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 21C: Calculus: Partial Derivatives and Series
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; $150.00-216.00.
Search by ISBN on Amazon: 978-0321884077

Prerequisites:

MAT (16C, 17C, 21B or MAT 21BH) with C- or above or MT 17B with a B or above.

Suggested Schedule:

Lecture(s)

Sections

Comments/Topics

1

10.1

Sequences

1

10.2

Infinite series

1

10.3

The integral test

1.5

10.4

Comparison tests

1.5

10.5

The ratio and root tests

1

10.6

Alternating series, absolute and conditional convergence

1

10.7

Power series

1

10.8

Taylor and maclaurin series

1

10.9

Convergence of taylor series

1

10.10

The binomial series and applications of taylor series

0.5

12.1

Three-dimensional coordinate systems

0.5

12.2

Vectors

1

12.3

The dot product

1

12.4

The cross product

1

12.5

Lines and planes in space

1

13.1

Curves in space and their tangents

1

13.2

Integrals of vector functions, projectile motion

1

14.1

Functions of several variables

1

14.2

Limits and continuity in higher dimensions

1

14.3

Partial derivatives

1

14.4

The Chain Rule

1

14.5

Directions derivatives and gradient vectors

1

14.6

Tangent planes and differentials

1.5

14.7

Extreme values and saddle points

1.5

14.8

Lagrange multipliers

Additional Notes:

Total number of lectures = 26. This leaves time for exams and lecture time adjustments. If time runs out, consider omitting 10.10.

Learning Goals:


A goal of this course is to help students develop effective strategies for solving both mathematical and real world problems. Although students often do not like “word problems” probing applications of their mathematical skills, it is very important that instructors emphasize these types of problems so that students become experts 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.

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.