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Calculus. Early Transcendental Functions. Single Variable 3ed

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CHAPTER 0 PRELIMINARIES..1
0.1 Polynominals and Rational Functions..2
0.2 Graphing Calculators and Computer Algebra Systems..20
0.3 Inverse Functions..29
0.4 Trigonometric and Inverse Trigonometric Functions..36
0.5 Exponential and Logarithmic Functions..48
0.6 Transformations of Functions..61

CHAPTER 1 LIMITS AND CONTINUITY..73
1.1 A Brief Preview of Calculus: Tangent Lines and the Length of a Curve..74
1.2 The Concept of Limit..79
1.3 Computation of Limits..87
1.4 Continuity and Its Consequences..97
1.5 Limits Involving Infinity..110
1.6 Formal Definition of the Limit..121
1.7 Limits and Loss-of-Significance Errors..134

CHAPTER 2 DIFFERENTIATION..145
2.1 Tangent Lines and Velocity..146
2.2 The Derivative..159
2.3 Computatin of Derivatives: The Power Rule..170
2.4 The Product and Quotient Rules..180
2.5 The Chain Rule..189
2.6 Derivatives of Trigonometric Functions..186
2.7 Derivatives of Exponential and Logarithmic Functions..206
2.8 Implicit Differentiation and Inverse Trigonometric Function..216
2.9 The Mean Value Theorem..226

CHAPTER 3 APPLICATIONS OF DIFFERENTIATION..241
3.1 Linear Approximations and Newton's Method..242
3.2 Indeterminate Forms and L'Hospital's Rule..255
3.3 Maximum and Minimum Values..265
3.4 Increasing and Decreasing Functions..277
3.5 Concavity and the Second Derivative Test..286
3.6 Overview of Curve Sketching..296
3.7 Optimization..308
3.8 Related Rates..321
3.9 Rates of Change in Economics and the Sciences..327

CHAPTER 4 INTEGRATION..343
4.1 Antiderivatives..344
4.2 Sums and Sigma Notation..354
4.3 Area..362
4.4 The Definite Integral..369
4.5 The Fundamental Theorem of Calculus..383
4.6 Integration by Substitution..393
4.7 Numerical Integration..402
4.8 The Natural Logarithm as an Integral..416

CHAPTER 5 APPLICATIONS OF THE DEFINITE INTEGRAL..431
5.1 Area Between Curves..432
5.2 Volume: Slicing, Disks, and Washers..441
5.3 Volumes by Cylindrical Shells..456
5.4 Arc Length and Surface Area..464
5.5 Projectile Motion..472
5.6 Applications of Integration to Physics and Engineering..484
5.7 Probability..496

CHAPTER 6 INTEGRATION TECHNIQUES..509
6.1 Review of Formulas and Techniques..510
6.2 Integration by Parts..514
6.3 Trigonometric Techniques of Integration..521
6.4 Integration of Rational Function Using Partial Fractions..530
6.5 Integration Tables and Computer Algebra Systems..538
6.6 Improper Integrals..546

CHAPTER 7 FIRST-ORDER DIFFERENTIAL EQUATIONS..565
7.1 Modelling with Differential Equations..566
7.2 Separable Differential Equations..577
7.3 Direction Fields and Euler's Method..587
7.4 Systems of First-Order Differential Equations..599

CHAPTER 8 INFINITE SERIES..611
8.1 Sequances of Real Numbers..612
8.2 Infinite Series..626
8.3 The Integral Test and Comparison Tests..636
8.4 Alternating Series..648
8.5 Absolute Convergence and the Ratio Test..656
8.6 Power Series..664
8.7 Taylor Series..672
8.8 Applications of Taylor Series..685
8.9 Fourier Series..694

CHAPTER 9 PARAMETRIC EQUATIONS AND POLAR COORDINATES..715
9.1 Plane Curves and parametric Equations..716
9.2 Calculus and Parametric Equations..726
9.3 Arc Length and Surface Area in Parametric Equations..734
9.4 Polar Coordinates..742
9.5 Calculus and Polar Coordinates..755
9.6 Conic Secions..764
9.7 Conic Sections in Polar Coordinates..774

CHAPTER 10 VECTORS AND THE GEOMETRY OF SPACE..785
10.1 Vectors in the Plane..786
10.2 Vectors in Space..796
10.3 The Dot Product..804
10.4 The Cross Product..815
10.5 Lines and Planes in Space..828
10.6 Surfaces in Space..837

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Ketersediaan

Informasi Detail

Judul Seri

-

No. Panggil

515 SMI c

Penerbit

New York : McGraw-Hill., 2007

Deskripsi Fisik

xxxii, 851 hal. : ilus. ; 26 cm

Bahasa

English

ISBN/ISSN

978-0-07-287030-5

Klasifikasi

515

Tipe Isi

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Tipe Media

-

Tipe Pembawa

-

Edisi

3

Subjek

Kalkulus

Info Detail Spesifik

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Pernyataan Tanggungjawab

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