vcc.ca
MATH 2251: Calculus 3
Effective date
September 2017
Department
UT Math
School
Arts and Sciences
Description
This course explores the calculus of several variables and is intended for students in Science, Engineering and Computer Science degree programs. Students are introduced to the concepts of three-dimensional analytic geometry, vectors, partial differentiation, multiple integration and vector calculus.
It is recommended that MATH 2251 be taken concurrently with or after MATH 1221.
Credits
3.0
Year of study
2nd Year Post-secondary
Prerequisites
MATH 1200 with a C- or equivalent.
Corequisites
None
Course Learning Outcomes
Upon successful completion of this course, students will be able to:
- Perform vector operations and obtain vector representation for equations of lines and planes.
- Use cylindrical or spherical coordinate systems to represent points, curves and surfaces.
- Solve max/min problems by computing partial derivatives, and characterize motion on a 3 dimensional surface by computing directional derivatives and gradients.
- Use the method of Lagrange Multipliers to solve optimization problems with constraints.
- Compute double integrals (over rectangular, general and polar regions), and triple integrals (in cylindrical and spherical coordinates).
- Change variables in multiple integrals and calculate the Jacobian of a transformation.
- Determine gradient vector fields and find potential functions.
- Apply the fundamental theorem of line integrals and use Green’s theorem to evaluate line integrals along simple closed contours on the plane.
Prior Learning Assessment & Recognition (PLAR)
None
Hours
Lecture, Online, Seminar, Tutorial: 60
Total Hours: 60
Total Hours: 60
Instructional Strategies
The course uses a combination of lectures, presentations, guest speakers, applied problems, and a computer algebra system for visualization and calculation of multivariable calculus concepts.
Grading System
Letter Grade (A-F)
Passing grade
D
Evaluation Plan
|
Type |
Percentage |
Assessment activity |
|
Assignments |
15 |
|
|
Midterm Exam |
25 |
|
|
Midterm Exam |
25 |
|
|
Final Exam |
35 |
|
Course topics
- Review of conic sections and polar coordinates.
- Three dimensional coordinate systems, vectors, dot and cross product, equations of lines and planes, cylindrical and quadric surfaces.
- Functions of several variables, partial derivatives, tangent planes and linear approximation, chain rule, directional derivatives and gradient vector, optimization and Lagrange multipliers.
- Double integrals over rectangles, iterated integrals, double integrals over general regions and in polar coordinates, applications of double integrals, triple integrals in cylindrical and spherical coordinates, change of variables in multiple integrals.
- Vector calculus: vector fields, line integrals, Fundamental Theorem of Line Integrals, Green's Theorem.
Notes:
- Course contents and descriptions, offerings and schedules are subject to change without notice.
- Students are required to follow all College policies including ones that govern their educational experience at VCC. Policies are available on the VCC website at:
https://www.vcc.ca/about/governance--policies/policies/. - To find out if there are existing transfer agreements for this course, visit the BC Transfer Guide at https://www.bctransferguide.ca.