# SRJC Course Outlines

 5/25/2022 12:03:00 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
Repeatability:  00 - Two Repeats if Grade was D, F, NC, or NP
Also Listed As:
Formerly:

Catalog Description:
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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: Untitled document
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
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: BMC Communication and Analytical ThinkingMath 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:

Certificate/Major Applicable: Major Applicable Course

COURSE CONTENT

Student Learning Outcomes:
Upon completion of the course, students will be able to:
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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: Untitled document
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
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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
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:
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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).