Yuba Community College District
Yuba College Course Outline
Course Information
Course Number:
MATH 1C
Full Course Title:
Multivariable Calculus
Short Title:
Multivar Calculus
Effective Term:
Fall 2013
Course Standards
Lecture Hours:
72.000
Total Units:
4.000
Total Hours:
72.00
Repeatable:
No
Grading Method:
Letter Grade Only
Minimum Qualifications
 Mathematics (Masters Required)
Course Description
Vector valued functions, calculus of functions of more than one variable, partial derivatives, multiple integration, Green’s theorem, Stokes’ theorem, divergence theorem.Conditions of Enrollment
Completion with a C or better in: MATH 1B
Advisories

Language  recommended eligibility for English 1A

Mathematics  recommended eligibility for Math 52
Content
Course Lecture Content
 Vectors and vector operations in two and three dimensions
 Vector and parametric equations of lines and planes; rectangular equation of a plane
 Dot, cross, and triple products and projections
 Differentiability and differentiation including partial derivatives, chain rule, higherorder derivatives, directional derivatives, and the gradient
 Arc length and curvature; tangent, normal, binormal vectors
 Vectorvalued functions and their derivatives and integrals; finding velocity and acceleration
 Realvalued functions of several variables, level curves and surfaces
 Limits, continuity, and properties of limits and continuity
 Local and global maxima and minima extrema, saddle points, and Lagrange multipliers
 Vector fields including the gradient vector field and conservative fields
 Double and triple integrals
 Applications of multiple integration such as area, volume, center of mass, or moments of inertia
 Change of variables theorem
 Integrals in polar, cylindrical, and spherical coordinates
 Line and surface integrals including parametrically defined surfaces
 Integrals of realvalued functions over surfaces
 Divergence and curl
 Green’s, Stokes’, and divergence theorems
Objectives

Perform vector operations.

Determine equations of lines and planes.

Find the limit of a function at a point.

Evaluate derivatives.

Write the equation of a tangent plane at a point.

Determine differentiability.

Find local extrema and test for saddle points.

Solve constraint problems using Lagrange multipliers.
**Requires Critical Thinking**

Compute arc length.

Find the divergence and curl of a vector field.

Evaluate two and three dimensional integrals.

Apply Green’s, Stokes’, and divergence theorems.
**Requires Critical Thinking**
Student Learning Outcomes
 Computation – Compute partial derivatives, the gradient and extrema of functions.
 Computation – Evaluate double and triple integrals.
Methods of Instruction

Lecture/Discussion
Assignments
Hours per week on assignments outside of the class:
Reading Assignments
Writing Assignments
Methods of Evaluation
 Exams
 Homework
 Portfolio
 Problem Solving Exercises
 Quizzes

OtherGroup or individual projects.
Course Materials
Textbooks:

Robert T. Smith and Roland B. Minton. Calculus: Early Transcendental Functions, 4th ed. PrenticeHall, 2012, ISBN: McGraw HillEquivalent text is acceptable