# Vector Calculus (MATH 223)

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The Math Department offers free online tutoring for Math 223, Monday-Friday. Click here to see the schedule.

## COURSE OBJECTIVES AND LEARNING OUTCOMES:

Course Objectives

• Recognize and sketch surfaces in three-dimensional space;

• Recognize and apply the algebraic and geometric properties of vectors and vector functions in two and three dimensions;

• Compute dot products and cross products and interpret their geometric meaning;

• Compute partial derivatives of functions of several variables and explain their meaning;

• Compute directional derivatives and gradients of scalar functions and explain their meaning;

• Compute and classify the critical points;

• Parameterize curves in 2- and 3-space;

• Set up and evaluate double and triple integrals using a variety of coordinate systems;

• Evaluate integrals through scalar or vector fields and explain some physical interpretation of these integrals;

• Recognize and apply Fundamental theorem of line integrals, Green’s theorem, Divergence Theorem, and Stokes’ theorem correctly.

Expected Learning Outcomes

Upon completion of this course, students should be able to:

• Perform vector operations, determine equations of lines and planes, parametrize 2D & 3D curves.

• Graphically and analytically synthesize and apply multivariable and vector-valued functions and their derivatives, using correct notation and mathematical precision.

• Synthesize the key concepts differential, integral and multivariate calculus.

• Evaluate double integrals in Cartesian and polar coordinates; evaluate triple integrals in rectangular, cylindrical, and spherical coordinates; and calculate areas and volumes using multiple integrals.

• Use double, triple and line integrals in applications, including Green's Theorem, Stokes' Theorem, Divergence Theorem and Fundamental theorem of line integrals.

## SECTIONS AND INSTRUCTORS

Section information and links to instructor class webpages are found here.

MATH 223 (4 credits)

MATH 196V (1 unit)

## ELIGIBILITY

Students must meet eligibility requirements.

See the current Math Course Placement Chart here.

## TEXTBOOK

Math 223 covers chapters 12 - 20 of Multivariable Calculus; 6th edition; McCallum, Hughes-Hallett, Gleason, et al.; Wiley.

The Textbook and WebAssign access for homework are being delivered digitally via D2L through the Inclusive Access program.

Inclusive Access FAQs

## CALCULATORS

A graphing calculator is required for Math 223. We recommend any model in the TI-83 or TI-84 series. Students are not allowed to share calculators during exams and quizzes.

## HOMEWORK

Math 223 uses a computer grading program called WebAssign for textbook assignments. Logging into WebAssign can only be done through the WebAssign Login link in your Math 223 D2L site.

Additional homework and/or quizzes may be assigned by instructors. Be sure to check with your instructor.

Precalculus Review (University of MI)

Maximize Success in Calculus

## COURSE POLICIES AND CALENDAR

Individual course sections may deviate from the suggested calendar and policies. Be sure to check with your instructor.

Spring 2022 Math 223 General Course Policies

## COMMON FINAL EXAM INFORMATION

A common comprehensive final exam will be given for all sections of Math 223 on Tuesday, May 10th from 1:00pm - 3:00pm.

See instructor or syllabus for more details regarding your final exam.

Final Exam Info (Spring 2022)

Final Exam Study Guide (Spring 2022), Answers

Final Exam Room Locations

## TECHNOLOGY TOOLS AND REFERENCE SHEETS

On-line Calculator

Math 223 demonstrations (Wolfram Project)

Cross Product (Syracuse University)

Plotting surfaces and contours (Kaskosz & Ensley)

Plotting (MIT Open Courseware)

Surfaces (JavaView)

Vector Field Analyzer (Matthias Kawski - ASU)

3-D Vector Field Applet (Paul Falstad)

3-D Vector Fields (OR State University)

Integral Table