# SRJC Course Outlines

 5/12/2021 5:02:06 PM MATH 1A Course Outline as of Fall 2009 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 completion of MATH 25 and MATH 58

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 completion of MATH 25 and MATH 58
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

Outcomes and Objectives:
Upon completion of the course, students will be able to:
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Upon completion of the course, students will be able to:
1.  Calculate limits and use limit notation.
2.  Determine derivatives of polynomial, rational, algebraic, exponential,
logarithmic, and trigonometric functions.
3.  Use techniques of differentiation, including product, quotient, and
chain rules, and determine derivatives implicitly.
4.  Apply derivatives to graphing, optimization, and science applications.
5.  Determine antiderivatives of polynomial, rational, algebraic,
exponential, logarithmic, and trigonometric functions.
6.  Evaluate definite integrals using the fundamental theorem of
calculus.
7.  Use numerical integration to approximate definite integrals.
8.  Apply definite integration to compute area, volumes, and arc length,
and to solve problems in science and related fields.
9.  Evaluate integrals with the use of tables or a computer algebra system.

Topics and Scope
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I.    Limits and Continuity
A. Definitions
1. Limit
2. Basic limit theorems
B. Limits from graphs
C. Continuity
II.  The Derivative
A. Definition
B. Difference quotients
C. Slope of tangent line
D. Velocity, acceleration and rates of change
E. Product, quotient, and chain rules
F. Basic differentiation formulas for algebraic, trigonometric,
logarithmic, exponential, inverse trigonometric and hyperbolic
functions
G. Antiderivatives
III. Applications of the Derivative
A. Implicit differentiation
B. Mean value theorem
C. Differentials
D. Related rates
E. Optimization
F. Separable differential equations
G. Other applications and modeling
H. Indeterminate forms and L'Hospital's rule
IV. The Integral
A. 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
G. Evaluation by tables or computer algebra systems
V.  Applications of the Integral
A. Area
B. Volumes
C. Arc length
D. 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(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).