The ABC's of Calculus
Publisher: The Nolan Company
Published: 2011
Place of publication: Ottawa, Canada
Language: eng
Format: Paperback
Number of pages: 730
ISBN-13: 9780969888956
Description: Single variable differential and integral Calculus and its applications. 2011 Edition.
Table of contents: label: Preface to the e-text edition
title: vii; label: 1
title: Functions and Their Properties
pagenum: 1; label: 1.1
title: The Meaning of a Function
pagenum: 1; label: 1.2
title: Function Values and the Box Method
pagenum: 5; label: 1.3
title: The Absolute Value of a Function
pagenum: 12; label: 1.4
title: A Quick Review of Inequalities
pagenum: 21; label: 1.4 .1
title: The triangle inequalities
pagenum: 23; label: 1.5
title: Chapter Exercises
pagenum: 30; label: 1.6
title: Using Computer Algebra Systems (CAS),
pagenum: 31; label: 2
title: Limits and Continuity
pagenum: 33; label: 2.1
title: One-Sided Limits of Functions
pagenum: 35; label: 2.2
title: Two-Sided Limits and Continuity
pagenum: 40; label: 2.3
title: Important Theorems About Continuous Functions
pagenum: 59; label: 2.4
title: Evaluating Limits at Inﬁnity
pagenum: 63; label: 2.5
title: How to Guess a Limit
pagenum: 66; label: 2.6
title: Chapter Exercises
pagenum: 76; label: 3
title: The Derivative of a Function
pagenum: 79; label: 3.1
title: Motivation
pagenum: 80; label: 3.2
title: Working with Derivatives
pagenum: 89; label: 3.3
title: The Chain Rule
pagenum: 95; label: 3.4
title: Implicit Functions and Their Derivatives
pagenum: 108; label: 3.5
title: Derivatives of Trigonometric Functions
pagenum: 113; label: 3.6
title: Important Results About Derivatives
pagenum: 121; label: 3.7
title: Inverse Functions
pagenum: 128; label: 3.8
title: Inverse Trigonometric Functions
pagenum: 136; label: 3.9
title: Derivatives of Inverse Trigonometric Functions
pagenum: 140; label: 3.1.0
title: Relating Rates of Change
pagenum: 143; label: 3.1.1
title: Newton’s Method for Calculating Roots
pagenum: 151; label: 3.1.2
title: L’Hospital’s Rule
pagenum: 161; label: 3.1.3
title: Chapter Exercises
pagenum: 173; label: 3.1.4
title: Challenge Questions
pagenum: 174; label: 3.1.5
title: Using Computer Algebra Systems
pagenum: 175; label: 4
title: Exponentials and Logarithms
pagenum: 177; label: 4.1
title: Exponential Functions and Their Logarithms
pagenum: 178; label: 4.2
title: Euler’s Number, e = 2.718281828
pagenum: 184; label: 4.3
title: Euler’s Exponential Function and the Natural Logarithm
pagenum: 189; label: 4.4
title: Derivative of the Natural Logarithm
pagenum: 193; label: 4.5
title: Diﬀerentiation Formulae for General Exponential Functions . . .
pagenum: 196; label: 4.6
title: Diﬀerentiation Formulae for General Logarithmic Functions . . .
pagenum: 201; label: 4.7
title: Applications
pagenum: 204; label: 4.8
title: Chapter Exercises
pagenum: 210; label: 4.9
title: Using Computer Algebra Systems
pagenum: 211; label: 5
title: Curve Sketching
pagenum: 213; label: 5.1
title: Solving Polynomial Inequalities
pagenum: 213; label: 5.2
title: Solving Rational Function Inequalities
pagenum: 225; label: 5.3
title: Graphing Techniques
pagenum: 232; label: 5.4
title: Application of Derivatives to Business and Economics
pagenum: 256; label: 5.5
title: Single variable optimization problems
pagenum: 258; label: 5.6
title: Chapter Exercises
pagenum: 259; label: 6
title: Integration
pagenum: 261; label: 6.1
title: Antiderivatives and the Indeﬁnite Integral
pagenum: 262; label: 6.2
title: Deﬁnite Integrals
pagenum: 277; label: 6.3
title: The Summation Convention
pagenum: 286; label: 6.4
title: Area and the Riemann Integral
pagenum: 291; label: 6.5
title: Chapter Exercises
pagenum: 304; label: 6.6
title: Using Computer Algebra Systems
pagenum: 306; label: 7
title: Techniques of Integration
pagenum: 309; label: 7.1
title: Trigonometric Identities
pagenum: 309; label: 7.2
title: The Substitution Rule
pagenum: 311; label: 7.3
title: Integration by Parts
pagenum: 323; label: 7.3 .1
title: The Product of a Polynomial and a Sine or Cosine
pagenum: 328; label: 7.3 .2
title: The Product of a Polynomial and an Exponential
pagenum: 331; label: 7.3 .3
title: The Product of a Polynomial and a Logarithm
pagenum: 334; label: 7.3 .4
title: The Product of an Exponential and a Sine or Cosine . . .
