Multivariable Calculus - Math 2730.002

Spring 2011

Instructor: Dr. Matthew Dulock Office Location:422 GAB

Email: hone: (940)-565-4375

Office hours: 10 – 11 MW, 1-2 MW Class Meets: MWF 11:00 – 11:50

Course Description:MATH 2730Multivariable Calculus. 3 hours. Vectors and analytic geometry in 3-space; partial and directional derivatives; extrema; double and triple integrals and applications; cylindrical and spherical coordinates. Prerequisite(s): MATH 1720.

Learning Objectives:

  • Students will demonstrate an understanding of vectors basic 3 dimensional geometry
  • Students will demonstrate an understanding of the calculus of vector valued functions
  • Students will demonstrate and understanding of limits, continuity, and differentiation of real valued functions of 2 and 3 variables.
  • Students will demonstrate an understanding of optimization problems for functions of several variables.
  • Students will demonstrate an understanding of integration in several variables using various coordinate systems
  • Students will demonstrate and understanding of line integrals and Green’s Theorem

Textbook: Calculus, 11th ed. (part 2), George B. Thomas

Course Content:

We will cover most of the sections in Chapters 12, 13, 14, and 15. We will cover as much of chapter 16 as time permits. I hope to make it to 16.4 on Green’s Theorem.

Homework: Homework will typically be given out on Mondays, and will be due the following Monday. I will also post copies of the assignment on blackboard. Go to and sign in using your EUID. Click on your section, and then click on course content. The homework folder should be visible. Homework is essential to mastering this material. Your lowest 3 homework grades will be dropped.

Grading: Your grade will be calculated as follows:

Homework 25%

Exams 50% (Best 2 of 3)

Final Exam 25%

Make-up Policy: Make ups will only be given in emergency situations. The student must be able to produce proof (e.g. a note from a hospital, or doctor) of their emergency.

Summary of Key Dates for Spring 2011:

Following are schedule dates of which you need to be aware. Please review these dates and note:

JANUARY 18, TUESDAY

Classes begin.

JANUARY 31, MONDAY

Last day to drop a course and receive refund. Drops after this date require instructor's written consent.

FEBRUARY 25, FRIDAY

Last day to drop a course or withdraw from the university with a grade of “W” for courses that a student is not passing; after this date a grade of “WF” may be recorded. (Your attendance policy must be written on your syllabus in order to drop students for non-attendance.)

FEBRUARY 28, MONDAY

Beginning this date instructors may drop students with a grade of “WF” for non-attendance. (Your attendance policy must be written on your syllabus in order to drop students for non-attendance.)

MARCH 9, WEDNESDAY

Midsemester.

MARCH 14 – 20, MONDAY - SUNDAY

Spring Vacation – classes do not meet.

MARCH 29, TUESDAY

Last day to drop a course with consent of instructor.

APRIL 1, FRIDAY

Beginning this date a student may request a grade of “I”, incomplete, a non-punitive grade given only if a student (1) is passing, (2) has justifiable reason why the work cannot be completed on schedule; and (3) arranges with the instructor to complete the work.

APRIL 22, FRIDAY

Last day for an instructor to drop a student with a grade of “WF” for non-attendance.

Last day to withdraw from the semester.

APRIL 30 – MAY 5, SATURDAY – THURSDAY

Pre-final week. No student activities may be scheduled.

MAY 6, FRIDAY

Reading Day. No classes.

May 7 - 13, SATURDAY - FRIDAY

Final examinations. Terms ends.

MAY 14, SATURDAY

Commencement.

COURSE SCHEDULE:

1/19 – Introduction and 12.1 Coordinate Systems

1/21 – 12.1 cont’d, 12.2 Vectors

1/24 – 12.2 cont’d, 12.3 Dot Product

1/26 – 12.3 cont’d, 12.4 Cross Product

1/28 – 12.5 Lines and Planes, 12.6 Quadric Surfaces

1/31 – 12.6 cont’d, 13.1 Vector Valued Functions

2/2 – 13.1 cont’d, 13.2 Projectiles

2/4 – 13.3 Arclength and Tangents

2/7 – 13.4 Curvature and Normal Vectors

2/9 – 13.5 Torsion and Binormal Vectors

2/11 – Review

2/14 –Exam 1

2/16 – 14.1 Functions of Several Variables

2/18 – 14.1 cont’d, 14.2 Limits and Continuity

2/21 – 14.2 cont’d, 14.3 Partial Derivatives

2/23 – 14.3 cont’d, 14.4 The Chain Rule(s)

2/25 – 14.4 cont’d, 14.5 Directional Derivatives and the Gradient

2/28 – 14.5 cont’d, 14.6 Tangent Planes and Differentials

3/2 – 14.6 cont’d

3/4 – 14.7 Extrema

3/7 – 14.7 cont’d

3/9 – 14.8 Lagrange Multipliers

3/11 – 14.8 cont’d, 14.9 Partial Derivatives w/Constraints

3/14 – Spring Break

3/16 – Spring Break

3/18 – Spring Break

3/21 – 14.9 cont’d 14.10 Taylor’s Theorem

3/23 –14.10 cont’d, Review

3/25 – Review

3/28 – Exam 2

3/30 – 15.1 Double Integrals

4/1 – 15.1 cont’d

4/4 – 15.2 Centers of Mass

4/6 – 15.3 Double Integrals in Polar Coordinates

4/8 – 15.4 Triple Integrals

4/11 – 15.4 Triple Integrals

4/13 – 15.5 Centers of Mass in 3D, 15.6 Triple Integrals in Cylindrical Coordinates

4/15 – 15.6 Triple Integrals in Spherical Coordinates

4/18 – 15.7 Substitution

4/20 – 16.1 Line Integrals

4/22 – 16.2 Vector Fields, 16.3 Path Independence

4/25 – 16.3 Cont’d, 16.4 Green’s Theorem

4/27 – Review

4/29 – Exam 3

5/2 – 16.4 cont’d, 16.5 Surfaces

5/4 – Review for Final Exam

I reserve the right to change this schedule as necessary throughout the semester.