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.
General Math 223 Information
The specific calendar & policy for your Math 223 section should be made available to you by your instructor.
The general policies and calendar can be found below.
THINK TANK (free tutoring for UA students)
The Math Department offers free tutoring for Math 223. Click here to see the schedule.
- Graphing Calculator (TI-83 or TI-84 are recommended)
- A graphing calculator is required for Math 129. We recommend any model in the TI-83 or TI-84 series.
- Models that can perform symbolic calculations (also known as CAS) are NOT allowed on exams and quizzes. CAS models include (but are not limited to) the TI-89, TI NSpire CAS, HP 50g, and Casio Classpad 330.
- More calculator info can be found HERE.
- Students are not allowed to share calculators during exams and quizzes.
- Textbook:
- Math 223 covers chapters 12 - 20 of Multivariable Calculus; 6th edition; McCallum, Hughes-Hallett, Gleason, et al.; Wiley.
- The Textbook will be delivered digitally via D2L through the Inclusive Access program.
- Inclusive Access FAQs
- WebAssign:
- 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.
- Things to Know About WebAssign at the UA
- Written Homework
- Inclusive Access FAQs
- Enrollment Requirements/Eligibility:
- Students must meet eligibility requirements.
- See the Math Course Placement Chart HERE.
- On-line Calculator
- On-line Graphing Tool (browser)
- Calculator Programs
- Math 223 demonstrations (Wolfram Project)
- Dot Product (Paul Falstad)
- Plotting surfaces and contours (Kaskosz & Ensley)
- Surfaces (JavaView)
- 3-D Vector Field Applet (Paul Falstad)
- Trig Formulas
- Derivative Rules
- Basic Integral Rules
- Integral Table
- Geometry Formulas
- Area Formulas
- Worksheets
- Precalculus Review (University of MI)
- Calculus at the UA
- Maximize Success in Calculus
-
Calculus Videos (Khan Academy)
Exam Information (Fall 2024)
Common Final Exam
Tuesday, December 17th, 2024 @ 1:00pm - 3:00pm
A comprehensive final exam is given in all sections of Math 223 at the time shown above.
See instructor or syllabus for more details regarding your final exam.
- Final Exam Info
- Final Exam Study Guide with Answers
- Final Exam Room Locations
Archived Exams:
