Markus Schmidmeier
Mathematical Sciences
Florida Atlantic University

# Calculus - Analytic Geometry III

Spring 2013

Hi, here is some information about my course Calculus - Analytic Geometry 3 (CRN: 13295, MAC 2313-002, 4 credits). We meet Tuesdays and Thursdays, 2:00 - 3:50 p.m. in BU 409.

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 this course Calculus III, we will apply differentiation and integration to vector valued functions (e.g. a rocket moving in three dimensional space), to functions in several variables (e.g. the temperature distribution in a room) and to vector fields (e.g. water moving in a whirl pool).

Prerequisite

Calculus - Analytic Geometry 2 with a minimum grade of C.

Textbook and Topics

We will use 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

For pdfs of the sections, and for additional materials have a look at the page:

Strang, Calculus

To warm up for the course, have a look at the videos! For extra reading, I recommend a printed version of a calculus textbook, for example Stewart, Calculus: Early Transcendentals. Note that some used and earlier versions of the textbook are really inexpensive :).

We are going to cover the following chapters:

 Chapter 11 Strang-Chapter 11 Vectors and Matrices(2 weeks) We develop vector artithmetic to deal with the geometry in higher dimensional spaces: Think of points, lines and planes in three dimensions. Using vector arithmetic, we compute distances, angles and projections. Chapter 12Strang-Chapter 12 Motion along a Curve(2 weeks) As example, consider a car on a race track. It's position, as a function in time, is given by a vector. The velocity and accelleration functions can easily be derived (sic!) using componentwise differentiation. Those functions yield an internal coordinate system which leads to concepts like tangential versus normal accelleration --- which as you know from car driving feel quite different. Chapter 13 Strang-Chapter 13 Partial Derivatives(4 weeks) If a map describes the height of a given point in the plane, then the partial derivatives at that point represent the slopes in x- and y-direction. We detect local maxima and minima, as in that easy Calculus I course. But now, new features occur, like saddle points... Midterm Exam The 50 minute exam will be about the material covered so far. It is scheduled for Thursday, February 21, during class time. Chapter 14 Strang-Chapter 14 Multiple Integrals(2 weeks) If integration is fun for you, then you'll really love double and triple integrals! Many quantities in mathematics, the sciences and engineering can be expressed in terms of multiple integrals --- of which we discuss and compute many examples. Some computations are done by hand, otherwise we use a computer algebra system. Excursion to Computer Lab We will visit the computer lab to explore how computer algebra (Maple) can be used to define and plot functions in several variables, and to compute multiple integrals. You can earn extra credit for using computer algebra to solve Calculus problems. Chapter 15 Strang-Chapter 15 Vector Calculus(4 weeks) Vector fields are functions which have several variables, and which have as output a vector. Think of the force that acts on a particle in space. Note that the force has a direction which depends on the coordinates of the particle! Now assume that a motion of the particle is given by a vector valued function. It turns out that the work which the field performs on the particle is given by a line integral. Combining vector fields and line integrals we obtain Green's Theorem --- a generalization of the Fundamental Theorem of Calculus.

Objectives

• Visualize points, lines and planes in 3 space, and use vector arithmetic to compute angles, distances and projections.
• Use calculus methods to plot and analyze vector valued functions, like the position of a car on a race track.
• Sketch functions in two variables, discuss their behaviour, and use calculus to specify extremal points.
• Use multiple integrals to express and compute a variety of quantities which occur in math, science and engineering.
• For extra credit, demonstrate familiarity with computer algebra systems like maple.

Tutoring
There is free math tutoring available in the Math Learning Center in GS 211.

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 Thursday; the ten best quizzes count for 40 % 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.

Midterm Exam:  The midterm exam on Thursday, February 21, counts for 20 % of the grade.

Final Exam: The final exam is comprehensive and will count for 40 % of your grade. It has been scheduled for Sunday, April 28, 4:00 - 6:30 p.m. in SO 250. 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:  Tuesdays and Thursdays, 10 a.m. - noon in SE 230.