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

The ABC's of Calculus

by Angelo B. Mingarelli

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

The ABC's of Calculus

by Angelo B. Mingarelli

16 Want to read
1 Currently reading
1 Have read

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

Publish Date

2011

Publisher

The Nolan Company

Language

English

Pages

730

Check nearby libraries

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Previews available in: English

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1 The ABC's of Calculus 2011, The Nolan Company Paperback in English 0969888953 9780969888956	aaaa Read Listen

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Book Details

Table of Contents

Preface to the e-text edition. vii

1. Functions and Their Properties

1.1. The Meaning of a Function

1.2. Function Values and the Box Method

1.3. The Absolute Value of a Function

1.4. A Quick Review of Inequalities

1.4 .1. The triangle inequalities

1.5. Chapter Exercises

1.6. Using Computer Algebra Systems (CAS),

2. Limits and Continuity

2.1. One-Sided Limits of Functions

2.2. Two-Sided Limits and Continuity

2.3. Important Theorems About Continuous Functions

2.4. Evaluating Limits at Inﬁnity

2.5. How to Guess a Limit

2.6. Chapter Exercises

3. The Derivative of a Function

3.1. Motivation

3.2. Working with Derivatives

3.3. The Chain Rule

3.4. Implicit Functions and Their Derivatives

3.5. Derivatives of Trigonometric Functions

3.6. Important Results About Derivatives

3.7. Inverse Functions

3.8. Inverse Trigonometric Functions

3.9. Derivatives of Inverse Trigonometric Functions

3.1.0. Relating Rates of Change

3.1.1. Newton’s Method for Calculating Roots

3.1.2. L’Hospital’s Rule

3.1.3. Chapter Exercises

3.1.4. Challenge Questions

3.1.5. Using Computer Algebra Systems

4. Exponentials and Logarithms

4.1. Exponential Functions and Their Logarithms

4.2. Euler’s Number, e = 2.718281828

4.3. Euler’s Exponential Function and the Natural Logarithm

4.4. Derivative of the Natural Logarithm

4.5. Diﬀerentiation Formulae for General Exponential Functions . . .

4.6. Diﬀerentiation Formulae for General Logarithmic Functions . . .

4.7. Applications

4.8. Chapter Exercises

4.9. Using Computer Algebra Systems

5. Curve Sketching

5.1. Solving Polynomial Inequalities

5.2. Solving Rational Function Inequalities

5.3. Graphing Techniques

5.4. Application of Derivatives to Business and Economics

5.5. Single variable optimization problems

5.6. Chapter Exercises

6.1. Antiderivatives and the Indeﬁnite Integral

6.2. Deﬁnite Integrals

6.3. The Summation Convention

6.4. Area and the Riemann Integral

6.5. Chapter Exercises

6.6. Using Computer Algebra Systems

7. Techniques of Integration

7.1. Trigonometric Identities

7.2. The Substitution Rule

7.3. Integration by Parts

7.3 .1. The Product of a Polynomial and a Sine or Cosine

7.3 .2. The Product of a Polynomial and an Exponential

7.3 .3. The Product of a Polynomial and a Logarithm

7.3 .4. The Product of an Exponential and a Sine or Cosine . . .

7.4. Partial Fractions

7.4 .1. Review of Long Division of Polynomials

7.4 .2. The Integration of Partial Fractions

7.5. Products of Trigonometric Functions

7.5 .1. Products of Sines and Cosines

7.5 .2. Fourier Coeﬃcients

7.5 .3. Products of Secants and Tangents

7.6. Trigonometric Substitutions

7.6 .1. Completing the Square in a Quadratic (Review)

