SRJC Course Outlines

7/13/2024 12:18:22 AMMATH 1C Course Outline as of Fall 2014

Changed Course

Discipline and Nbr:  MATH 1CTitle:  CALCULUS 3  
Full Title:  Calculus, Third Course
Last Reviewed:9/14/2020

UnitsCourse Hours per Week Nbr of WeeksCourse Hours Total
Maximum4.00Lecture Scheduled4.0017.5 max.Lecture Scheduled70.00
Minimum4.00Lab Scheduled017.5 min.Lab Scheduled0
 Contact DHR0 Contact DHR0
 Contact Total4.00 Contact Total70.00
 Non-contact DHR0 Non-contact DHR Total0

 Total Out of Class Hours:  140.00Total 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: 

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)

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)
(Grade Only)

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


Associate Degree:Effective:Fall 2010
Communication and Analytical Thinking
Math Competency
CSU GE:Transfer Area Effective:Inactive:
IGETC:Transfer Area Effective:Inactive:
CSU Transfer:TransferableEffective:Fall 2010Inactive:
UC Transfer:TransferableEffective:Fall 2010Inactive:
 CID Descriptor: MATH 230 Multivariable Calculus SRJC Equivalent Course(s): MATH1B AND MATH1C

Certificate/Major Applicable: Major Applicable Course


Student Learning Outcomes:
At the conclusion of this course, the student should 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
14. Use computer graphing technology to visualize three dimensional curves, surfaces and vector
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
      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

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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).

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%
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%
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%

Representative Textbooks and Materials:
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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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