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Calculus 2 Simplified: Integration and Infinite Series

Calculus 2 Simplified: Integration and Infinite Series (Paperback)

오스카 E. 페르난데스 (지은이)

Princeton University Press

45,220원

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Calculus 2 Simplified: Integration and Infinite Series

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· 제목 : Calculus 2 Simplified: Integration and Infinite Series (Paperback)
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 미적분학
· ISBN : 9780691263755
· 쪽수 : 256쪽
· 출판일 : 2025-04-01

목차

Preface
Before You Begin
To the Student
To the Instructor

1 The Fast-Track Introduction to Calculus 2

1.1 First Things First: What Is Calculus?

1.2 Limits: (Still) The Foundation of Calculus

1.3 The Three Di?cult Questions That Drove the Development of Calculus 2

2 Integration Techniques and Approximations

2.1 Integrating, Leibniz’s Way

2.2 Approximating Integrals, Riemann’s Way

2.3 The Trapezoidal Rule

2.4 How to Approximate Integrals to Any Desired Accuracy

2.5 Integration by Parts

2.6 Trigonometric Integrals

2.7 Trigonometric Substitution

2.8 Partial Fraction Decomposition

2.9 Parting Thoughts

Chapter 2 Exercises

Chapter 2 Appendix

A2.1 Evaluating Riemann Sums Using Summation Formulas

A2.2 Additional Error Theorems for Riemann Sums and the Trapezoidal Rule

A2.3 The Tabular Method for Integration by Parts

A2.4 Integrands That Are Products of Powers of Sine and Cosine

A2.5 Integrands That Are Sine-Cosine Products with Di?erent Arguments

A2.6 A Brief Review of Long Division and Its Uses in Partial Fraction Decomposition

3 Applications of Integration

3.1 A Quick Preview of What’s to Come

3.2 Area between Curves

3.3 Volumes by Cross Sections

3.4 Volumes of Revolution: The Disk Method

3.5 Volumes of Revolution: The Washer Method

3.6 Volumes of Revolution: The Shell Method

3.7 Calculating the Length of a Curve

3.8 Calculating the (Lateral) Area of a Surface

3.9 Parting Thoughts

Chapter 3 Exercises

Chapter 3 Appendix

A3.1 Area between Two Curves: The Riemann Sums Approach

A3.2 Riemann Sums Approach to Volumes by Cross Sections

A3.3 Riemann Sums Approach to the Disk Method

A3.4 Riemann Sums Approach to the Washer Method

A3.5 Riemann Sums Approach to the Shell Method

A3.6 Volumes of Revolution: Noncoordinate Axes of Revolution

4 Sequences and Series

4.1 Introduction to Sequences

4.2 Convergence of Sequences

4.3 In?nite Series

4.4 Special Series and the Series Laws

4.5 The Limit and Direct Comparison Tests

4.6 Alternating Series

4.7 The Ratio Test

4.8 Approximating the Sum of an Alternating Series

4.9 Taylor Polynomials

4.10 Taylor’s Theorem

4.11 Power Series and Their Convergence

4.12 Power Series as Functions

4.13 Taylor Series

4.14 Convergence of Taylor Series

4.15 Applications of Taylor Series

4.16 Parting Thoughts

Chapter 4 Exercises

5 Connections between Integration and Series

5.1 Partial Fractions and Telescoping Series

5.2 Power/Taylor Series and Integration

5.3 Improper Integrals

5.4 The Integral Test for Series

5.5 Parting Thoughts

Chapter 5 Exercises

Epilogue
Acknowledgments

Appendixes A--D: Precalculus and Calculus Review

A Algebra and Geometry Review

B Precalculus (Functions) Review

C Calculus Review I—Through Di?erentiation

D Calculus Review II—Integration

Appendix E: Integration Basics

E.1 The Fundamental Theorem of Calculus

E.2 Antiderivatives and the Evaluation Theorem

E.3 Properties of Integrals

E.4Net Signed Area

E.5 Integrating Transcendental Functions

E.6 The Substitution Rule

Appendix F: L’Hopital’s Rule

Appendix F Exercises

Answers to Exercises
Bibliography
Index of Applications
Subject Index

저자소개

오스카 E. 페르난데스 (지은이) 정보 더보기

웰즐리 대학 수학과 조교수이다. 아내와 딸과 함께 매사추세츠 주 뉴턴 시에 살고 있다. 트위터 계정 @EverydayCalc에서 저자의 수학적 사고를 엿볼 수 있으며, surroundedbymath.com에서 저자의 작업에 대해 자세히 살펴볼 수 있다. 저서로 《미적분으로 바라본 하루》, 《수학의 참견》(이상 프리렉)이 있다.

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