12/3/2025 11:20:18 PM	MATH 1C Course Outline as of Fall 2027	Changed Course
CATALOG INFORMATION
Discipline and Nbr:  MATH 1C	Title:  CALCULUS 3
Full Title:  Calculus, Third Course
Last Reviewed:11/24/2025

Units		Course Hours per Week			Nbr of Weeks	Course Hours Total
Maximum	5.00	Lecture Scheduled	5.00		17.5 max.	Lecture Scheduled	87.50
Minimum	5.00	Lab Scheduled	0		8 min.	Lab Scheduled	0
		Contact DHR	0			Contact DHR	0
		Contact Total	5.00			Contact Total	87.50
		Non-contact DHR	0			Non-contact DHR Total	0

Total Out of Class Hours:  175.00

Total Student Learning Hours: 262.50

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:

In this course, students will learn 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.

Prerequisites/Corequisites:
Course Completion of MATH C2220 ( or MATH 1B)

Recommended Preparation:

Limits on Enrollment:

Schedule of Classes Information
Description:

In this course, students will learn 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.

(Grade Only)
Prerequisites:Course Completion of MATH C2220 ( or 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): MATHC2220 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. Define and apply topics from solid analytic geometry including quadric surfaces, lines and planes in space, and vectors.

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

5. Use technology to analyze multivariable functions.

 

Objectives:

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

1. Use three dimensional rectangular coordinates.

2. Compute and use determinants, dot products, cross products, and projections.

3. Determine lines and planes in space.

4. Describe velocity and acceleration of particles in the plane and in space using vector functions.

5. Interpret graphs in rectangular, cylindrical, and spherical coordinate systems.

6. Determine a limit of a multivariable function at a point.

7. Determine whether or not a multivariable function is continuous at a point.

8. Determine the differentiability of a multivariable function at a point.

9. Compute partial derivatives including higher order derivatives, directional derivatives, and gradients of functions of two or more variables.

10. Find tangent planes to surfaces.

11. Find extrema and saddle points of two-variable functions using the second derivative test.

12. Find extrema of constrained multivariable functions using the closed bounded set method and Lagrange multipliers.

13. Apply chain rules to multivariable and vector functions.

14. Compute double integrals in rectangular and polar coordinate systems.

15. Compute triple integrals in rectangular, cylindrical, and spherical coordinate systems.

16. Apply multiple integration to find area, surface area, volume, mass, center of mass, and moments of inertia.

17. Evaluate integrals using change of variables.

18. Compute line integrals and surface integrals of scalar functions and over vector fields.

19. Apply independence of path, Green's Theorem, Divergence Theorem (Gauss), and Stokes' Theorem.

20. Use a Computer Algebra System (CAS) to solve problems in multivariable calculus.

21. Use computer graphing technology to plot graphs relevant to multivariable calculus.

Topics and Scope

I. Vectors

    A. Vectors in the plane and in space

    B. Determinants

    C. Dot and cross products

    D. Projections

    E. Lines and planes in space

    F. Differentiation and integration of vector valued functions

    G. Velocity and acceleration

    H. Tangent and normal vectors

    I. Curvature

II. Topics from Solid Analytic Geometry

    A. Rectangular coordinate system

    B. Quadric surfaces

III. Functions of Several Variables

   A. Surfaces, level curves, contour maps

   B. Introduction to cylindrical and spherical coordinates

   C. Limits and continuity

   D. Partial derivatives

   E. Chain rules

   F. Directional derivatives and gradients

   G. Tangent planes and differentiability

   H. Local and absolute extrema of two-variable functions

        1. Second derivative test

        2. Closed bounded set method

        3. Lagrange multipliers

IV. Multiple Integration

   A. Double integrals over general regions

        1. Rectangular coordinates

        2. Polar coordinates

   B. Triple integrals over general regions

        1. Rectangular coordinates

        2. Cylindrical coordinates

        3. Spherical coordinates

   C. Applications

        1. Area in plane

        2. Surface area

        3. Volume

        4. Mass

        5. Center of mass and moments of inertia

   D. Change of variables

V. Vector Analysis

   A. Vector fields, potential functions, gradient fields

   B. Curl and divergence

   C. Line integrals of scalar functions and over vector fields

   D. Conservative vector fields, independence of path and the Fundamental Theorem of Line Integrals

   E. Surface Integrals of scalar functions and over vector fields

   F. Applications of line and surface integrals

        1. Work

        2. Circulation

        3. Flux

        4. Surface area

   G. Green's Theorem, Stokes' Theorem and Divergence Theorem (Gauss)

VI. Technology

   A. Solving problems in multivariable calculus with a CAS.

   B. Producing plots relevant to multivariable calculus using computer graphing technology.

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 (2-7 per term)

5. Final Exam

6. 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%
Quizzes, exams, final exam
Other: Includes any assessment tools that do not logically fit into the above categories.		Other Category 0 - 10%
Projects

Representative Textbooks and Materials:

Calculus Volume 3. Strang, G., Herman, E., et al. https://openstax.org/details/books/calculus-volume-3 4.0 International License (CC BY-NC-SA)

Stewart, J., et al. Calculus: Single Variable Calculus Early Transcendentals. 9th ed.: Cengage. 2021

Briggs, W., et al. Calculus: Early Transcendentals. 3rd ed.: Pearson. 2019. (classic).

Hass, J., et al. Thomas' Calculus: Early Transcendentals. 15th ed.: Pearson. 2023

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