pagenum: 337; label: 7.4
title: Partial Fractions
pagenum: 346; label: 7.4 .1
title: Review of Long Division of Polynomials
pagenum: 347; label: 7.4 .2
title: The Integration of Partial Fractions
pagenum: 350; label: 7.5
title: Products of Trigonometric Functions
pagenum: 365; label: 7.5 .1
title: Products of Sines and Cosines
pagenum: 365; label: 7.5 .2
title: Fourier Coeﬃcients
pagenum: 374; label: 7.5 .3
title: Products of Secants and Tangents
pagenum: 378; label: 7.6
title: Trigonometric Substitutions
pagenum: 386; label: 7.6 .1
title: Completing the Square in a Quadratic (Review)
pagenum: 386; label: 7.6 .2
title: Trigonometric Substitutions
pagenum: 390; label: 7.7
title: Numerical Integration
pagenum: 400; label: 7.7 .1
title: The Trapezoidal Rule
pagenum: 401; label: 7.7 .2
title: Simpson’s Rule for n Even
pagenum: 408; label: 7.8
title: Improper Integrals
pagenum: 414; label: 7.9
title: Rationalizing Substitutions
pagenum: 429; label: 7.9 .1
title: Integrating rational functions of trigonometric expressions
pagenum: 432; label: 7.10
title: Chapter Exercises
pagenum: 437; label: 7.11
title: Using Computer Algebra Systems
pagenum: 443; label: 8
title: Applications of the Integral
pagenum: 445; label: 8.1
title: Motivation
pagenum: 445; label: 8.2
title: Finding the Area Between Two Curves
pagenum: 448; label: 8.3
title: The Volume of a Solid of Revolution
pagenum: 464; label: 8.4
title: Measuring the length of a curve
pagenum: 477; label: 8.5
title: Moments and Centers of Mass
pagenum: 489; label: 8.6
title: Chapter Exercises
pagenum: 502; label: 8.7
title: Using Computer Algebra Systems
pagenum: 502; label: 9
title: Simple Diﬀerential Equations
pagenum: 505; label: 9.1
title: Why Study Diﬀerential Equations?
pagenum: 505; label: 9.2
title: First-order Separable Equations
pagenum: 512; label: 9.3
title: Laws of Growth and Decay
pagenum: 518; label: 9.4
title: Using Computer Algebra Systems
pagenum: 525; label: 10
title: Multivariable Optimization Techniques
pagenum: 527; label: 10.1
title: Functions of More Than One Variable
pagenum: 527; label: 10.2
title: Continuity
pagenum: 528; label: 10.2 .1
title: Discontinuity at a point
pagenum: 529; label: 10.3
title: Partial Derivatives
pagenum: 531; label: 10.4
title: Higher Order Partial Derivatives
pagenum: 533; label: 10.5
title: The Chain Rule for Partial Derivatives
pagenum: 535; label: 10.6
title: Extrema of Functions of Two Variables
pagenum: 540; label: 10.6 .1
title: Maxima and Minima
pagenum: 540; label: 10.6 .2
title: The method of Lagrange multipliers
pagenum: 544; label: 10.7
title: Chapter Exercises
pagenum: 551; label: 11
title: Advanced Topics
pagenum: 553; label: 11.1
title: Inﬁnite Sequences
pagenum: 553; label: 11.2
title: Sequences with Inﬁnite Limits
pagenum: 560; label: 11.3
title: Limits from the Right
pagenum: 563; label: 11.4
title: Limits from the Left
pagenum: 569; label: 11.5
title: Summary
pagenum: 575; label: 11.6
title: Continuity
pagenum: 576; label: 11.7
title: Limits of Functions at Inﬁnity
pagenum: 578; label: 11.8
title: Inﬁnite Limits of Functions
pagenum: 581; label: 11.9
title: The Epsilon-Delta Method of Proof
pagenum: 585; label: 12
title: Appendix A: Review of Exponents and Radicals
pagenum: 597; label: 13
title: Appendix B: The Straight Line
pagenum: 603; label: 14
title: Appendix C: A Quick Review of Trigonometry
pagenum: 609; label: 14.1
title: The right-angled isosceles triangle (RT45)
