12/27/2024 5:37:21 AM	MATH 1C Course Outline as of Fall 2014	Changed Course
CATALOG INFORMATION
Discipline and Nbr:  MATH 1C	Title:  CALCULUS 3
Full Title:  Calculus, Third Course
Last Reviewed:9/14/2020

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

Total Out of Class Hours:  140.00

Total Student Learning Hours: 210.00

Title 5 Category:  AA Degree Applicable
Grading:  Grade Only
Repeatability:  00 - Two Repeats if Grade was D, F, NC, or NP
Also Listed As: 
Formerly: 

Catalog Description:

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/Corequisites:
Course Completion of MATH 1B

Recommended Preparation:

Limits on Enrollment:

Schedule of Classes Information
Description:

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)

(Grade Only)
Prerequisites:Course Completion of MATH 1B
Recommended:
Limits on Enrollment:
Transfer Credit:CSU;UC.
Repeatability:00 - Two Repeats if Grade was D, F, NC, or NP

ARTICULATION, MAJOR, and CERTIFICATION INFORMATION

Associate Degree:		Effective:	Fall 2010	Inactive:
Area:	B MC	Communication and Analytical Thinking Math Competency
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:
C-ID:
CID Descriptor: MATH 230	Multivariable Calculus	SRJC Equivalent Course(s): MATH1B AND MATH1C

Certificate/Major Applicable: Major Applicable Course

COURSE CONTENT

Student Learning Outcomes:
At the conclusion of this course, the student should be able to:

1.   State and apply basic definitions, properties and theorems of multivariable calculus.

2.   Compute and apply derivatives and multiple integrals of functions of two or more variables.

3.   Compute and apply vector fields, line integrals, and surface integrals.

4.   Use technology to analyze multivariable functions.

 

Objectives:

Upon completion of the course, students will be able to:

1.  Interpret graphs in cylindrical and spherical coordinate systems.

2.  Determine a limit of a multivariate function at a point.

3.  Determine whether or not a multivariate function is continuous at a point.

4.  Determine the differentiability of a multivariate function at a point.

5.  Compute partial derivatives including higher order derivatives, directional derivatives and gradients,

      tangent planes, extrema and saddle points of functions of two variables.

6.  Find extrema of constrained multivariate functions using the method of Lagrange multipliers.

7.  Apply chain rules to multivariable and vector functions.

8.  Compute and apply area in the plane, double integrals and volume,

      center of mass, and moments of inertia.

9.  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.

10. Apply change of variables to evaluate integrals.

11. Apply vector fields, line integrals, independence of path, surface integrals, and the

       theorems of Green, Gauss, & Stokes.

12. Use a computer algebra system to evaluate partial derivatives and multiple integrals in

       various coordinate systems, including rectangular, cylindrical and spherical.

13. Use a computer algebra system to solve problems involving optimization, moments, area, and

      volume.

14. Use computer graphing technology to visualize three dimensional curves, surfaces and vector

      fields.

15. Identify career objectives related to mathematics.

Topics and Scope

I.   Functions of Several Variables

      A. Introduction to cylindrical and spherical coordinates

      B. Existence of limits and determination of continuity

      C. Existence of derivatives

      D. Surfaces in space

      E. Partial derivatives

      F. Chain rules

      G. Directional derivatives and gradients

      H. Tangent planes

       I.  Extrema of functions of two variables

       J. Lagrange multiplier method

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

IV. Technology

      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

Assignments:

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.

Writing: Assessment tools that demonstrate writing skill and/or require students to select, organize and explain ideas in writing.		Writing 0 - 0%
None
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%
Problem set assigments
Skill Demonstrations: All skill-based and physical demonstrations used for assessment purposes including skill performance exams.		Skill Demonstrations 0 - 0%
None
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%
Projects

Representative Textbooks and Materials:

Calculus:  Early Transcendentals (7th).  Stewart, James.  Thomson

Brooks/Cole:  2012.

Thomas' Calculus, Early Transcendentals (12th).  Thomas, Weir, and Haas

Addison Wesley,  2009.

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