MATH-2630 A (CRN 1650) Fall 2017 Course Syllabus

When, where, and who

My job is to help you to succeed in this class. I will be happy to discuss issues related to this course (or anything mathematical) in person or via email. In addition to the normal office hours listed above, alternative meeting time may be arranged (please give me at least 48hr advanced notice).

What we will learn

Multivariable calculus is a fundamental pillar for modern science and engineering:

  • It extends single variable calculus to higher dimensions as if we are putting on 3D glasses. It turns out the higher dimensional structures are much richer than in the single variable cases, and many familiar concepts and theorems have much more interesting generalizations.

  • It provides the basic vocabulary for mathematical descriptions of fundamental processes and phenomena.

  • It forms the basic building blocks for geometrical objects like curves, surfaces, solids, and even higher dimensional analogs.

  • It develops intuition needed in other fields like linear algebra or data analysis.

  • It prepares you for further study in many other fields (not only in mathematics and its direct applications).

  • It makes you smarter (… I hope).

This is the third course in the calculus sequence. We will extend calculus to functions with more than one variables. In particular, we will cover…

  • Coordinate systems for 3-dimensional spaces
  • Basic algebra using vectors and matrices
  • Calculus of functions in multiple variables
  • Calculus of vector-valued functions and vector fields
  • Geometry of space curves
  • Geometry of curved surfaces
  • Lagrange multipliers and optimization problems
  • Double and triple integrals
  • Line integrals
  • Green’s theorem
  • (Optional) Stokes’ and Gauss’s theorems
  • (Optional) Fourier transformation and DCT

Prerequisite

In order to succeed in this class, a solid understanding of basic calculus is necessary. These prerequisite can be satisfied by MATH-1610 and MATH-1620 (or an appropriate score in the AUM Math Placement Test).

Textbook

Reading assignment and homework problems will be assigned from these textbook.

Attendance and participation

Participation in in-class discussions and activities is an important part of the learning process. Therefore class attendance is expected.

Code of conduct

Please be respectful of other people in the classroom and use common sense. In particular, please…

  • DO NOT use cell phones
  • DO NOT use social media
  • DO NOT take photos without permission
  • DO NOT sleep

Students who violate these rules will be asked to leave the classroom and will not be allowed to return until they have spoken privately with me.

Policy for calculators and smart devices

Scientific calculators or equivalent software programs can be helpful in doing homework problems. According to AUM Mathematics Department Calculator Policy, students are required to have a graphing calculator (TI-84 is recommended). The use of such calculators may be required for certain homework problems or in-class activities. However, all the quizzes and exams are designed so that no calculator will be needed. Therefore calculators or any smart devices with Internet capabilities are not allowed on any of the quizzes and exams.

Weekly quizzes

There will be a short quiz every week to test our understanding of the material discussed in the previous meetings. No makeup quiz will be offered. However, a missing quiz may be excused if valid reasons (military assignments, medical issues, family emergency, etc) and proper documentation are provided in advance. Otherwise, a missing quiz receives a score of zero.

Projects

Projects are more complicated mathematical problems that will guide you to gain deeper understanding of the material we learn in class. They will be a major part of your course grade. The list of suggested project problems can be found here.

Homework problems

Practice is a crucial component in the learning process. Suggested exercise problems can be found at the end of each section.

Reading assignments

You are expected to read the book in preparation of each class meetings. Reading assignments, i.e., sections (from the required textbook) are listed in the course schedule below. The reading assignments are to be completed before each class meeting.

Participation

Participation in in-class and online discussions is a crucially important component of the learning process. Your participation will be recorded and graded, and it constitutes a major part of your course grade.

Final exam

The mandatory final exam is scheduled at 11:00am—12:00pm Dec. 6. If you miss the final exam, your grade will be FA.

Grade composition

Your final grade is determined according to the following weighted average.

Component Points
Projects 500
Discussions 250
Quizzes 150
Final Exam 100

Grading scale

  • A: 90% - 100%
  • B: 80% - 89.9%
  • C: 70% - 79.9%
  • D: 60% - 69.9%
  • F: below 60%

Other policies

Academic dishonesty: Cheating of any kind will not be tolerated. In particular, you cannot copy (totally or partially) someone else’s solutions or allow someone else to copy your solutions on quizzes or exams. You will receive an “F” in the course if you are caught. Please consult Student Handbook for additional guidelines.