pagenum: 610; label: 14.2
title: The RT30 triangle
pagenum: 610; label: 14.3
title: The basic trigonometric functions
pagenum: 611; label: 14.4
title: Identities
pagenum: 613; label: 14.4.1
title: The Law of Sines
pagenum: 614; label: 14.4.2
title: The Law of Cosines
pagenum: 615; label: 14.4.3
title: Identities for the sum and diﬀerence of angles
pagenum: 616; label: 15
title: Appendix D: The Natural Domain of a Function
pagenum: 623; label: Solutions Manual
title: 627; label: 1.1
title: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
pagenum: 627; label: 1.2
title: Exercise Set 1 (page 10)
pagenum: 627; label: 1.3
title: Exercise Set 2 (page 19)
pagenum: 627; label: 1.4
title: Exercise Set 3 (page 28)
pagenum: 628; label: 1.5
title: Chapter Exercises (page 30 )
pagenum: 629; label: Solutions
pagenum: 631; label: 2.1
title: Exercise Set 4 (page 39)
pagenum: 631; label: 2.2
title: Exercise Set 5 (page 45)
pagenum: 631; label: 2.2
title: Exercise Set 6 (page 49)
pagenum: 631; label: 2.2
title: Exercise Set 7 (page 56)
pagenum: 632; label: 2.2
title: Exercise Set 8 (page 57)
pagenum: 632; label: 2.3
title: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
pagenum: 633; label: 2.4
title: Exercise Set 9 (page 65)
pagenum: 633; label: 2.5
title: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
pagenum: 633; label: 2.6
title: Chapter Exercises (page 76)
pagenum: 633; label: Solutions
pagenum: 635; label: 3.1
title: Exercise Set 10 (page 88)
pagenum: 635; label: 3.2
title: Exercise Set 11 (page 93)
pagenum: 635; label: 3.3
title: Exercise Set 12 (page 105)
pagenum: 636; label: 3.4
title: Exercise Set 13 (page 112)
pagenum: 637; label: 3.5
title: Exercise Set 14 (page 119)
pagenum: 637; label: 3.6
title: Exercise Set 15 (page 127)
pagenum: 637; label: 3.7
title: Exercise Set 16 (page 134)
pagenum: 639; label: 3.8
title: Exercise Set 17 (page 139)
pagenum: 639; label: 3.9
title: Exercise Set 18 (page 142)
pagenum: 639; label: 3.1.0
title: Special Exercise Set (page 149)
pagenum: 640; label: 3.1.1
title: Exercise Set 19 (page 160)
pagenum: 640; label: 3.1.2
title: Exercise Set 20 (page 172)
pagenum: 641; label: 3.1.3
title: Chapter Exercises (page 173)
pagenum: 641; label: Solutions
pagenum: 643; label: 4.1
title: Exercise Set 21 (page 183)
pagenum: 643; label: 4.2
title: Exercise Set 22 (page 188)
pagenum: 643; label: 4.3
title: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
pagenum: 644; label: 4.4
title: Exercise Set 23 (page 196)
pagenum: 644; label: 4.5
title: Exercise Set 24 (page 199)
pagenum: 644; label: 4.6
title: Exercise Set 25 (page 203)
pagenum: 645; label: 4.7
title: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
pagenum: 646; label: 4.8
title: Chapter Exercises (page 210)
pagenum: 646; label: Solutions
pagenum: 649; label: 5.1
title: Exercise Set 26 (page 216)
pagenum: 649; label: 5.2
title: Exercise Set 27 (page 223)
pagenum: 649; label: 5.3
title: Exercise Set 28 (page 230)
pagenum: 650; label: 5.4
title: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
pagenum: 652; label: 5.5
title: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
pagenum: 652; label: 5.6
title: Single variable optimization problems (page 258)
pagenum: 653; label: 5.7
title: Chapter Exercises: Use Plotter (page 259)
pagenum: 654; label: Solutions
pagenum: 657; label: 6.1
title: Exercise Set 29 (page 275)
pagenum: 657; label: 6.2
title: Exercise Set 30 (page 289)
