CALCULUS OF SEVERAL VARIABLES
Instructor: Dr. Turker Topcu
Lectures:
MWF 12:20-1:10 am in SEITZ 207 — Sec. 16476
Welcome to MATH 3214 (Spring 2020). Please refer to the course policies sheet below for information regarding course schedules, online homework, and grading policy. Homework sets and course-related announcements will be posted on Canvas throughout the semester.
We will cover material that extends the calculus of multivariable functions to vector fields. The main goal is to understand and learn how to use the three integral theorems: Green’s theorem, Stokes’ Theorem, and Divergence Theorem, which generalizations of the Fundamental Theorem of Calculus into higher dimensions. Following an extensive review of the multivariable functions, partial derivates, and multiple integrals, the students will be able to use the concepts of divergence, curl and flux, and apply Green’s, Stokes’, and Divergence Theorems to solve problems related to vector fields including both conservative and non-conservative vector fields. The emphasis in this course will be placed on understanding the underlying concepts rather than memorization: knowing why is the key to knowing how.
The student is responsible for reading the course policies sheet, which includes all the necessary information regarding the exams, homework, and procedures. The course policies sheet can be downloaded here from Canvas.
Homework: There will be both online and written homework assignments. Weekly online homework sets will be posted on WebAssign, which accompanies the textbook. The student will access WebAssign for this course through Canvas. Written homework sets will be posted on Canvas. If you need help integrating your WebAssign account with Canvas, you can find some information here. If you need further help, you can see a Cengage representative on campus. Please see the related announcement on Canvas for available times, dates, and locations.
Below is the tentative Spring 2020 schedule for the course. The program below is meant to give you a rough idea of what to expect as we will deviate from this schedule throughout the semester. We will cover selected sections from chapters 1-8.
| Week of | Chapter | Subject |
| Jan. 20 | Ch. 1.1, 1.2, 1.3 | Vectors, Inner/Cross products |
| Jan. 27 | Ch. 1.4, 1.5, 2.1, 2.2, 2.3 | Cylindrical and spherical coordinates, n-dim Euclidean space, Geometry of Real valued functions, Limits and continuity, Differentiation |
| Feb. 3 | Ch. 2.4, 2.5, 2.6, 3.1, 3.2 | Intro to paths and curves, properties of the derivative, Gradient and directional derivative, iterated partial derivatives, Taylor’s theorem |
| Feb. 10 | Ch. 3.2, 3.3, 3,4 | Taylor’s theorem, Extrema of real-valued funcs, Lagrange multipliers |
| Feb. 17 | Ch. 3.4, 3.5, 4.1 | Lagrange multipliers, Implicit function theorem, acceleration |
| Feb. 24 | Ch.4.2, 4.3, 4.4 | Arclength, Vector fields, Divergence and Curl |
| Mar. 2 | Ch. 5, 6.1, 6.2 | Double and triple integrals, Geometry of planar maps, Change of variables |
| Mar. 9 | (Spring Break) | |
| Mar. 16 | Ch. 6.2, 6.3, 6.4, 7.1 | Change of variables, Applications, Improper integrals, Path integrals |
| Mar. 23 | Ch. 7.2, 7.3, 7.4 | Line integrals, parametrized surfaces, Surface area |
| Mar. 30 | Ch. 7.5, 7.6, 8.1 | Integral of scalar funcs over surfaces, Surface integrals of vector fields, Green’s theorem |
| Apr. 6 | Ch. 8.1, 8.2 | Green’s Theorem |
| Apr. 13 | Ch. 8.2, 8.3 | Stokes’ theorem, Conservative fields |
| Apr. 20 | Ch. 8.4 | Gauss’ divergence theorem |
| Apr. 27 | Ch. 8.5 | Differential forms |
| May. 4 | Review | |
| May. 7 | Reading Day | Reading Day |