Markus Schmidmeier
Mathematical Sciences
Florida Atlantic University

# Calculus - Analytic Geometry II

Fall 2014

Hi, here is some information about my course Calculus II (CRN: 94413, MAC 2312-003, 4 credits). We meet Mondays and Wednesdays, 5:00 - 6:50 p.m. in BU 104.

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 will review integrals, study integration techniques, apply integration to a variety of problems from science, engineering, and --- of course --- mathematics. In the second part, we will 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!

Prerequisite

Calculus I with a minimum grade of C.

Textbook and Topics

James Stewart: Calculus, Early Transcendentals, 7th Edition

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 Integrals(2 weeks) We discuss a variety of applications of integration in mathematics (areas, volumes) and physics (work.) Chapter 7 Techniques of Integration(3 weeks) 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. Excursion. We will explore how computer algebra (Maple) can be used to define functions, compute integrals, and to assist us in graphing. You can earn extra credit for using Maple or another computer algebra system to solve Calculus problems. Chapter 8 Further Applications of Integrals(2 weeks) We use integrals to define and compute quantities from mathematics and physics: The length of an arc, the area of a surface, moments and center of mass. Chapter 11 Taylor Series(7 weeks) 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

• Ability to apply a variety of integration methods,
• learn to use integrals to define --- and work with --- magnitudes which occur in applications,
• apply calculus techniques to a variety of math, science and engineering problems, and
• practise graphing and use calculus tools in computer algebra systems like maple.

Tutoring

There is free math tutoring available in the Math Learning Center in GS 211. See MLC for opening hours, appointments for one-to-one tutoring, and online tutoring.

Credit

Homework:  I will assign homework problems every week. The problems will not be graded, but some may show up on a quiz:   Homework problems.

Quizzes:  We will have a quiz every Wednesday of about 20 minutes each; the twelve best quizzes count for 60 % of the grade. No calculators can be used during the quiz.

Extra Credit:  You can obtain extra credit counting towards your quiz grade for assignments done on a computer algebra system, for example Maple.

Final Exam:  The final exam on Sunday, December 7, 4:00 - 6:30 p.m., in KH 102 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:  Mondays and Wednesdays, 3 - 5 p.m. in SE 230.