| 12/21/2024 6:01:15 AM |
| Inactive 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
Grading:
Grade Only
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 of exponential, logarithmic, and trigonometric functions, as well as applications and calculator techniques. For life or social science majors. Students will not receive credit for both Math 8A and Math 1A.
Prerequisites/Corequisites:
Completion of MATH 27 or higher (VF); OR Course Completion of MATH 25 and MATH 58; OR Qualifying Test Score in Math Algebra and Course Completion of MATH 58; OR Qualifying Test Score in Math Trigonometry and Course Completion of MATH 25; OR Qualifying Test Score in Math Algebra and Qualifying Test Score in Math Trigonometry
Recommended Preparation:
Limits on Enrollment:
Schedule of Classes Information
Description:
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Limits, continuity, differentiation, analytic geometry, maxima and minima, rates of change and differentials, integration, calculus of exponential, logarithmic, and trigonometric functions, as well as applications and calculator techniques. For life or social science majors. Students will not receive credit for both Math 8A and Math 1A.
(Grade Only)
Prerequisites:Completion of MATH 27 or higher (VF); OR Course Completion of MATH 25 and MATH 58; OR Qualifying Test Score in Math Algebra and Course Completion of MATH 58; OR Qualifying Test Score in Math Trigonometry and Course Completion of MATH 25; OR Qualifying Test Score in Math Algebra and Qualifying Test Score in Math Trigonometry
Recommended:
Limits on Enrollment:
Transfer Credit:
Repeatability:00 - Two Repeats if Grade was D, F, NC, or NP
ARTICULATION, MAJOR, and CERTIFICATION INFORMATION
| Associate Degree: | Effective: | | Inactive: | |
| Area: | | |
| |
| 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: | | Effective: | | Inactive: | |
| |
| UC Transfer: | | Effective: | | Inactive: | |
| |
| 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
C. Exponents and radicals
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. Homework assignments (10-35).
3. Exams (3-5) and quizzes (0-6) including final exam.
4. Projects (0-2).
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% |
| Homework assignments | |
| 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% |
| Problem solving exams, objective exams and quizzes | |
| Other: Includes any assessment tools that do not logically fit into the above categories. | Other Category
0 - 10% |
| Projects | |
Representative Textbooks and Materials:
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Brief Calculus With Applications (7th ed.). Larson, Ron; Hostetler,
Robert; Edwards, Bruce. Houghton-Mifflin: 2006.
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