11/28/2025 2:01:28 PM	MATH C2210 Course Outline as of Fall 2027	Changed Course
CATALOG INFORMATION
Discipline and Nbr:  MATH C2210	Title:  CALCULUS 1
Full Title:  Calculus I: Early Transcendentals
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:  MATH 1A

Catalog Description:

A first course in differential and integral calculus of a single variable. Topics include limits and continuity of functions, techniques and applications of differentiation, an introduction to integration, and the Fundamental Theorem of Calculus. This course is primarily intended for Science, Technology, Engineering, and Mathematics (STEM) majors.

 

Additionally, at SRJC, students who have not passed Precalculus or its equivalent or have a high school GPA below 2.7 in high school are required to take Math 201 concurrently with this course. All students are welcome to enroll concurrently in Math 201 if they would like additional support in this class.

Prerequisites/Corequisites:
Pre-calculus, or college algebra and trigonometry, or equivalent, or placement as determined by the college’s multiple measures assessment process.

Recommended Preparation:

Limits on Enrollment:

Schedule of Classes Information
Description:

A first course in differential and integral calculus of a single variable. Topics include limits and continuity of functions, techniques and applications of differentiation, an introduction to integration, and the Fundamental Theorem of Calculus. This course is primarily intended for Science, Technology, Engineering, and Mathematics (STEM) majors.

 

Additionally, at SRJC, students who have not passed Precalculus or its equivalent or have a high school GPA below 2.7 in high school are required to take Math 201 concurrently with this course. All students are welcome to enroll concurrently in Math 201 if they would like additional support in this class.

(Grade Only)
Prerequisites:Pre-calculus, or college algebra and trigonometry, or equivalent, or placement as determined by the college’s multiple measures assessment process.
Recommended:
Limits on Enrollment:
Transfer Credit:UC.
Repeatability:00 - Two Repeats if Grade was D, F, NC, or NP

ARTICULATION, MAJOR, and CERTIFICATION INFORMATION

Associate Degree:		Effective:	Fall 2025	Inactive:
Area:	B L2 MC	Communication and Analytical Thinking Mathematical Concepts & Quantitative Reasoning Math Competency
CSU GE:	Transfer Area			Effective:	Inactive:
	B4	Math/Quantitative Reasoning		Fall 1981
IGETC:	Transfer Area			Effective:	Inactive:
	2A	Mathematical Concepts & Quantitative Reasoning		Fall 1981
CSU Transfer:		Effective:		Inactive:
UC Transfer:	Transferable	Effective:	Fall 1981	Inactive:
C-ID:
CID Descriptor: MATH 900S	Single Variable Calculus Sequence	SRJC Equivalent Course(s): MATHC2210 AND MATHC2220

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 first semester calculus.

2. Calculate limits, derivatives, definite integrals, and indefinite integrals of algebraic and transcendental functions.

3. Model and solve application problems using derivatives and integrals of algebraic and transcendental functions.

 

Objectives:

Statewide Required Objectives/Outcomes:

 

At the conclusion of this course, the student should be able to (Identical and Required):

1. Compute the limit of a function and evaluate indeterminate forms using L'Hôpital's Rule.

2. Determine the continuity of a function.

3. Find the derivative of a function as a limit.

4. Find the equation of a tangent line to the graph of a function.

5. Compute derivatives using differentiation formulas.

6. Use differentiation to solve applications such as related rate problems and optimization problems.

7. Use implicit differentiation and find derivatives of transcendental functions.

8. Graph functions using methods of calculus.

9. Evaluate a definite integral as a limit.

10. Evaluate integrals using the Fundamental Theorem of Calculus.

11. Apply integration to find areas.

 

Expanded and Additional Local Objectives:

 

 

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

1. Calculate limits and use limit notation.

2. Determine continuity of a function at a real value.

3. Determine derivatives of polynomial, rational, algebraic, exponential, logarithmic, and trigonometric functions.

4. Use techniques of differentiation, including product, quotient, and chain rules; determine derivatives implicitly and determine derivatives of inverse functions.

