Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 21D: Vector Analysis
Approved: 2007-04-01 (revised 2013-01-01, J. DeLoera)

ATTENTION:

This course is part of the inclusive access program, in which your textbook and other course resources will be made available online. Please consult your instructor on the FIRST DAY of instruction.

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Thomas' Calculus Early Transcendentals, 13th Edition by George B. Thomas, Maurice Weir, and Joel Hass; Addison Wesley Publishers.
Search by ISBN on Amazon: 978-0321884077

Prerequisites:

MAT (21C or MAT 21CH) with C- or above; or MAT 17C with B or above.

Suggested Schedule:

Lecture(s)

Sections

Comments/Topics

1

15.1

Double and Iterated Integrals Over Rectangles

1.5

15.2

Double Integrals Over General Regions

0.5

15.3

Area by Double Integration

1

15.4

Double Integrals in Polar Form

1

15.5

Triple Integrals in Rectangular Coordinates

1

15.6

Moments and Centers of Mass

1

15.7

Triple Integrals in Cylindrical and Spherical Coordinates

2

15.8

Substitutions in Multiple Integrals

1

12, 13.1, 13.2

Review of Vectors

1

13.3

Arc Length in Space

1.5

13.4

Curvature and Normal Vectors of a Curve

0.5

13.5

Tangential and Normal Components of Acceleration

1

16.1

Line Integrals

2

16.2

Vector Fields and Line Integrals: Work, Circulation, and Flux

1

16.3

Path Independence, Conservative Fields. Potential Functions

2

16.4

Green’s Theorem in the Plane

2

16.5

Surfaces and Area

1

16.6

Surface Integrals

2

16.7

Stokes’ Theorem

2

16.8

The Divergence Theorem and a Unified Theory

Additional Notes:

Total number of lectures = 26. This leaves fours days for exams and time adjustments.

Learning Goals:

A goal of this course is to help students develop effective strategies for solving both mathematical and real world problems. Although students don’t often like “word problems” probing applications of their mathematical skills, it is very important that instructors emphasize these types of problems so that students become expert at them. In particular, students should be taught how to create mathematical models, develop effective strategies for solving problems in applied settings and non-routine situations.

Students will master both integral and differential multivariable calculus, with special emphasis placed on two and three dimensions. By this stage, students are expected to be experts at “word problems” requiring them to convert real world problems into mathematics. The course begins with multiple integrals and then introduces the main differential operators in two and three dimensions. These themes are unified by Stoke's theorem at the end of the course.

By the end of this course, students will have the mathematical skills to succeed in a wide range of science classes, especially those involving motions and flows in the three dimensional world surrounding us.

Note: Care should be taken in this course to teach students how to produce simple yet meaningful sketches of the three dimensional geometric objects studied. Use appropriate visualization technology.

Assessment:

Student progress will be monitored by quizzes, midterms, regular homework, and a comprehensive examination.