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CALCULUS
II |
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Class Hours: 4.0 |
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Credit Hours: 4.0 |
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Laboratory Hours: 0 |
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Date Revised: Fall 09 |
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Catalog Course Description: |
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Integral calculus with applications. Topics include methods of integration, sequences, series, and an introduction to polar coordinates and differential equations. Applications include real world problems in physics, engineering, economics, and biology. |
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Entry Level Standards: |
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A thorough knowledge of differential calculus including trigonometric functions. |
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Prerequisite: |
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MATH 1910 |
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Textbook(s) and Other Reference Materials Basic to the Course: |
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Textbook: Calculus: Early Transcendentals
by Jon Rogawski,, First Edition, W.H. Freeman and Company, 2008.
Stewart, James. Calculus Concepts and Contexts, Third
Edition. Brooks/Cole, 2001. |
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I. Week/Unit/Topic Basis: |
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Week |
Topic |
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1 |
Antiderivatives, approximating areas, definite integrals |
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2 |
The fundamental theorem of calculus, net change, substitution method |
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3 |
Substitution method |
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4 |
Transcendental functions |
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5 |
Area between curves, volume, density, average value |
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6 |
Volume, numerical integration |
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7 |
Integration by parts, trigonometric integrals, trigonometric substitution, partial fractions |
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8 |
Improper integrals |
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9 |
Arc length, surface area, center of mass |
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10 |
Modeling with differential equations |
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11 |
Sequences, infinite series, convergence |
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12 |
Ratio and root tests, power series, Taylor series |
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13 |
Parametric equations, arc length and speed |
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14 |
Polar coordinates, area and arc length |
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15 |
Final exam |
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II. Course Objectives*: |
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A. |
Evaluate integrals of algebraic and transcendental functions. VI.1-6 |
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B. |
Become familiar with several techniques of integration. VI.1-6 |
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C. |
Evaluate integrals with indeterminate forms. VI.1-6 |
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D. |
Understand the behavior of infinite series. VI.1-6 |
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E |
Solve problems using polar coordinates. VI.1-6 |
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F. |
Apply calculus techniques to real world applications. VI.1-6 |
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*Roman numerals after course objectives reference goals of the TBR program. |
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III. Instructional Processes*: |
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Students will: |
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1. |
Analyze real life problems such as displacement, velocity, acceleration, total area, mass, volume. Mathematics Outcome, Technological Literacy Outcome, Transitional Strategy, Active Learning Strategy |
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2. |
Advance skills in analysis, symbol manipulation, and graphical conceptualization. Mathematics Outcome, Technological Literacy Outcome, Transitional Strategy, Active Learning Strategy |
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3. |
Use graphing calculators and/or computer software to explore integrals. Mathematics Outcome, Technological Literacy Outcome |
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*Strategies and outcomes
listed after instructional processes reference TBR’s goals for strengthening
general education knowledge and skills, connecting coursework to experiences
beyond the classroom, and encouraging students to take active and responsible
roles in the educational process. |
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IV. Expectations for Student Performance*: |
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Upon successful completion of this course, the student should be able to: |
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1. |
Integrate exponential, trigonometric, inverse trigonometric, natural and general logarithmic functions. A |
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2. |
Integrate by parts and by substitution. B |
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3. |
Integrate trigonometric integral using identities. A, B |
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4. |
Integrate rational functions by partial fraction decomposition. B |
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5. |
Use a table of integrals to evaluate an integral. B |
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6. |
Integrate indeterminate forms and improper integral. B, C |
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7. |
Test for convergence and divergence of infinite series. D |
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8. |
Give power series representation of a function. D |
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9. |
Model with differential equations. F |
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10. |
Graph parametric and polar equations. E |
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11. |
Work calculus applications in polar coordinates. E, F |
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*Letters after performance expectations reference the course objectives listed above. |
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V. Evaluation: |
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A. Testing Procedures: |
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Students are evaluated primarily on the basis of tests and quizzes. A minimum of four major tests is recommended. See individual instructor's syllabus. |
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B. Laboratory Expectations: |
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None |
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C. Field Work: |
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None |
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D. Other Evaluation Methods: |
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See individual instructor's syllabus. |
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E. Grading Scale: |
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93 -
100 A |
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VI. Policies: |
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A. Attendance Policy: |
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B. Academic Dishonesty: |
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Academic dishonesty in any form is prohibited and will be dealt with severely. Penalties range from an F or a zero for the specific project or examination to automatic failure for the course for all students involved. Individual instructors must distribute their policy on academic dishonesty during the first week of class. |
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C. Accommodations for Disabilities: |
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Students who need accommodations because of a disability,
have emergency medical information to share, or need special arrangements in
case the building must be evacuated should inform the instructor immediately,
privately after class or in her or his office. Students must present a
current accommodation plan from a staff member in Services for Students with
Disabilities (SSWD) in order to receive accommodations in this course.
Services for Students with Disabilities may be contacted by going to Goins
134 or 126 or by phone: 694-6751(Voice/TTY) or 539-7153. More information is
available at www.pstcc.edu/departments/swd/ |
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D. Cell phones: |
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Cell phones are to be
either turned off or put on vibration mode while in class. Instructor discretion as to penalty. |
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