5. Apply derivatives to graphing, optimization, and science problems.

6. Determine antiderivatives of polynomial, rational, algebraic, exponential, logarithmic, and trigonometric functions.

7. Use limits of Riemann sums to evaluate definite integrals to find areas.

8. Evaluate definite integrals using the fundamental theorem of calculus.

9. Use Trapezoidal and Simpson's Rules to approximate definite integrals.

10. Apply definite integration to compute area, volumes, and arc length, and to solve problems in science and related fields.

11. Evaluate integrals with the use of tables or a computer algebra system.

Topics and Scope

Statewide Required Topics:

 

1. Limits: intuitive and precise definitions; computation using numerical, graphical, and algebraic approaches

2. Continuity and differentiability of functions

3. Derivative as a limit

4. Interpretation of derivatives as slopes of tangent lines and rates of change

5. Differentiation formulas: constants, power rule, product rule, quotient rule, and chain rule

6. Derivatives of transcendental functions including trigonometric, exponential, and logarithmic

7. Implicit differentiation, differentiation of inverse functions, including inverse trigonometric functions

8. Applications of differentiation, including related rates and optimization

9. Higher-order derivatives

10. Indeterminate forms and L'Hôpital's Rule

11. Maximum and minimum values, Extreme Value Theorem

12. Graphing functions using first and second derivatives, concavity, and asymptotes

13. Mean Value Theorem

14. Antiderivatives and indefinite integrals

15. Definite integrals as limits of Riemann sums

16. Interpretation of the integral as area under a curve and net change

17. Basic integration rules and properties of integrals

18. Fundamental Theorem of Calculus

19. Integration by substitution

 

Expanded and Additional Local Topics:

 

I. Limits

    A. Definition

     B. Limits from graphs

    C. Limits evaluated analytically

         1. Limit laws

         2. Limits at infinity

         3. Infinite limits

         4. Indeterminate forms

II. Continuity

    A. Definition

    B. Determining continuity from definition

    C. Continuity from graphs

III. The Derivative

    A. Difference quotient

         1. Slope of the secant line

         2. Average rate of change

    B. Limit definition and evaluating the derivative from the definition

    C. Interpreting the derivative

         1. Slope of the tangent line

         2. Instantaneous rate of change, velocity, acceleration

    D. Rules of differentiation

    E. Product, quotient, and chain rules

    F. Basic differentiation formulas

         1. Algebraic

         2. Trigonometric

         3. Exponential

         4. Logarithmic

         5. Hyperbolic

         6. Inverses of functions

    G. Antiderivatives

IV. Applications of the Derivative

    A. Implicit differentiation

    B. Mean value theorem

    C. Graphing curves

    D. Linearization and differentials

    E. Related rates

    F. Optimization

    G. Other applications and modeling

    H. L'Hôpital's Rule

V.The Integral

    A. Definite integrals as limits of Riemann sums

    B. Definite and indefinite integrals

    C. Fundamental theorem of calculus

    D. Integration of polynomial, logarithmic, exponential, and trigonometric functions

    E. Integration by substitution

    F.  Application of the Integral: Area

Assignments:

1. Reading assignments (20-50 pages per week)

2. Problem sets (1-6)

    a. Assignments from required text(s)

     b. Supplementary materials chosen by the instructor

3. Project(s) (0-10 per term)

    a. Computer explorations

    b. Modeling activities

4. Quizzes (0-4 per week)

5. Exams (2-7)

6. Final Exam

 

Statewide Required Methods of Evaluation:

 

Students should demonstrate their mastery of the learning objectives and their ability to devise, organize, and present complete solutions to problems.

Examples of potential methods of evaluation include, but are not limited to, exams, quizzes, homework, classwork, technology-based activities, laboratory work, projects, and research demonstrations.

Methods of evaluation are at the discretion of local faculty.

 

Expanded and Additional Local Methods of Evaluation: See table below.

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 sets
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:

Statewide Representative Textbooks:

 

A college level textbook designed for science, technology, engineering and math majors, and supporting the learning objectives of this course.

Representative texts:

 

• Strang, G., Herman, E., et al. (2016 & Web 2025). Calculus Volume 1. OER: OpenStax. https://openstax.org/details/books/calculus-volume-1/

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

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

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

 

Texts used by individual institutions and even individual sections will vary.

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