Calculus II - Tunc Geveci.pdf

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Calculus II
{
Tunc Geveci
Copyright © 2011 by Tunc Geveci. All rights reserved. No part of this publication may be reprinted,
reproduced, transmitted, or utilized in any form or by any electronic, mechanical, or other means,
now known or hereafter invented, including photocopying, microfilming, and recording, or in any
information retrieval system without the written permission of University Readers, Inc.
First published in the United States of America in 2011 by Cognella, a division of University
Readers, Inc.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and
are used only for identification and explanation without intent to infringe.
15 14 13 12 11
12345
Printed in the United States of America
ISBN:
978-1-935551-44-7  
Contents
6 Techniques of Integration
6.1 Integration by Parts . . . . . . . . . . . . .
6.2 Integrals of Rational Functions . . . . . . .
6.3 Integrals of Some Trigonometric and
Hyperbolic Functions . . . . . . . . . . . . .
6.4 Trigonometric and Hyperbolic Substitutions
6.5 Numerical Integration . . . . . . . . . . . .
6.6 Improper Integrals: Part 1 . . . . . . . . . .
6.7 Improper Integrals: Part 2 . . . . . . . . . .
7 Applications of Integration
7.1 Volumes by Slices or Cylindrical Shells . .
7.2 Length and Area . . . . . . . . . . . . . .
7.3 Some Physical Applications of the Integral
7.4 The Integral and Probability . . . . . . .
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1
1
13
27
43
55
65
79
89
89
99
111
121
133
133
148
157
171
179
187
187
197
207
217
228
241
253
264
272
285
285
294
305
310
316
325
8 Differential Equations
8.1 First-Order Linear Differential Equations . . . . . . . . .
8.2 Applications of First-Order Linear Differential Equations
8.3 Separable Differential Equations . . . . . . . . . . . . . .
8.4 Applications of Separable Differential Equations . . . . .
8.5 Approximate Solutions and Slope Fields . . . . . . . . . .
9 Infinite Series
9.1 Taylor Polynomials: Part 1 . . . . . . .
9.2 Taylor Polynomials: Part 2 . . . . . . .
9.3 The Concept of an Infinite Series . . . .
9.4 The Ratio Test and the Root Test . . .
9.5 Power Series: Part 1 . . . . . . . . . . .
9.6 Power Series: Part 2 . . . . . . . . . . .
9.7 The Integral Test and Comparison Tests
9.8 Conditional Convergence . . . . . . . . .
9.9 Fourier Series . . . . . . . . . . . . . . .
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10 Parametrized Curves and Polar Coordinates
10.1 Parametrized Curves . . . . . . . . . . . . . .
10.2 Polar Coordinates . . . . . . . . . . . . . . .
10.3 Tangents and Area in Polar Coordinates . . .
10.4 Arc Length of Parametrized Curves . . . . . .
10.5 Conic Sections . . . . . . . . . . . . . . . . .
10.6 Conic Sections in Polar Coordinates . . . . .
iii
iv
H Taylor’s Formula for the Remainder
I
Answers to Some Problems
CONTENTS
335
341
371
J Basic Differentiation and Integration formulas

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