disabilities (OSD) -- in Boca Raton, SU 133 (561-297-3880).