MATH C280: Calculus 3
| Item | Value |
|---|---|
| Curriculum Committee Approval Date | 09/25/2017 |
| Top Code | 170100 - Mathematics, General |
| Units | 5 Total Units |
| Hours | 90 Total Hours (Lecture Hours 90) |
| Total Outside of Class Hours | 0 |
| Course Credit Status | Credit: Degree Applicable (D) |
| Material Fee | No |
| Basic Skills | Not Basic Skills (N) |
| Repeatable | No |
| Grading Policy | Standard Letter (S),
|
| Local General Education (GE) |
|
| California General Education Transfer Curriculum (Cal-GETC) |
|
| Intersegmental General Education Transfer Curriculum (IGETC) |
|
| California State University General Education Breadth (CSU GE-Breadth) |
|
Course Description
Multivariable calculus including vectors, vector-valued functions, functions of several variables, partial derivatives, multiple integrals, calculus of vector fields, Green's Theorem, Stokes' Theorem, and the Divergence Theorem. PREREQUISITE: MATH C185. Transfer Credit: CSU; UC. C-ID: MATH 230.C-ID: MATH 230.
Course Level Student Learning Outcome(s)
- Apply multiple integrals, principles of differential calculus, and integration to solve problems involving vector fields and calculate partial derivatives.
Course 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;
- 9. Compute arc length;
- 10. Find the divergence and curl of a vector field;
- 11. Evaluate two and three dimensional integrals; and
- 12. Apply Greens, Stokes, and divergence theorems.
Lecture Content
Vectors and vector operations in two and three dimensions Level curves and surfaces, divergence and curl The gradient vector field; and the change of variables theorem 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, higher-order derivatives, directional derivatives, and the gradient Arc length and curvature; tangent, normal, binormal vectors Vector-valued functions and their derivatives and integrals; finding velocity and acceleration Real-valued 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 real-valued functions over surfaces Divergence and curl Greens, Stokes, and divergence theorems
Method(s) of Instruction
- Lecture (02)
- DE Online Lecture (02X)
- Video one-way (ITV, video) (63)
Instructional Techniques
Deliver lectures of course content. Assign homework and quizzes. Relate material in the course to real life and the outside world. Require participation including student-to-student and student-to-instructor interaction through the use of small-group activities and whole-class discussion. Apply technologies to increase learner motivation such as Scientific and/or Graphing Calculator and computer software such as Wolfram
Reading Assignments
Alpha. Objective Examinations Midterm Exam (comprehensive) Final Exam (comprehensive)
Writing Assignments
MyMathLab online assignments
Out-of-class Assignments
Topics covered and examples from textbook
Demonstration of Critical Thinking
Final Exam Midterm Exam Objective Examinations Problem Solving Exercises Projects (ind/group) Report Short Quizzes Skills Demonstration Written Assignments
Required Writing, Problem Solving, Skills Demonstration
Demonstrate understanding of concepts and provide the appropriate solutions through homework problems, quizzes, and exams in writing.
Eligible Disciplines
Mathematics: Masters degree in mathematics or applied mathematics OR bachelors degree in either of the above AND masters degree in statistics, physics, or mathematics education OR the equivalent. Masters degree required.
Manuals Resources
1. Required Briggs, William; Chchran, Lyle; Gillett, Bernard. Calculus; Early Transcendentals, 2nd ed. Pearson, 2015