Mathematics (MATH) 365
Calculus—Several Variables (Revision 4)
Revision 4 closed, replaced by current version.
Delivery Mode: Individualized study or grouped study
Credits: 3
Area of Study: Science
Prerequisite: MATH 266
Centre: Centre for Science
MATH 365 has a Challenge for Credit option.
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Overview
In MATH 365: Calculus—Several Variables, is designed to introduce students to practical applications of calculus to problems in two and three dimensions, and to a theoretical understanding of some aspects of calculus in higher dimensions.
Outline
Unit 1: Analytic Geometry
- Polar Coordinates
- Tangent Lines and Arc Length for Parametric and polar Curves
- Area in Polar Coordinates
- Conic Sections
Unit 2: Three Dimensional Space
- Rectangular Coordinates; Sphere; Cylindrical Surfaces
- Vectors
- Dot Product; Projections
- Cross Product
- Parametric Equations of Lines
- Planes in 3-Space
- Quadratic Surfaces
- Cylindrical and Spherical coordinates
Unit 3: Vector Valued Functions
- Calculus of Vector-Valued Functions
- Change of Parameter; Arc Length
- Unit Tangent, Normal and Binormal Vectors
- Curvature
- Motion Along a Curve
Unit 4: Partial Derivatives
- Functions of Two or More Variables
- Limits and Continuity
- Partial Derivatives
- Differentiability; Differentials, and Local Linearity
- The Chain Rule
- Directional Derivatives an Gradients
- Tangent Planes and Normal Vectors
- Maxima and Minima of Functions of Two Variables
- Lagrange Multipliers
Unit 5: Multiple Integrals
- Double Integrals
- Double Integrals in Polar Coordinates
- Parametric Surfaces
- Triple Integrals
- Centroid, Center of Gravity
- Triple Integrals in Cylindrical and Spherical coordinates
- Change of Variables in Multiple Integrals; Jacobians
Unit 6: Topics in Vector Calculus
- Vector Fields
- Line Integrals
- Green's Theorem
- Surface Integrals
- Flux
- The Divergence Theorem
- Stroke's Theorem
Evaluation
To receive credit for MATH 365, you must submit both of the course assignments and complete them to the satisfaction of your tutor. You must also achieve a grade of at least 50 per cent on each examination, and a course composite grade of at least “D” (50 per cent). The weighting of the composite grade is as follows:
| Assignment 1 | 15% |
| Mid-term Exam | 30% |
| Assignment 2 | 15% |
| Final Exam | 40% |
| Total | 100% |
To learn more about assignments and examinations, please refer to Athabasca University's online Calendar.
Course Materials
Textbook
Anton, H., Bivens, I. & Davis, S. (2008). Selected Chapters from Anton: Calculus Late Transcendentals Combined, 8th Edition and Anton: Multivariable Calculus, 8th Edition. A Wiley Canada Custom Publication for Athabasca University MATH 365. Mississauga, ON: Wiley Canada Custom Service.
Other materials
The course materials include a study guide and a student manual.
Challenge for Credit Course Overview
The Challenge for Credit process allows students to demonstrate that they have acquired a command of the general subject matter, knowledge, intellectual and/or other skills that would normally be found in a university level course.
Full information for the Challenge for Credit can be found in the Undergraduate Calendar.
- Undergraduate Challenge for Credit Policy
- Undergraduate Challenge for Credit Procedures
Challenge Evaluation
To receive credit for the MATH 365 challenge registration, you must complete the two parts of the challenge exam and achieve a grade of at least “D” (50 percent) on both parts.
| Part 1: Exam | Part 2: Exam | Total |
|---|---|---|
| 50% | 50% | 100% |
Undergraduate Challenge for Credit Course Registration Form
- Challenge for Credit Form
Athabasca University reserves the right to amend course outlines occasionally and without notice. Courses offered by other delivery methods may vary from their individualized-study counterparts.
Opened in Revision 4, March 17, 2009.
View previous syllabus
Last updated by G. Zahara 03/24/2014 10:10:31
