|9/25/2023 11:53:31 AM||
||New Course (First Version)
|Discipline and Nbr:
Calculus, Third Course
|Units||Course Hours per Week|| ||Nbr of Weeks||Course Hours Total
|Maximum||4.00||Lecture Scheduled||4.00||17.5 max.||Lecture Scheduled||70.00
|Minimum||4.00||Lab Scheduled||0||17.5 min.||Lab Scheduled||0
| ||Contact DHR||0|| ||Contact DHR||0
| ||Contact Total||4.00|| ||Contact Total||70.00
| ||Non-contact DHR||0|| ||Non-contact DHR Total||0
Title 5 Category:
AA Degree Applicable
00 - Two Repeats if Grade was D, F, NC, or NP
Also Listed As:
| ||Total Out of Class Hours: 140.00||Total Student Learning Hours: 210.00||
Multivariable calculus including partial differentiation and multiple integration, vector analysis including vector fields, line integrals, surface integrals, and the theorems of Green, Gauss & Stokes. (Formerly taught as MATH 2A)
Course Completion of MATH 1B
Limits on Enrollment:
Schedule of Classes Information
Multivariable calculus including partial differentiation and multiple integration, vector analysis including vector fields, line integrals, surface integrals, and the theorems of Green, Gauss, and Stokes. (Formerly taught as MATH 2A)
Prerequisites:Course Completion of MATH 1B
Limits on Enrollment:
Repeatability:00 - Two Repeats if Grade was D, F, NC, or NP
ARTICULATION, MAJOR, and CERTIFICATION INFORMATION
Major Applicable Course
Outcomes and Objectives:
At the conclusion of this course, the student should be able to:
|Associate Degree:||Effective:||Fall 2010||Inactive:||
|Communication and Analytical Thinking
|CSU GE:||Transfer Area|| ||Effective:||Inactive:
|IGETC:||Transfer Area|| ||Effective:||Inactive:
|CSU Transfer:||Transferable||Effective:||Fall 2010||Inactive:||
|UC Transfer:||Transferable||Effective:||Fall 2010||Inactive:||
| CID Descriptor: MATH 230|| Multivariable Calculus|| SRJC Equivalent Course(s): MATH1B AND MATH1C
Upon completion of the course, students will be able to:
1. Compute partial derivatives, directional derivatives and gradients,
tangent planes and extrema of functions of two variables.
2. Apply chain rules to multivariable and vector functions.
3. Compute and apply area in the plane, double integrals and volume,
center of mass, and moments of inertia.
4. Compute and apply surface area, triple integrals and volume, double integrals in
rectangular and polar coordinate systems, and triple integrals in rectangular, cylindrical,
and spherical coordinate systems.
5. Apply change of variables to evaluate integrals.
6. Apply vector fields, line integrals, independence of path, surface integrals, and the
theorems of Green, Gauss, & Stokes.
7. Use a computer algebra system (CAS) to evaluate partial derivatives and multiple integrals in
various coordinate systems, including rectangular, cylindrical and spherical.
8. Use a computer algebra system to solve problems involving optimization, moments, area, and
9. Use computer graphing technology to visualize three dimensional curves, surfaces and vector
Topics and Scope
I. Functions of Several Variables
A. Surfaces in space
B. Partial derivatives
C. Chain rules
D. Directional derivatives and gradients
E. Tangent planes
F. Extrema of functions of two variables
II. Multiple Integration
A. Area in the plane
B. Double integrals and volume
C. Center of mass and moments of inertia
D. Surface area
E. Triple integrals and volume
F. Triple integrals in cylindrical and spherical coordinate systems
G. Change of variables
III. Vector Analysis
A. Vector fields
B. Line integrals
C. Independence of path
D. Surface integrals
E. Theorems of Green, Gauss & Stokes
A. Computer algebra systems
1. Partial derivatives and multiple integrals
2. Volume and area
B. Visualization of three dimensional graphs
1. Rectangular, cylindrical, spherical coordinate systems
2. Curves, surfaces, contour maps
3. Vector fields
1. Daily reading outside of class (20-50 pages per week).
2. Problem set assignments from required text(s) or supplementary
materials chosen by the instructor (1-6 per week).
3. Quizzes (0-4 per week).
4. Exams (3-8 per term).
5. Projects (for example, computer explorations or modeling activities, 0-10 per term).
Methods of Evaluation/Basis of Grade.
Representative Textbooks and Materials:
|Writing: Assessment tools that demonstrate writing skill and/or require students to select, organize and explain ideas in writing.||Writing
0 - 0%
|This is a degree applicable course but assessment tools based on writing are not included because problem solving assessments are more appropriate for this course.
|Problem solving: Assessment tools, other than exams, that demonstrate competence in computational or non-computational problem solving skills.||Problem Solving
5 - 20%
|Skill Demonstrations: All skill-based and physical demonstrations used for assessment purposes including skill performance exams.||Skill Demonstrations
0 - 0%
|Exams: All forms of formal testing, other than skill performance exams.||Exams
70 - 95%
|Multiple choice and free response exams; quizzes||
|Other: Includes any assessment tools that do not logically fit into the above categories.||Other Category
0 - 10%
Calculus: Early Transcendentals (6th). Stewart, James. Thomson
Thomas' Calculus, Early Transcendentals (11th). Thomas, George, et al.