Cover of: The ABC's of Calculus by
An edition of The ABC's of Calculus (2011)

The ABC's of Calculus

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

The ABC's of Calculus

by

  • 0 Ratings
  • 16 Want to read
  • 0 Currently reading
  • 1 Have read
Publish Date
Publisher
The Nolan Company
Language
English
Pages
730

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Previews available in: English

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

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Subjects
Calculus, mathematics
People
Angelo Mingarelli, Angelo B Mingarelli
Times
2011

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Edition Availability
Cover of: The ABC's of Calculus
The ABC's of Calculus
2011, The Nolan Company
Paperback in English
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Book Details

Published in

Ottawa, Canada

Table of Contents

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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History

Download catalog record: RDF / JSON / OPDS | Wikipedia citation
August 22, 2020 Edited by ISBNbot2 normalize ISBN
September 14, 2014 Edited by Angelo B. Mingarelli Edited without comment.
September 14, 2014 Edited by Angelo B. Mingarelli Edited without comment.
September 14, 2014 Edited by Angelo B. Mingarelli Edited without comment.
September 13, 2014 Created by Angelo B. Mingarelli Added new book.