# SRJC Course Outlines

 9/18/2024 7:04:10 AM MATH 8A Course Outline as of Fall 2006 Changed Course CATALOG INFORMATION Discipline and Nbr:  MATH 8A Title:  BRIEF CALCULUS 1 Full Title:  Brief Calculus 1 Last Reviewed:4/19/2010

 Units Course Hours per Week Nbr of Weeks Course Hours Total Maximum 3.00 Lecture Scheduled 3.00 17.5 max. Lecture Scheduled 52.50 Minimum 3.00 Lab Scheduled 0 6 min. Lab Scheduled 0 Contact DHR 0 Contact DHR 0 Contact Total 3.00 Contact Total 52.50 Non-contact DHR 0 Non-contact DHR Total 0

 Total Out of Class Hours:  105.00 Total Student Learning Hours: 157.50

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, continuity, differentiation, analytic geometry, maxima and minima, rates of change and differentials, integration, calculus for exponential and logarithmic functions, calculus of the trigonometric functions, applications and calculator techniques.  The 8A/8B sequence constitutes a complete Brief Calculus course and is intended for students majoring in the life or social sciences.  Students will not receive credit for both Math 8A and Math 1A.

Prerequisites/Corequisites:
Completion of MATH 27 or higher (VF) OR Course Completion or Current Enrollment in MATH 27 ( or MATH 57)

Recommended Preparation:

Limits on Enrollment:

Schedule of Classes Information
Description: Untitled document
Limits, continuity, differentiation, analytic geometry, maxima and minima, rates of change and differentials, integration, calculus for exponential and logarithmic functions, calculus of the trigonometric functions, applications and calculator techniques.  For life or social science majors. Students will not receive credit for both Math 8A and Math 1A

Prerequisites:Completion of MATH 27 or higher (VF) OR Course Completion or Current Enrollment in MATH 27 ( or MATH 57)
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: Fall 2013 Area: BMC Communication and Analytical ThinkingMath Competency CSU GE: Transfer Area Effective: Inactive: B4 Math/Quantitative Reasoning Fall 1992 Fall 2013 IGETC: Transfer Area Effective: Inactive: 2A Mathematical Concepts & Quantitative Reasoning Fall 1993 Fall 2013 CSU Transfer: Transferable Effective: Spring 1992 Inactive: Fall 2013 UC Transfer: Transferable Effective: Spring 1992 Inactive: Fall 2013 C-ID:

Certificate/Major Applicable: Major Applicable Course

COURSE CONTENT

Outcomes and Objectives:
At the conclusion of this course, the student should be able to:
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Upon successful completion of the course, students will be able to:
1.  Calculate limits and use limit notation.
2.  Determine derivatives of polynomial, rational, algebraic,
exponential, and logarithmic functions.
3.  Use techniques of differentiation, including product, quotient,
and chain rules to determine derivatives.
4.  Use derivatives to solve and analyze graphing, optimization, and
science applications.
5.  Determine antiderivatives of polynomial, rational, algebraic,
exponential and logarithmic functions.
6.  Evaluate definite integrals using the fundamental theorem of
calculus.
7.  Apply definite integration to compute area, volume, arc length, and
to solve problems in life sciences, economics and related fields.
8.  Find derivatives and integrals of trigonometric functions.

Topics and Scope
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Instructional methodology may include, but is not limited to:  lecture,
demonstrations, oral recitation, discussion, supervised practice,
independent study, outside project or other assignments.
I.   Precalculus
A. Real number line and order
B. Absolute value
D. Polynomials
E. Rational expressions
F. Functions and graphs
G. Limits and continuity
H. Slope
I. Distance
II.  The Derivative
A. Slope of a curve
B. Rates of change
C. Chain rule
D. Higher order derivatives
E. Implicit differentiation
F. Differentiation of algebraic, logarithmic and exponential
functions
G. Applications of the first and second derivative
1. Curve sketching
2. Optimization problems
3. Related rates
4. Differentials
III. The Integral
A. Antiderivatives and indefinite integrals
B. Definite integral as limit of sum
C. Integration of algebraic, logarithmic and exponential functions
D. Midpoint rule for approximating definite integrals
E. Integration by substitution
F. Applications of the definite integral
1. Area
2. Volume
3. Marginal analysis
IV.  Trigonometric Functions
A. Trigonometric functions and their graphs
B. Derivative and Integral formulas for the trigonometric functions

Assignments:
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1. Daily reading outside of class (approximately 0-50 pages per week).
2. Problem set assignments from required text(s) or supplementary
materials chosen by the instructor.
3. Exams and quizzes.
4. Projects.