7.6 .2. Trigonometric Substitutions

7.7. Numerical Integration

7.7 .1. The Trapezoidal Rule

7.7 .2. Simpson’s Rule for n Even

7.8. Improper Integrals

7.9. Rationalizing Substitutions

7.9 .1. Integrating rational functions of trigonometric expressions

7.10. Chapter Exercises

7.11. Using Computer Algebra Systems

8. Applications of the Integral

8.1. Motivation

8.2. Finding the Area Between Two Curves

8.3. The Volume of a Solid of Revolution

8.4. Measuring the length of a curve

8.5. Moments and Centers of Mass

8.6. Chapter Exercises

8.7. Using Computer Algebra Systems

9. Simple Diﬀerential Equations

9.1. Why Study Diﬀerential Equations?

9.2. First-order Separable Equations

9.3. Laws of Growth and Decay

9.4. Using Computer Algebra Systems

10. Multivariable Optimization Techniques

10.1. Functions of More Than One Variable

10.2. Continuity

10.2 .1. Discontinuity at a point

10.3. Partial Derivatives

10.4. Higher Order Partial Derivatives

10.5. The Chain Rule for Partial Derivatives

10.6. Extrema of Functions of Two Variables

10.6 .1. Maxima and Minima

10.6 .2. The method of Lagrange multipliers

10.7. Chapter Exercises

11. Advanced Topics

11.1. Inﬁnite Sequences

11.2. Sequences with Inﬁnite Limits

11.3. Limits from the Right

11.4. Limits from the Left

11.6. Continuity

11.7. Limits of Functions at Inﬁnity

11.8. Inﬁnite Limits of Functions

11.9. The Epsilon-Delta Method of Proof

12. Appendix A: Review of Exponents and Radicals

13. Appendix B: The Straight Line

14. Appendix C: A Quick Review of Trigonometry

14.1. The right-angled isosceles triangle (RT45)

14.2. The RT30 triangle

14.3. The basic trigonometric functions

14.4. Identities

14.4.1. The Law of Sines

14.4.2. The Law of Cosines

14.4.3. Identities for the sum and diﬀerence of angles

15. Appendix D: The Natural Domain of a Function

Solutions Manual. 627

1.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.2. Exercise Set 1 (page 10)

1.3. Exercise Set 2 (page 19)

1.4. Exercise Set 3 (page 28)

1.5. Chapter Exercises (page 30 )

2.1. Exercise Set 4 (page 39)

2.2. Exercise Set 5 (page 45)

2.2. Exercise Set 6 (page 49)

2.2. Exercise Set 7 (page 56)

2.2. Exercise Set 8 (page 57)

2.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.4. Exercise Set 9 (page 65)

2.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.6. Chapter Exercises (page 76)

3.1. Exercise Set 10 (page 88)

3.2. Exercise Set 11 (page 93)

3.3. Exercise Set 12 (page 105)

3.4. Exercise Set 13 (page 112)

3.5. Exercise Set 14 (page 119)

3.6. Exercise Set 15 (page 127)

3.7. Exercise Set 16 (page 134)

3.8. Exercise Set 17 (page 139)

3.9. Exercise Set 18 (page 142)

3.1.0. Special Exercise Set (page 149)

3.1.1. Exercise Set 19 (page 160)

3.1.2. Exercise Set 20 (page 172)

3.1.3. Chapter Exercises (page 173)

4.1. Exercise Set 21 (page 183)

4.2. Exercise Set 22 (page 188)

4.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.4. Exercise Set 23 (page 196)

4.5. Exercise Set 24 (page 199)

4.6. Exercise Set 25 (page 203)

4.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.8. Chapter Exercises (page 210)

5.1. Exercise Set 26 (page 216)

5.2. Exercise Set 27 (page 223)

5.3. Exercise Set 28 (page 230)

5.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.6. Single variable optimization problems (page 258)

5.7. Chapter Exercises: Use Plotter (page 259)

6.1. Exercise Set 29 (page 275)

6.2. Exercise Set 30 (page 289)

6.3. Exercise Set 31 (page 284)

6.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.5. Chapter Exercises (page 304)

Solutions. 665

7.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7.2. Exercise Set 32 (page 321)

7.3. Exercise Set 33 (page 345)

7.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7.4 .1. Exercise Set 34 (page 349)

7.4 .2. Exercise Set 35 (page 364)

7.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7.5 .1. Exercise Set 36 (page 373)

7.5 .2. Exercise Set 37 (page 385)

7.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7.6 .1. Exercise Set 38 (page 390)

7.6 .2. Exercise Set 39 (page 398)

7.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7.7 .1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7.7 .2. Exercise Set 40 (page 411)

7.8. Exercise Set 41 (page 426)

7.9. Chapter Exercises (page 437)

8.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8.2. Exercise Set 42 (page 452)

8.2 .1. Exercise Set 43 (page 462)

8.3. Exercise Set 44 (page 476)

8.4. Exercise Set 45 (page 487)

8.5. Exercise Set 46 (page 500)

8.6. Chapter Exercises (page 502)

9.1. Exercise Set 47 (page 511)

9.2. Exercise Set 48 (page 518)

9.3. Exercise Set 49 (page 523)

10.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.4. Exercise Set 50 (page 535)

10.5. Exercise Set 51 (page 548)

10.6. Chapter Exercises (page 551)

11.1. Exercise Set 52 (page 559)

11.2. Exercise Set 53 (page 563)

11.3. Exercise Set 54 (page 574)

11.4. Exercise Set 55 (page 580)

11.5. Exercise Set 56 (page 584)

11.6. Exercise Set 57 (page 594)

Solutions to Problems in the Appendices.

1. APPENDIX A - Exercise Set 58 (page 601)

12.2. APPENDIX B - Exercise Set 59 (page 607)

12.3. APPENDIX C - Exercise Set 60 (page 620)

12.4. APPENDIX D - Exercise Set 61 (page 626)

Acknowledgments. 719

Credits. 721

About the Author. 723

Index. 724

Edition Notes

Published in: Ottawa, Canada

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

Created September 13, 2014
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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.