| 12/21/2024 6:13:36 AM |
| Inactive Course |
| CATALOG INFORMATION
|
| Discipline and Nbr:
MATH 8B | Title:
BRIEF CALCULUS 2 |
|
| Full Title:
Brief Calculus 2 |
| Last Reviewed:3/29/2010 |
| 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 | 17.5 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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Continuation of Math 8A. Techniques of integration; probability and density functions; differential equations; partial derivatives; optimization with constraints; double integrals; applications; series and Taylor polynomials. For life or social science majors. Students will not receive credit for both Math 8B and Math 1B.
Prerequisites/Corequisites:
Completion of MATH 8A or higher (VF)
Recommended Preparation:
Limits on Enrollment:
Schedule of Classes Information
Description:
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Continuation of Math 8A. Techniques of integration; probability and density functions; differential equations; partial derivatives; optimization with constraints; double integrals; applications; series and Taylor polynomials. For life or social science majors. Students will not receive credit for both Math 8B and Math 1B.
(Grade Only)
Prerequisites:Completion of MATH 8A or higher (VF)
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 | Spring 2007 | 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. Evaluate integrals using various methods of integration, including
integration by parts, partial fractions and the use of tables or a
computer algebra system.
2. Approximate definite integrals using numerical integration.
3. Compute variance and analyze probability density functions using
integration and differentiation.
4. Determine partial derivatives of multivariable functions.
5. Analyze series with constant terms using convergence tests.
6. Compute and use Taylor polynomials and Taylor series for elementary
functions.
7. Solve elementary differential equations, including separable and
linear differential equations.
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. L'Hopital's Rule
II. The Integral
A. Techniques of Integration for Algebraic and Trigonometric
Functions
1. Substitution
2. Parts
3. Tables
4. Numerical Methods
B. Improper Integrals
C. Applications
1. Area and Volume
2. Average Value
3. Present Value
III. Probability and Density Functions
A. Continuous Random Variables
B. Expected Value
C. Variance
D. Probability Density Functions
IV. Multivariable Calculus
A. Analytical Geometry in 3-D
B. Functions of Several Variables
C. Level Curves
D. Partial Differentiation
E. Optimization and Constrained Optimization
F. Double Integrals
G. Applications
V. Sequences and Series
A. Convergence and Tests
1. P-series
2. Ratio Test
B. Power Series
1. Taylor's Theorem
2. Taylor Polynomials
C. Newton's Method
VI. Differential Equations
A. Solutions to Differential Equations
B. Separation of Variables
C. First-order Linear Differential Equations
D. Applications
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).
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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