Calculus 2, Topics and Exercises for Test 3 and beyond
Dr. Brenton LeMesurier, Spring 2007
The topics to be covered on Test 3 and in the week of classes after that test come from the end of Chapter 11 along with Chapters 9 and 10.
Exercises were previously given for some of these sections but not others, so I will gather them all here to help with Test 3 and Final Exam study.
Chapter 9, Differential Equations
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Section 9.1 Modeling with Differential Equations,
Exercises 1, 6, 7 and 9.
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Section 9.3 Separation of Variables,
Exercises 2, 3, 8, 14.
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Section 9.4 Exponential Growth and Decay,
Exercises 3. 5. 7. 9. 13, 19.
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Section 9.5 The Logistic Equation,
Exercises 3, 5, 7.
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Section 9.6 Linear Equations,
Exercises 2, 4, 5, 10, 11, 15, 17.
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Chapter 9 Review Concept Check 1, 2, 5, 6, 7, 8
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Chapter 9 Review True-False Quiz: all of it.
Chapter 10, Parametric Equations and Polar Coordinates
This Chapter combines calculus with geometry, looking at curves in the plane and the regions inside them using both cartesian and polar coordinates.
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Section 10.1 Curves Defined by Parametric Equations
introduces parametric curves, where both the x and y position coordinates are given as functions of some other variable like t for time.
Exercises 1, 2, 9 and 11.
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Section 10.2 Tangents and Areas,
Exercises 1, 5, 19, 25.
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Section 10.3 Arc Length only (omit surface area).
Exercises 1, 5, 9.
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Section 10.4 Polar Coordinates,
Exercises 16, 17; 35, 42; 57, 63.
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Section 10.5 Areas and Lengths in Polar Coordinates,
Exercises 1, 9, 14, 46, 50.
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Chapter 10 Review Concept Check 1, 2, 3(a), 4, 5.
Chapter 11, last topics
Just the final topics from Chapter 11 will be covered on Test 3: Taylor series and some applications.
Note that a "Maclaurin Series" is simply a Taylor series in the common and simple case where the center "a" is 0, so the form is
f(0)+f'(0)x + f''(0)/2 x2 + ...
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Section 11.10 Taylor (and Maclaurin) Series,
Exercises 1, 2, 3, 8, 13, 23, 27, 33, 37, 41, 49, 53, 56, 58.
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Section 11.11 The Binomial Series,
Exercises 1, 3, 11, 18.
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Chapter 11 Review Concept Check 8, 9, 10(a-c), 11, 12.
http://www.cofc.edu/~lemesurierb/math220/math220-Test3-Study-etc.html
Brenton leMesurier, Department of Mathematics, College of Charleston
Friday April 13, 2007.