# SRJC Course Outlines

5/25/2022 12:03:00 AM | MATH 1C Course Outline as of Fall 2014
| Changed Course |

CATALOG INFORMATION |
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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 |

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 |
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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:

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% |
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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% |
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Problem set assigments | |||

Skill Demonstrations: All skill-based and physical demonstrations used for assessment purposes including skill performance exams. | Skill Demonstrations 0 - 0% |
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None | |||

Exams: All forms of formal testing, other than skill performance exams. | Exams 70 - 95% |
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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% |
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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.