Markus Schmidmeier
Mathematical Sciences
Florida Atlantic University

# Calculus - Analytic Geometry III

Spring 2015

Hi, here is some information about my course Calculus III (CRN: 22678, MAC 2313-007, 4 credits). We meet Mondays, Wednesdays, Thursdays and Fridays, 1:00 - 1:50 p.m. in BU 208.

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.

This course Calculus III is about Calculus in three-dimensional space. We can describe the the motion of objects in terms of vector valued functions:

f(t)= (x(t),y(t),z(t))

and use calculus methods to derive the velocity and accelleration (which now has a tangential and a normal component) of the moving object, and properties of its track, like the distance travelled and the curvature at a given point. Functions in several variables, for example
f(x,y) or g(x,y,z)

describe the elevation of a surface or the densitiy of a three-dimensional substance. They can be analyzed using partial derivates, the gradient vector and multiple integrals. The gradient vector itself is an example of a vector valued function in several variables. Such functions are the topic of vector calculus, of which we will get a first glimpse in the final chapter of this course.

Prerequisite

Calculus II with a minimum grade of C.

Textbook and Topics

James Stewart: Calculus, Early Transcendentals, 7th Edition

We are going to cover the following chapters:

 Chapter 12 Vectors and the Geometry of Space(2 weeks) We review vectors and operations on vectors (dot product, cross product) to study points, lines and planes in three-space. Chapter 13 Vector Valued Functions(2 weeks) We use derivatives and integrals to study the motion of objects in three-dimensional space. Chapter 14 Partial Derivatives(3 weeks) Complicated quantities may depend on several input variables. Using partial derivatives we can solve maximum and minumum value problems. 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 15 Multiple Integrals(3 weeks) Suppose the height z of a solid S depends on the x- and the y-coordinate of the base point. Then the volume of S can be expressed as a double integral. We study multiple integrals and explore their applications. Chapter 16 Vector Calculus(4 weeks) Vector fields are vector valued functions in several variables, for example the direction of the flux in a liquid. Integrals can express, and integral theorems can relate, properties of such functions.

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

Objectives

• Use vector valued functions and functions in several variables to express quantities in three-dimensional space.
• Apply derivatives to study motion in higher dimensional spaces.
• Use multiple integrals to express and evaluate quantities that depend on several variables.
• Practise graphing and use calculus tools in computer algebra systems like maple.
• Apply variations of the Fundamental Theorem of Calculus to vector fields.

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. For one-to-one tutoring, please e-mail mlc@sci.fau.edu or see the Assistant Director in GS 211E.

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 Friday of about 25 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, April 26, 4:00 - 6:30 p.m., in SO 250 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:  MWRF 2:00 - 2:50 in SE 230.