Yuba Community College District

Yuba College Course Outline

### Course Information

Course Number: MATH 1C
Full Course Title: Multivariable Calculus
Short Title: Multivar Calculus
TOP Code: 1701.00 - Mathematics, General
Effective Term: Fall 2013

### Course Standards

Course Type: Credit - Degree Applicable
Units: 4.0
Total class hours: 216.0
Total contact hours in class: 72.0
Lecture hours: 72.0
Hours outside of class: 144.0
Repeatable: No

### Minimum Qualifications for Instructors

• 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

Satisfactory completion of: MATH 1B

• Language - recommended eligibility for English 1A
• Mathematics - recommended eligibility for Math 52

### Content

Course Lecture Content
1. Vectors and vector operations in two and three dimensions
2. Vector and parametric equations of lines and planes; rectangular equation of a plane
3. Dot, cross, and triple products and projections
4. Differentiability and differentiation including partial derivatives, chain rule, higher-order derivatives, directional derivatives, and the gradient
5. Arc length and curvature; tangent, normal, binormal vectors
6. Vector-valued functions and their derivatives and integrals; finding velocity and acceleration
7. Real-valued functions of several variables, level curves and surfaces
8. Limits, continuity, and properties of limits and continuity
9. Local and global maxima and minima extrema, saddle points, and Lagrange multipliers
10. Vector fields including the gradient vector field and conservative fields
11. Double and triple integrals
12. Applications of multiple integration such as area, volume, center of mass, or moments of inertia
13. Change of variables theorem
14. Integrals in polar, cylindrical, and spherical coordinates
15. Line and surface integrals including parametrically defined surfaces
16. Integrals of real-valued functions over surfaces
17. Divergence and curl
18. Green’s, Stokes’, and divergence theorems

### Objectives

1. Perform vector operations.

2. Determine equations of lines and planes.

3. Find the limit of a function at a point.

4. Evaluate derivatives.

5. Write the equation of a tangent plane at a point.

6. Determine differentiability.

7. Find local extrema and test for saddle points.

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

9. Compute arc length.

10. Find the divergence and curl of a vector field.

11. Evaluate two and three dimensional integrals.

12. Apply Green’s, Stokes’, and divergence theorems. **Requires Critical Thinking**

### Student Learning Outcomes

1. Computation – Compute partial derivatives, the gradient and extrema of functions.
2. Computation – Evaluate double and triple integrals.

### Methods of Instruction

• Lecture/Discussion

### Assignments

Writing Assignments

### Methods of Evaluation

• Exams
• Homework
• Portfolio
• Problem Solving Exercises
• Quizzes
• Other
Group or individual projects.

### Course Materials

Textbooks:
1. Robert T. Smith and Roland B. Minton. Calculus: Early Transcendental Functions, 4th ed. Prentice-Hall, 2012, ISBN: McGraw Hill
Equivalent text is acceptable