An edition of The ABC's of Calculus (2011)

# The ABC's of Calculus

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August 22, 2020 | History
An edition of The ABC's of Calculus (2011)

# The ABC's of Calculus

• 0 Ratings
Publish Date
Publisher
Language
English
Pages
730

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Previews available in: English

Single variable differential and integral Calculus and its applications. 2011 Edition.

Edition Availability
The ABC's of Calculus
2011, The Nolan Company
Paperback in English

## Book Details

### Published in

 Preface to the e-text edition vii 1 Functions and Their Properties 1 1.1 The Meaning of a Function 1 1.2 Function Values and the Box Method 5 1.3 The Absolute Value of a Function 12 1.4 A Quick Review of Inequalities 21 1.4 .1 The triangle inequalities 23 1.5 Chapter Exercises 30 1.6 Using Computer Algebra Systems (CAS), 31 2 Limits and Continuity 33 2.1 One-Sided Limits of Functions 35 2.2 Two-Sided Limits and Continuity 40 2.3 Important Theorems About Continuous Functions 59 2.4 Evaluating Limits at Inﬁnity 63 2.5 How to Guess a Limit 66 2.6 Chapter Exercises 76 3 The Derivative of a Function 79 3.1 Motivation 80 3.2 Working with Derivatives 89 3.3 The Chain Rule 95 3.4 Implicit Functions and Their Derivatives 108 3.5 Derivatives of Trigonometric Functions 113 3.6 Important Results About Derivatives 121 3.7 Inverse Functions 128 3.8 Inverse Trigonometric Functions 136 3.9 Derivatives of Inverse Trigonometric Functions 140 3.1.0 Relating Rates of Change 143 3.1.1 Newton’s Method for Calculating Roots 151 3.1.2 L’Hospital’s Rule 161 3.1.3 Chapter Exercises 173 3.1.4 Challenge Questions 174 3.1.5 Using Computer Algebra Systems 175 4 Exponentials and Logarithms 177 4.1 Exponential Functions and Their Logarithms 178 4.2 Euler’s Number, e = 2.718281828 184 4.3 Euler’s Exponential Function and the Natural Logarithm 189 4.4 Derivative of the Natural Logarithm 193 4.5 Diﬀerentiation Formulae for General Exponential Functions . . . 196 4.6 Diﬀerentiation Formulae for General Logarithmic Functions . . . 201 4.7 Applications 204 4.8 Chapter Exercises 210 4.9 Using Computer Algebra Systems 211 5 Curve Sketching 213 5.1 Solving Polynomial Inequalities 213 5.2 Solving Rational Function Inequalities 225 5.3 Graphing Techniques 232 5.4 Application of Derivatives to Business and Economics 256 5.5 Single variable optimization problems 258 5.6 Chapter Exercises 259 6 Integration 261 6.1 Antiderivatives and the Indeﬁnite Integral 262 6.2 Deﬁnite Integrals 277 6.3 The Summation Convention 286 6.4 Area and the Riemann Integral 291 6.5 Chapter Exercises 304 6.6 Using Computer Algebra Systems 306 7 Techniques of Integration 309 7.1 Trigonometric Identities 309 7.2 The Substitution Rule 311 7.3 Integration by Parts 323 7.3 .1 The Product of a Polynomial and a Sine or Cosine 328 7.3 .2 The Product of a Polynomial and an Exponential 331 7.3 .3 The Product of a Polynomial and a Logarithm 334 7.3 .4 The Product of an Exponential and a Sine or Cosine . . . 337 7.4 Partial Fractions 346 7.4 .1 Review of Long Division of Polynomials 347 7.4 .2 The Integration of Partial Fractions 350 7.5 Products of Trigonometric Functions 365 7.5 .1 Products of Sines and Cosines 365 7.5 .2 Fourier Coeﬃcients 374 7.5 .3 Products of Secants and Tangents 378 7.6 Trigonometric Substitutions 386 7.6 .1 Completing the Square in a Quadratic (Review) 386 7.6 .2 Trigonometric Substitutions 390 7.7 Numerical Integration 400 7.7 .1 The Trapezoidal Rule 401 7.7 .2 Simpson’s Rule for n Even 408 7.8 Improper Integrals 414 7.9 Rationalizing Substitutions 429 7.9 .1 Integrating rational functions of trigonometric expressions 432 7.10 Chapter Exercises 437 7.11 Using Computer Algebra Systems 443 8 Applications of the Integral 445 8.1 Motivation 445 8.2 Finding the Area Between Two Curves 448 8.3 The Volume of a Solid of Revolution 464 8.4 Measuring the length of a curve 477 8.5 Moments and Centers of Mass 489 8.6 Chapter Exercises 502 8.7 Using Computer Algebra Systems 502 9 Simple Diﬀerential Equations 505 9.1 Why Study Diﬀerential Equations? 505 9.2 First-order Separable Equations 512 9.3 Laws of Growth and Decay 518 9.4 Using Computer Algebra Systems 525 10 Multivariable Optimization Techniques 527 10.1 Functions of More Than One Variable 527 10.2 Continuity 528 10.2 .1 Discontinuity at a point 529 10.3 Partial Derivatives 531 10.4 Higher Order Partial Derivatives 533 10.5 The Chain Rule for Partial Derivatives 535 10.6 Extrema of Functions of Two Variables 540 10.6 .1 Maxima and Minima 540 10.6 .2 The method of Lagrange multipliers 544 10.7 Chapter Exercises 551 11 Advanced Topics 553 11.1 Inﬁnite Sequences 553 11.2 Sequences with Inﬁnite Limits 560 11.3 Limits from the Right 563 11.4 Limits from the Left 569 11.5 Summary 575 11.6 Continuity 576 11.7 Limits of Functions at Inﬁnity 578 11.8 Inﬁnite