- Properties and applications of points, curves and surfaces for various coordinates in R3.
- Operations, properties and applications of vectors and vector functions.
- Partial Derivatives: Limits, partial derivative rules and properties, gradients and optimization principles. Applications.
- Multiple Integrals: Double and triple integrals over general domains in appropriate coordinate systems (rectangular, polar, cylindrical, spherical or other defined coordinates). Applications.
- Vector Calculus: Vector fields, line integrals, Fundamental Theorem of Line Integrals. Applications. (If time permits)
Lecture, problems sessions, written and computer exercises.
At the completion of the course a student will be expected to:
- Use and apply vector notation and the properties of vectors to describe various physical quantities
- Compute dot and cross-products and use the results to determine angle/orientation between two vectors or one vector and standard basis vectors
- Find scalar and vector projection of one vector onto another
- Find area and volume defined by sets of vectors
- Find vector, parametric or symmetric representations for equations of lines and planes in R3
- Determine whether two lines intersect, are parallel, perpendicular or skew
- Determine and describe the orientation of two planes using the angle between their normal vectors
- Determine the distance between a point and a line or plane, between two lines or between two planes.
- Identify and sketch quadric surfaces
- Use cylindrical or spherical coordinate systems to describe points, curves and surfaces in R3
- Evaluate limits involving vector functions
- Find the domain of a vector function and subsets of the domain where a vector function is continuous
- Sketch graphs of vector functions
- Differentiate and integrate vector functions, use differentiation rules for vector functions
- Find unit tangent, principal normal vectors and tangent lines to space curves
- Find the length of a space curve over an interval and its curvature at a point
- Apply the ideas of tangent and normal vectors and curvature to motion in space
- Sketch level curves for functions of two variables and level surfaces for functions of three variables
- Calculate limits (or prove the non-existence) for functions of two or three variables
- Find subsets of a function’s domain for which the function is continuous
- Calculate partial derivatives of a function, establish and apply chain rules, find and interpret implicit partial derivatives
- Find the equation of the tangent plane to a surface at a point
- Use differentials to approximate values and errors for a function of two or three variables
- Find directional derivatives and gradients of functions
- Find and classify critical points of a function of two variables; solve associated optimization problems
- Use the Method of Lagrange Multipliers to solve constrained optimization problems
- Set up and evaluate double and triple Riemann sums over rectangular regions and convert notation to multiple integrals
- Identify different classes of domains of integration to set up and evaluate general multiple integrals
- Change the order of integration variables
- Set up and evaluate Riemann sums in polar coordinates and convert to multiple integrals
- Change the representation of an integral from one set of coordinates to another
- Calculate the Jacobian of a transformation of coordinates to re-express integrals
- Solve geometric and applied problems involving integration
- Sketch vector fields on R2
- Find the gradient vector field of a multi-variable function
- Evaluate line integrals for vector fields
- Determine whether or not a vector field is conservative
- Find conditions for and use the fundamental theorem of line integrals, apply the results
Textbook varies by semester, please see College Bookstore for current version.
Typical texts include:
Stewart, James. Multivariable Calculus 7e, Brooks/Cole, 2012.
Briggs and Cochran. Multivariable Calculus, Pearson, 2011.
Course Guidelines for previous years are viewable by selecting the version desired. If you took this course and do not see a listing for the starting semester / year of the course, consider the previous version as the applicable version.
|Institution||Transfer Details||Effective Dates|
|Alexander College (ALEX)||ALEX MATH 251 (3)||2021/09/01 to -|
|Camosun College (CAMO)||CAMO MATH 2XX (3)||2013/01/01 to -|
|Camosun College (CAMO)||DOUG MATH 2321 (3) & DOUG MATH 2440 (3) = CAMO MATH 220 (4) & CAMO MATH 2XX (3)||2013/01/01 to -|
|Capilano University (CAPU)||CAPU MATH 230 (3)||2004/09/01 to -|
|Coquitlam College (COQU)||COQU MATH 201 (3)||2004/09/01 to -|
|Kwantlen Polytechnic University (KPU)||KPU MATH 2321 (3)||2004/09/01 to -|
|Langara College (LANG)||LANG MATH 2371 (3)||2004/09/01 to -|
|Okanagan College (OC)||OC MATH 212 (3)||2005/09/01 to -|
|Simon Fraser University (SFU)||SFU MATH 251 (3)||2004/09/01 to -|
|Thompson Rivers University (TRU)||TRU MATH 2110 (3)||2010/09/01 to -|
|Thompson Rivers University (TRU)||TRU MATH 211 (3)||2004/09/01 to 2010/08/31|
|Trinity Western University (TWU)||TWU MATH 223 (3)||2004/09/01 to -|
|University of British Columbia - Okanagan (UBCO)||UBCO MATH 200 (3)||2004/09/01 to -|
|University of British Columbia - Vancouver (UBCV)||UBCV MATH 200 (3)||2004/09/01 to -|
|University of Northern BC (UNBC)||UNBC MATH 2XX (3)||2004/09/01 to -|
|University of the Fraser Valley (UFV)||UFV MATH 211 (3)||2004/09/01 to -|
|University of Victoria (UVIC)||UVIC MATH 200 (1.5)||2004/09/01 to -|
|Vancouver Community College (VCC)||VCC MATH 2251 (3)||2017/09/01 to -|
It is recommended that students purchase the textbook for this course directly from the College Bookstore in order to ensure they receive a valid activation key for the online homework system.