Calculus III --- Spring 2021

Markus Schmidmeier
Florida Atlantic University
Calculus - Analytic Geometry 3

Spring 2021

Welcome to my calculus course!
We meet Wednesdays and Fridays, 8:00 - 9:50 a.m., either online-live on Zoom or in person in ED 116 on the Boca Raton campus.
Note that this course will be not recorded to encourage active live participation.
Course numbers: MAC 2313-7, CRN: 12086, 4 credits
For this course, internet access, a webcam and zoom is required (at least for the final exam). Participants will receive meeting id and passcode by e-mail.

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. Both Gottfried Wilhelm Leibniz and Sir Isaac Newton are credited for inventing modern calculus. The later used it to explain the motion of the planets around the sun, the former developed the formalism and rules which are still in use. 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 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
Calculus Volume 3, OpenStax College, PDF
We are going to cover the following chapters:

Chapters 2+3 Vectors and vector valued functions
(3 weeks) We review vectors and operations on vectors (dot product, cross product) to study points, lines and planes in three-space. We use derivatives and integrals to study the motion of objects in three-dimensional space.

Chapter 4 Functions in several variables
(4 weeks) Complicated quantities may depend on several input variables. Using partial derivatives we can solve maximum and minimum value problems.

Chapter 5 Multiple Integration
(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 6 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.

Objectives

Use vectors, vector arithmetic, vector valued functions and functions in several variables to discuss quantities in three-dimensional space.
Apply derivatives to study the motion in higher dimensional spaces, and also to describe the shape of surfaces.
Use multiple integrals to express and evaluate quantities from mathematics, physics and engineering that depend on several variables.
Communicate about calculus problems using computations, sketches and proper mathematical language.

Tutoring
There is free math tutoring available in the Math Learning Center. Online tutoring is available through zoom. For in-person tutoring, click here for appointments. For more details, please e-mail mlc@sci.fau.edu or see the Assistant Director in GS 211E.
Credit

I will assign homework problems every week, you can find the assignments here:
Homework problems
Please try to have solid solutions to most of the problems, then send me your work via e-mail, for example by scanning in handwritten work. Submit a single pdf-file, the file name should indicate your name. Together, the 11 best homework sets will count for 50% of the grade.
One presentation of at most 10 minutes is expected before April 2. The topic is a problem from the textbook which you may suggest (old homework problems won't do). The presentation counts for 10% of the grade.
The final exam will take place on Saturday, April 24, 10:30 a.m. - 1:00 p.m. It will count for 40% of the grade. The first part consists of solutions to three problems from our textbook, I'll give more details later. Please send me the solutions and a scanned copy of a picture ID by e-mail by Thursday, April 2 (Thursday, April 9 at the latest). Then I'll pick one of the problems for your talk. The second part is a presentation on Zoom during the time of the final exam. At the beginning of your talk please introduce yourself and turn your webcam on.

Update regarding the Final Exam (2021-03-19):
For the first part, please send me three problems by Friday, April 2. The problems should not be former homework problems or topics of previous presentations. One problem needs to be from Chapter 4, the second from Chapter 5 or 6, the third is your choice. Please include a copy of a picture id (drivers licence or Owl Card).

The second part on Saturday, April 24, is a presentation about one of the three problems (I'll pick it for you). As part of the presentation, please introduce yourself. The web cam needs to be kept on.

Further Information
For the Disability Policy, the Make-Up Policy, the Code of Academic Integrity, Religious Accommodation, my Grading Scale, some financial assistance opportunities and the possibility of this course going online, please visit Infos for all my courses.
Contact Me
Office hours: WF 10:00 - 11:30 a.m. online via zoom (Meeting ID: 395 037 9152, Password: Markus3to5, from the waiting room please call me by telephone); or in person in my office SE 272; or by appointment

Course page: http://math.fau.edu/markus/courses/calciii21.html
Phone: 561-459-1975 (home), 561-297-0275 (office)

E-mail: markus@math.fau.edu.

Last modified: by Markus Schmidmeier

Chapters 2+3	Vectors and vector valued functions (3 weeks)	We review vectors and operations on vectors (dot product, cross product) to study points, lines and planes in three-space. We use derivatives and integrals to study the motion of objects in three-dimensional space.
Chapter 4	Functions in several variables (4 weeks)	Complicated quantities may depend on several input variables. Using partial derivatives we can solve maximum and minimum value problems.
Chapter 5	Multiple Integration (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 6	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.