pagenum: 657; label: 6.3
title: Exercise Set 31 (page 284)
pagenum: 659; label: 6.4
title: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
pagenum: 660; label: 6.5
title: Chapter Exercises (page 304)
pagenum: 660; label: Solutions
title: 665; label: 7.1
title: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
pagenum: 665; label: 7.2
title: Exercise Set 32 (page 321)
pagenum: 665; label: 7.3
title: Exercise Set 33 (page 345)
pagenum: 666; label: 7.4
title: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
pagenum: 667; label: 7.4 .1
title: Exercise Set 34 (page 349)
pagenum: 667; label: 7.4 .2
title: Exercise Set 35 (page 364)
pagenum: 668; label: 7.5
title: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
pagenum: 670; label: 7.5 .1
title: Exercise Set 36 (page 373)
pagenum: 670; label: 7.5 .2
title: Exercise Set 37 (page 385)
pagenum: 671; label: 7.6
title: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
pagenum: 672; label: 7.6 .1
title: Exercise Set 38 (page 390)
pagenum: 672; label: 7.6 .2
title: Exercise Set 39 (page 398)
pagenum: 673; label: 7.7
title: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
pagenum: 675; label: 7.7 .1
title: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
pagenum: 675; label: 7.7 .2
title: Exercise Set 40 (page 411)
pagenum: 675; label: 7.8
title: Exercise Set 41 (page 426)
pagenum: 677; label: 7.9
title: Chapter Exercises (page 437)
pagenum: 678; label: Solutions
pagenum: 693; label: 8.1
title: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
pagenum: 693; label: 8.2
title: Exercise Set 42 (page 452)
pagenum: 693; label: 8.2 .1
title: Exercise Set 43 (page 462)
pagenum: 694; label: 8.3
title: Exercise Set 44 (page 476)
pagenum: 695; label: 8.4
title: Exercise Set 45 (page 487)
pagenum: 696; label: 8.5
title: Exercise Set 46 (page 500)
pagenum: 697; label: 8.6
title: Chapter Exercises (page 502)
pagenum: 698; label: Solutions
pagenum: 701; label: 9.1
title: Exercise Set 47 (page 511)
pagenum: 701; label: 9.2
title: Exercise Set 48 (page 518)
pagenum: 701; label: 9.3
title: Exercise Set 49 (page 523)
pagenum: 702; label: Solutions
pagenum: 705; label: 10.1
title: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
pagenum: 705; label: 10.2
title: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
pagenum: 705; label: 10.3
title: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
pagenum: 705; label: 10.4
title: Exercise Set 50 (page 535)
pagenum: 705; label: 10.5
title: Exercise Set 51 (page 548)
pagenum: 706; label: 10.6
title: Chapter Exercises (page 551)
pagenum: 707; label: Solutions
pagenum: 711; label: 11.1
title: Exercise Set 52 (page 559)
pagenum: 711; label: 11.2
title: Exercise Set 53 (page 563)
pagenum: 711; label: 11.3
title: Exercise Set 54 (page 574)
pagenum: 712; label: 11.4
title: Exercise Set 55 (page 580)
pagenum: 712; label: 11.5
title: Exercise Set 56 (page 584)
pagenum: 712; label: 11.6
title: Exercise Set 57 (page 594)
pagenum: 713; label: Solutions to Problems in the Appendices
pagenum: 715; label: 1
title: APPENDIX A - Exercise Set 58 (page 601)
pagenum: 715; label: 12.2
title: APPENDIX B - Exercise Set 59 (page 607)
pagenum: 716; label: 12.3
title: APPENDIX C - Exercise Set 60 (page 620)
pagenum: 716; label: 12.4
title: APPENDIX D - Exercise Set 61 (page 626)
pagenum: 718; label: Acknowledgments
title: 719; label: Credits
title: 721; label: About the Author
title: 723; label: Index
title: 724