| IV. |
Learning Objectives |
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A. Evaluating definite integrals by using substitution,
integration by parts, and tables. |
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B. Evaluate improper integrals. |
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C. Use integrals to find area, volume and arc length;
application to physics and engineering. |
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D. Evaluating differential equations by Euler’s method
and the separation of variables. |
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E. Evaluating infinite sequences and series. |
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F. Using convergence tests and estimating series. |
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G. Using power series and representing functions by power series. |
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H. Using Taylor and MacLaurin series. |
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I. Understand parametric equations and their applications to differentiation
and integration. |
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J. Understand polar equations and their application to differentiation
and integration. |
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K. Use technology for evaluating integrals, series, and polar and parametric
equations. |
| V. |
Academic Integrity |
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The very nature of higher education requires that students
adhere to accepted standards of academic integrity. Therefore Oakton Community
College has adopted a Code of Academic Conduct and a Statement of Student
Academic Integrity. These may be found in the Student Handbook. You may
also find a summary of the Code of Academic Conduct on the College Catalog.
Among the violations of academic integrity listed and defined are: Cheating,
plagiarism, falsification and fabrication of records and official documents,
personal misrepresentation and proxy, and bribes, favors, and threats. |
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It is the student's responsibility to be aware of behaviors
that constitute academic dishonesty. |
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Pursuant to the due process guarantees contained in the
Policy and Procedures on Student Academic Integrity, the minimum punishment
for the first offense for a student found in violation of the standards
of academic integrity is failure in the assignment. In addition, a disciplinary
record will be established and kept on file in the office of the Vice-President
for Student Affairs for a period of 3 years. |
| VI. |
COURSE TOPICS: |
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A. Techniques of Integration |
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1. Integration by parts |
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2. Integration by substitution |
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3. Integration using tables |
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B. Improper Integrals |
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1. L'Hopital's rule |
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2. Infinite limits of integration |
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3. Integration over discontinuities |
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C. Applications of the Definite Integral |
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1. Volumes using the cross-sectional area |
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2. Volumes of solids of revolution |
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3. Arc length and surface area |
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4. Work, hydrostatic pressure and force, moments and center
of mass |
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D. Modeling and Differential Equations |
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1. Exponential growth and decay |
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2. Separable differential equations |
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3. Logistic models |
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E. Infinite sequences and series |
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1. Sequences and series |
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2. Geometric series |
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3. Tests for positive terms (integral, comparison, ratio, n'th root) |
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4. Alternating series |
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5. Absolute and conditional convergence |
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6. Power series |
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7. Taylor and MacLaurin series |
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8. Applications including binomial series and solutions to differential
equations |
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F. Parametric equations and polar coordinates |
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1. Parametric equations and related calculus |
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2. Graphing with polar coordinates |
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3. Integration and differentiation using polar coordinates |
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4. Applications including area and arclength and surface area |
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G. Recommended Technology |
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1. Use of technology to evaluate integrals |
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2. Use of technology to investigate improper integrals |
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3. Use Euler's method and technology to evaluate differential equations |
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4. Use technology for graphing, integrating, and differentiating parametric
and polar equations |