Limits of Functions 581 11.9 The Epsilon-Delta Method of Proof 585 12 Appendix A: Review of Exponents and Radicals 597 13 Appendix B: The Straight Line 603 14 Appendix C: A Quick Review of Trigonometry 609 14.1 The right-angled isosceles triangle (RT45) 610 14.2 The RT30 triangle 610 14.3 The basic trigonometric functions 611 14.4 Identities 613 14.4.1 The Law of Sines 614 14.4.2 The Law of Cosines 615 14.4.3 Identities for the sum and diﬀerence of angles 616 15 Appendix D: The Natural Domain of a Function 623 Solutions Manual 627 1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627 1.2 Exercise Set 1 (page 10) 627 1.3 Exercise Set 2 (page 19) 627 1.4 Exercise Set 3 (page 28) 628 1.5 Chapter Exercises (page 30 ) 629 Solutions 631 2.1 Exercise Set 4 (page 39) 631 2.2 Exercise Set 5 (page 45) 631 2.2 Exercise Set 6 (page 49) 631 2.2 Exercise Set 7 (page 56) 632 2.2 Exercise Set 8 (page 57) 632 2.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633 2.4 Exercise Set 9 (page 65) 633 2.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633 2.6 Chapter Exercises (page 76) 633 Solutions 635 3.1 Exercise Set 10 (page 88) 635 3.2 Exercise Set 11 (page 93) 635 3.3 Exercise Set 12 (page 105) 636 3.4 Exercise Set 13 (page 112) 637 3.5 Exercise Set 14 (page 119) 637 3.6 Exercise Set 15 (page 127) 637 3.7 Exercise Set 16 (page 134) 639 3.8 Exercise Set 17 (page 139) 639 3.9 Exercise Set 18 (page 142) 639 3.1.0 Special Exercise Set (page 149) 640 3.1.1 Exercise Set 19 (page 160) 640 3.1.2 Exercise Set 20 (page 172) 641 3.1.3 Chapter Exercises (page 173) 641 Solutions 643 4.1 Exercise Set 21 (page 183) 643 4.2 Exercise Set 22 (page 188) 643 4.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644 4.4 Exercise Set 23 (page 196) 644 4.5 Exercise Set 24 (page 199) 644 4.6 Exercise Set 25 (page 203) 645 4.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646 4.8 Chapter Exercises (page 210) 646 Solutions 649 5.1 Exercise Set 26 (page 216) 649 5.2 Exercise Set 27 (page 223) 649 5.3 Exercise Set 28 (page 230) 650 5.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652 5.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652 5.6 Single variable optimization problems (page 258) 653 5.7 Chapter Exercises: Use Plotter (page 259) 654 Solutions 657 6.1 Exercise Set 29 (page 275) 657 6.2 Exercise Set 30 (page 289) 657 6.3 Exercise Set 31 (page 284) 659 6.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 660 6.5 Chapter Exercises (page 304) 660 Solutions 665 7.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665 7.2 Exercise Set 32 (page 321) 665 7.3 Exercise Set 33 (page 345) 666 7.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667 7.4 .1 Exercise Set 34 (page 349) 667 7.4 .2 Exercise Set 35 (page 364) 668 7.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 670 7.5 .1 Exercise Set 36 (page 373) 670 7.5 .2 Exercise Set 37 (page 385) 671 7.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672 7.6 .1 Exercise Set 38 (page 390) 672 7.6 .2 Exercise Set 39 (page 398) 673 7.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675 7.7 .1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675 7.7 .2 Exercise Set 40 (page 411) 675 7.8 Exercise Set 41 (page 426) 677 7.9 Chapter Exercises (page 437) 678 Solutions 693 8.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693 8.2 Exercise Set 42 (page 452) 693 8.2 .1 Exercise Set 43 (page 462) 694 8.3 Exercise Set 44 (page 476) 695 8.4 Exercise Set 45 (page 487) 696 8.5 Exercise Set 46 (page 500) 697 8.6 Chapter Exercises (page 502) 698 Solutions 701 9.1 Exercise Set 47 (page 511) 701 9.2 Exercise Set 48 (page 518) 701 9.3 Exercise Set 49 (page 523) 702 Solutions 705 10.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705 10.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705 10.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705 10.4 Exercise Set 50 (page 535) 705 10.5 Exercise Set 51 (page 548) 706 10.6 Chapter Exercises (page 551) 707 Solutions 711 11.1 Exercise Set 52 (page 559) 711 11.2 Exercise Set 53 (page 563) 711 11.3 Exercise Set 54 (page 574) 712 11.4 Exercise Set 55 (page 580) 712 11.5 Exercise Set 56 (page 584) 712 11.6 Exercise Set 57 (page 594) 713 Solutions to Problems in the Appendices 715 1 APPENDIX A - Exercise Set 58 (page 601) 715 12.2 APPENDIX B - Exercise Set 59 (page 607) 716 12.3 APPENDIX C - Exercise Set 60 (page 620) 716 12.4 APPENDIX D - Exercise Set 61 (page 626) 718 Acknowledgments 719 Credits 721 About the Author 723 Index 724

### The Physical Object

Format
Paperback
Pagination
xvii, 730p.
Number of pages
730
Dimensions
11 x 8.5 x 1.75 inches
Weight
1 pounds

### ID Numbers

Open Library
OL25620672M
Internet Archive
angelomingarelli
ISBN 13
9780969888956

#### Work Description

A course on single variable differential and integral calculus with a different twist.

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