MAT 211 Calculus III

Instructor:
Office:
Office hours:
Phone:
Email:

Course Description

Multivariable calculus: analytic geometry, scalar and vector products, partial differentiation, multiple integration, change of coordinates, gradient, optimization, line integrals, Green's theorem, elements of vector calculus.

5 units credit.

Prerequisite

MAT 193 or equivalent with a grade of "C" or better.

Text

Essential Calculus, by James Stewart. Brooks/Cole 2007. (Covers MAT 191, MAT 193, and MAT 211.)

Course Requirements, Tentative Schedule of Class Meetings and Topics, Readings, Assignments and Due dates, Exams

MAT 211 covers the following material from chapters 10-13 in the text.

• 10. VECTORS AND THE GEOMETRY OF SPACE
• Three-Dimensional Coordinate Systems
• Vectors
• The Dot Product
• The Cross Product
• Equations of Lines and Planes
• Vector Functions and Space Curves
• Arc Length and Curvature
• Motion in Space: Velocity and Acceleration
• 11. PARTIAL DERIVATIVES
• Functions of Several Variables
• Limits and Continuity
• Partial Derivatives
• Tangent Planes and Linear Approximations
• The Chain Rule
• Directional Derivatives and the Gradient Vector
• Maximum and Minimum Values
• Lagrange Multipliers
• 12. MULTIPLE INTEGRALS
• Double Integrals over Rectangles
• Double Integrals over General Regions
• Double Integrals in Polar Coordinates
• Applications of Double Integrals
• Triple Integrals
• Triple Integrals in Cylindrical Coordinates
• Triple Integrals in Spherical Coordinates
• Change of Variables in Multiple Integrals
• 13. VECTOR CALCULUS
• Vector Fields
• Line Integrals
• The Fundamental Theorem for Line Integrals
• Green's Theorem
• Curl and Divergence
• Parametric Surfaces and Their Areas
• Surface Integrals
• Stokes' Theorem
• The Divergence Theorem

A schedule of class meetings, topics, assignments, due dates, exam dates, etc. will be provided by instructor. See your class syllabus.

The final exam is given at the date and time announced in the Schedule of Classes.

Learning Objectives

After completing MAT 211 the student will

• Demonstrate an intuitive understanding of functions of several variables via level curves and surfaces, and related concepts of limit, continuity and differentiability.
• Perform partial differentiation and multiple integration of functions of several variables.
• Change from Cartesian co-ordinates to polar, cylindrical or spherical co-ordinates and vice versa, perform differential (partial or ordinary) and integration (multiple or single) in curvilinear co-ordinate systems and effect transformation via the Jacobian..
• Utilize vectors to deal with spatial curves and surfaces, and calculus of several variables
• Use the concepts of vector calculus: gradient, curl, divergence, line and surface integrals, Green's, Stokes' and the divergence theorem.
• Apply calculus of several variables to solve problems of optimization, differential geometry and physics

Computers and Calculators, Computer Literacy

Most instructors encourage the use of machines, calculators computers, phones etc., for analyzing data. The use of machines may be restricted during examinations or at certain other times. Ask your instructor for the policy in your class.

Students are not expected to be programmers or to know any particular computer language before starting this class. Some instructors may expect students to be able to access information on the internet, or to use calculators, or to learn to use particular software with instruction. Basic skill in algebra and the use of mathematical symbols, order of operations etc., and the willingness to read and follow instruction manuals and help files will suffice.

Students' grades are based on homework, class participation, short tests, and scheduled examinations covering students' understanding of the topics covered in this course. The instructor determines the relative weights of these factors and the grading scale. See the syllabus for your particular class.

Location of Class Meetings

Classes meet on the dates and room announced in the official Schedule of Classes. This is a traditional, face-to-face class.

Attendance Requirements

Attendance policy is set by the instructor.

Policy on Due Dates, Make-Up Work, Missed Exams, and Extra-Credit Assignments

Due dates and policy regarding make-up work and missed exams are set by the instructor. Instructors may, or may not, choose to offer extra credit assignments. If extra credit assignments are offered they will be available to all students.

The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity".)

Accomodations for Students with Disabilities

Cal State Dominguez Hills adheres to all applicable federal, state, and local laws, regulations, and guidelines with respect to providing reasonable accommodations for students with temporary and permanent disabilities. If you have a disability that may adversely affect your work in this class, I encourage you to register with Disabled Student Services (DSS) and to talk with me about how we best can help you. All disclosures of disabilities will be kept strictly confidential. Please note: you must register with DSS to arrange an no accommodation. For information call (310) 243-3660 or send an email message to dss@csudh.edu or visit the DSS website http://www4.csudh.edu/dss/contact-us/index or visit their office WH D-180

Behavioral Expectations

We all are adults so behavior rarely is an issue. Just follow the Golden Rule: "do unto others as you would have them do unto you" then everything will be fine.

The university must maintain a classroom environment that is suitable for learning, so anyone who insists on disrupting that environment will be expelled from the class.

Revision history:

Prepared 3/9/00 (C. Chang). Revised 1/19/01, 7/7/01, 7/13/03, 7/25/06 (G. Jennings), 8/21/07 (S. Raianu), 1/7/15 (G. Jennings).