Disability accommodations: Students who need accommodations are asked to arrange a meeting during office hours to discuss your accommodations. If you have a conflict with my office hours, an alternate time can be arranged. To set up this meeting, please contact me by e-mail. If you have not registered for accommodation services through the Center for Disability Services (CDS), but need accommodations, make an appointment with CDS, 147 Taylor Center, or call 334-244-3631 or e-mail CDS at cds@aum.edu

Free academic support: All students have the opportunity to receive free academic support at AUM. Visit the Learning Center (LC) in the WASC on second floor Library or the Instructional Support Lab (ISL) in 203 Goodwyn Hall. The LC and ISL offers writing consulting as well as tutoring in almost every class through graduate school. The LC may be reached at 244-3470 (call or walk-in for a session), and the ISL may be reached at 244-3265. ISL tutoring is first-come-first served. Current operating hours can be found at http://www.aum.edu/learningcenter.

Student Privacy Policy: The Family Education Rights and Privacy Act of 1974, as amended, (FERPA) requires institutions receiving federal monies to protect the privacy of students’ educational records. For details go to the AUM’s FERPA website: http://www.aum.edu/academics/Registrars-office

Schedule

Listed below are the topics of discussion of each day. Reading the book before the class meetings is very important. Reading assignments, i.e., sections (from the required textbook) that you should read to get ready for our class meeting are also listed below. The reading assignments are to be completed before each class meeting.

  • Day 0 : Overview and motivations
  • Day 1 : Coordinate systems for plane and space
    • Cartesian and polar coordinate systems for the plane
    • Cartesian, cylindrical, and spherical coordinate systems for the space
    • Reading: 10.3, 10.4, 11.1, 11.2
  • Day 2 : Vectors and matrices
    • Vectors in the plane
    • Vectors in space
    • Matrices
    • Matrix-vector product
    • Reading: 11.1, 11.2
  • Day 3 : Dot product, cross product, and matrix determinant
    • Reading: 11.3, 11.4
  • Day 4 : Review of planar curves
    • Reading: 10.1, 10.2, 10.3
  • Day 5 : Parametric curves
    • Reading: 10.1, 10.2, 10.3, 12.1
  • Day 6 : Calculus on planar curves
    • Tangent vectors and velocity
    • Curves as solutions of differential equations
    • Reading: 10.3, 12.1, 12.3, review Chapter 3
  • Day 7 : The arc-length problem
    • Computing arc-length for planar and space curves
    • Reading: 12.4, 12.5, review 7.4
  • Day 8 : (Optional) Planar curves: graph vs parametric vs implicit
    • Curves in the plane can be described in at least three ways. We shall review the differences among them.
  • Day 9 : Curves in space
    • Some basic examples
    • Reviewing basic calculus constructions
    • Putting everything together, we review the different kinds of calculus we can do on a curve in space
    • Reading: review 11.1, 12.1, 12.3, 12.4
  • Day 10 : Planes in space
    • Reading: 11.5
  • Day 11 : Surfaces in space
    • Surfaces as graphs
    • Surfaces as solutions to equations
    • Reading: 11.6, 13.1, 13.3
  • Day 12 : Calculus on surfaces
    • Reading: 13.1, 13.3, 13.4, 13.5, 13.6
  • Day 13 : The volume problem: boxes and slices
    • The basic idea of volume in space
    • How are the defined?
    • How to compute volume using integrals
    • Reading: review Chapter 7
  • Day 14 : Multiple integral and volume computation
    • Rethink volume computation
    • Concept of multiple integrals
    • Concept of iterated integrals
    • (Optional) Fubini’s Theorem
    • Reading: 14.1, 14.2
  • Day 15 : Differential equations on the plane
    • Reading: review Chapter 6
  • Day 16 : Solving differential equations
    • Reading: review Chapter 6
  • Day 17 : Functions of multiple variables
    • Surface as graphs
    • Partial derivatives
    • Directional derivatives
    • Reading: review Chapter 12 and 13
  • Day 18 : Vector fields
    • Concept of vector fields
    • Concept of gradient fields
    • Reading: 15.1
  • Day 19 : Line integrals
    • Reading: 15.2
  • Day 20 : Gradient Theorem (FTC for line integrals)
    • Reading: 15.3
  • Day 21 : Vector fields, revisited
    • Reading: review 15.1, 15.2, 15.3
  • Day 22 : Vector fields and differential equations
  • Day 23 : Operations on vector fields
    • Divergence
    • Curl
    • Reading: review 15.1, 15.2, 15.3
  • Day 24 : Differential equations in space
  • Day 25 : Divergence Theorem
    • Reading: 15.7
  • Day 26 : Green’s Theorem
    • Reading: 15.4
  • Day 27 : (Optional) Stokes’ Theorem
    • Reading: 15.8