J.D. Mireles James
Mathematical Sciences
Florida Atlantic University

# Calculus - Analytic Geometry II

Summer I 2017

(MAC 2312 003, 4 credits). We meet Tuesdays and Thursdays 10:00am-12:10p.m. in the Physical Sciences Bldg Boca - 113.

Contact Me

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

Phone:  561-297-2490

E-mail:  jmirelesjames@fau.edu.

(Description by Daiva Pucinskaite) The origins of calculus go back at least 2500 years to the ancient Greeks, who found areas using the "method of exhaustion". Limits arise not only when finding areas of a region, but also when computing the slope of a tangent line to a curve, the velocity of a car, or the sum of an infinite series. In each case, one quantity is computed as the limit of other, easily calculated quantities. Sir Isaac Newton invented his version of calculus in order to explain the motion of the planets around the sun. Today calculus is used in calculating the orbits of satellites and spacecraft, in predicting population sizes, in estimating how fast coffee prices rise, in forecasting weather, in measuring the cardiac output of the heart, in calculating life insurance premiums, and in a great variety of other areas.

In the first part of this course Calculus II, we review integrals, study integration techniques, apply integration to a variety of problems from science, engineering, and mathematics. In the second part, we study sequences of functions. We all can differentiate and integrate polynomials, wouldn't it be nice if all functions were as easy to handle? We will see, that many functions are --- namely those that are limits of polynomials. These are called power series.

Prerequisite

Calculus I with a minimum grade of C.

Textbook and Topics

Briggs' Calculus 2e: Early Transcendentals

For extra reading, I recommend the Calculus Online Textbook, Calculus by Gilbert Strang, Massachusetts Institute of Technology, Wellesley-Cambridge Press. The book is MIT open courseware, available online under the Creative Commons Licence: Calculus book

We are going to cover the following chapters:

 Chapter 6 Applications of Integration We discuss a variety of applications of integration in mathematics (areas, volumes) and physics (work.) Chapter 7 Techniques of Integration We review the substitution rule for integrals, and study three additional methods for integration: Integration by parts, trigonometric integrals and partial fractions. We also explore indefinite integrals, they let us study strange things like "Gabriel's horn" --- an amazing shape which has a finite volume yet an infinite surface area. Chapter 8 Sequences and Infinite Series In this chapter we’ll be taking a look at sequences and (infinite) series. This chapter will deal almost exclusively with series. However, we also need to understand some of the basics of sequences in order to properly deal with series. Series do play an important role in the field of ordinary differential equations. Chapter 9 Power Series Looking back, we recall how easy it was to differentiate and integrate polynomials. In this section we use differentiation to approximate arbitrary functions by polynomials, called Taylor polynomials. Whenever (even better, and almost true: wherever!) those polynomials converge against the given function, also the integrals converge. This allows us to compute integrals for functions like f(x)=sin(sin(x)) or f(x)=ex2, for which the antiderivative cannot be expressed in terms of functions known to us.

Objectives

• Use integrals to express and compute quantities like area, volume of work.
• Recognize that there are integrals which we may not be able to solve.
• Apply calculus techniques to a variety of math, science and engineering problems.
• Understand the conceptual problem of computing an "infinite sum".
• Approximate functions bu polynomials, and work with Taylor series.
• Practise graphing and use calculus tools in computer algebra systems like maple.

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 will 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% (Tenative dates) June 20 & July 27 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).