J.D. Mireles James
Mathematical Sciences
Florida Atlantic University

# Numerical Methods

Fall 2017

What, where, and when?.
(MAD 3400 003, 3 credits). Class meets on Mondays, Wednesdays, and Fridays from 10:00am-10:50am. IMPORTANT: On Mondays and Wednesdays we meet in the Sanson Life Scoences Bulding, Room 178. On Fridays we meet in Flemming Hall, Room 409 (Computer Lab).

Contact Me

Office hours:  Mondays and Wednesdays, 4pm-5pm in SE 262.

Phone:  561-297-2490

E-mail:  jmirelesjames@fau.edu.

(Description) This is an introductory course in Numerical Methods. The goal of the course is to understnad how the digital computer is used to solve problems in mathematical analysis. That is, we are interested in problems involving real numbers and real valued functions. Since all information stored and manipulated on a digital computer is discrete, this ivolves a layer -- or possibly many layers -- of approximation. Because of this, whenever we study problems involving the real numbers the answers we get using a digital computer are almost always wrong.

That bein said, scientific computing is at the core of rapid developments in engineering, chemestry, and physics that are reshaping the modern world. The ability to solve analytical problems on the digital computer is absolutely critical for the scientific community.

So the answers are almost always wrong... the question is: how wrong? This is one of the most important questions in scientific computing and leads to an entire field of error analysis.

We will learn to solve problems on the computer (or rather to approximately solve them), we will learn to write computer programs and then examine how well our programs work, and we will learn to measure our mistakes.

Prerequisite

MAC 2282 or MAC 2312 (Calculus II) with a minimum grade of C, and some experience programming.

Textbook and Topics

Numerical Mathematics and Computing, by Cheney and Kincaid

We are going to cover the following chapters:

 Chapter 1 Introduction Measuring errors, Rounding, Programming, and mathematical background Chapter2 Number representation and errors Bases and conversion, Floating Point number systems, loss of significance Chapter 3 Solving equations/extracting roots Bisection method, Newton's method, and modifications Chapter 4 Polynomial interpolation Lagrange and Newton. Existence and errors. Derivitives and Richardson Extrapolation Chapter 5 Numerical integration Review of the definite integral/Riemann sums. Trapezoid rule. Adaptive meshes. Gaussian quadrature.

Time permitting we may also talk about linear systems of equations, Approximation by splines, and/or ordinary differential equations.

Objectives

• Using the dgital computer to solve mathematical problems.
• Reading, writing, and implementing psudo-code. .
• Analyzing the performance of numerical methods.
• Measuring the error in a numerical computation.

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 the homework, but I may not return them during the semester. If you like to have your homework to study for exams then I suggest that you scan you homework, or take pictures with your cell phone, or otherwise make copies before turning them in. You should also keep your own reccords of which homework you have and have not turned in. If you would like to get your homework back at the end of the semester then you can pick them up from my office after final grades have been assigned. 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.

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

Item Homework/Quizzes Date Percentage Assigned/administered in class 30% (Ranges) Mid/Late September & Late November 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. Since it is a summer course the pace will be even faster than typical for Calculus (already considered a challenging college course). 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).

Last modified:  Created May 15, 2017, by J.D. Mireles James