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Math 259 Fall 2017
Course: Math 259
Calculus in Three Dimensions
Title: Calculus in Three Dimensions
Textbook: Calculus, Early Transcendentals, by James Stewart, 8th edition.
Subject Material: By now you have learned a lot about understanding functions that take as input one variable, and produce as output one variable. The aim of this course is to extend our understanding of functional change via derivatives and integrals to functions that take as input and/or output more than one variable. Primarily, we will focus on functions that exist in three dimensional space, although none of what we do here is really restricted to three dimensions. Specifically, we will study what derivatives and integrals mean in a higher dimensional context, how to compute them, and what they can tell us about the associated functions.
We will begin first by developing notation and intuition for objects in three dimensions, such as planes, lines, vectors, and operations on these objects. We then turn to derivatives on vector-valued functions, and then to partial derivatives on multivariable functions. Likewise, we will extend our notions of integration to these types of functions, as well as use integration to compute mass, surface area, and volume. Finally, we end with some classic theorems of multivariable calculus, Green's Theorem and Stokes' Theorem, relating the area (or volume) of a region to its perimeter (or surface)
We will cover most of Chapters 12-16 of the textbook.
Lecture: Attending the lecture is a fundamental part of the course; you will be responsible for material presented in lecture regardless of whether it is discussed in the textbook.
Reading: Reading the sections of the textbook corresponding to the class lectures and assigned homework exercises is considered part of the homework assignment; you will be responsible for material in the assigned sections regardless of whether it is discussed in lecture. You are expected to read the assigned material in advance of the lecture.
Classroom Conduct: In the classroom, a certain level of respect and attentiveness is expected. Please do not use phones or computers, play games, or talk to friends during lecture. This can be distracting to other students and the instructor.
Calculators: The use of a graphing calculator for checking ones work and gaining intuition about functions can be helpful in a calculus class. Indeed, occasionally you will have homework problems for which a calculator might be necessary. However, I encourage you to use the calculator as little as possible, and you’ll find out why in the following sentence.
The use of any calculators or other electronic equipment will NOT be permitted on exams.
Homework: Homework problems will be assigned on the course homework page, and should be completed and turned in by the beginning of recitation section on the indicated due date. You should make every effort to complete the homework assignments and seek help with problems you have been unable to solve. Please coordinate with your TA if you are unable to attend the recitation and need to make alternate arrangements for turning in your assignments. The lowest homework score will be dropped from your final grade.
Midterm Exams: There will be three midterms given during the regular lecture hour. The dates of the midterms are: Wednesday, 27 September; Wednesday, 25 October; and Friday, 1 December. More information, as well as practice and review materials, will be provided within 1 week of the midterm. See exam policies below.
Final Exam: The final exam will be cumulative. More information will be provided within 1 week of the exam. See exam policies below.
Exam Policies: No calculators or other electronic devices will be allowed during the exams. Unless you have a very serious, well documented, and compelling reason to miss an exam, there will be no makeup exams, for any reason.
Grading: Your final course grade will be based on the following weighted average:
A curve may be applied to final scores or individual examinations at the instructor's discretion. Regardless of the curve, the following basic rubric will be in place:
- 15% Homework (drop one)
- 18% each midterm
- 31% Final Exam
- Scores above 90%: A
- Scores above 80%: At least B
- Scores above 70%: At least C
- Scores above 60%: At least D
Academic Honesty: Academic dishonesty is a serious offense, carrying serious administrative sanctions. Any instance of dishonesty will be pursued by the instructor. It is in your best interest to follow all policies laid out here and elsewhere on this website, and familiarize yourself with the university guidelines for academic honesty. Please help maintain both your own integrity and the integrity of Carnegie Mellon University.
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