# SRJC Course Outlines

 2/6/2023 11:50:56 PM MATH 1A Course Outline as of Fall 2021 Changed Course CATALOG INFORMATION Discipline and Nbr:  MATH 1A Title:  CALCULUS 1 Full Title:  Calculus, First Course Last Reviewed:9/14/2020

 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
Repeatability:  00 - Two Repeats if Grade was D, F, NC, or NP
Also Listed As:
Formerly:

Catalog Description:
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Limits and continuity, differentiation, applications of the derivative, integration, applications of the integral.

Prerequisites/Corequisites:
Completion of MATH 27 or higher (MATH); OR Course Completion of MATH 25 and MATH 58; OR AB705 placement into Math Tier 4

Recommended Preparation:

Limits on Enrollment:

Schedule of Classes Information
Description: Untitled document
Limits and continuity, differentiation, applications of the derivative, integration, applications of the integral.

Prerequisites:Completion of MATH 27 or higher (MATH); OR Course Completion of MATH 25 and MATH 58; OR AB705 placement into Math Tier 4
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 1981 Inactive: Area: BMC Communication and Analytical ThinkingMath 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: Transferable Effective: Fall 1981 Inactive: UC Transfer: Transferable Effective: Fall 1981 Inactive: C-ID: CID Descriptor: MATH 900S Single Variable Calculus Sequence SRJC Equivalent Course(s): MATH1A AND MATH1B

Certificate/Major Applicable: Major Applicable Course

COURSE CONTENT

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 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.

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Students will 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
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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'Hospital'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. Numerical integration using Trapezoidal and Simpson's Rules
G. Evaluation by tables or computer algebra systems

VI. Applications of the Integral
A. Area
B. Volumes
C. Arc length
D. Separable differential equations
E. Other applications and modeling

Assignments:
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1. Daily reading outside of class (20-50 pages per week)
2. Problem set assignments from required text or supplementary materials chosen by the instructor (1-6 assignment sets 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)