Calculus Early Transcendentals Combined 9th Edition
November 2008, ©2009
0.2 New Functions from Old
0.4 Families of Functions
0.5 Inverse Functions; Inverse Trigonometric Functions
0.6 Exponential and Logarithmic Functions
Chapter 1 Limits and Continuity
1.1 Limits (An Intuitive Approach)
1.2 Computing Limits
1.3 Limits at Infinity; End Behavior of a Function
1.4 Limits (Discussed More Rigorously)
1.6 Continuity of Trigonometric, Exponential, and Inverse Functions
Chapter 2 The Derivative
2.1 Tangent Lines and Rates of Change
2.2 The Derivative Function
2.3 Introduction to Techniques of Differentiation
2.4 The Product and Quotient Rules
2.5 Derivatives of Trigonometric Functions
2.6 The Chain Rule
Chapter 3 Topics in Differentiation
3.1 Implicit Differentiation
3.2 Derivatives of Logarithmic Functions
3.3 Derivatives of Exponential and Inverse Trigonometric Functions
3.4 Related Rates
3.5 Local Linear Approximation; Differentials
3.6 L'Hôpital's Rule; Indeterminate Forms
Chapter 4 The Derivative in Graphing and Applications
4.1 Analysis of Functions I: Increase, Decrease, and Concavity
4.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials
4.3 Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents
4.4 Absolute Maxima and Minima
4.5 Applied Maximum and Minimum Problems
4.6 Rectilinear Motion
4.7 Newton's Method
4.8 Rolle's Theorem; Mean-Value Theorem
Chapter 5 Integration
5.1 An Overview of the Area Problem
5.2 The Indefinite Integral
5.3 Integration by Substitution
5.4 The Definition of Area as a Limit; Sigma Notation
5.5 The Definite Integral
5.6 The Fundamental Theorem of Calculus
5.7 Rectilinear Motion Revisited Using Integration
5.8 Average Value of a Function and its Applications
5.9 Evaluating Definite Integrals by Substitution
5.10 Logarithmic and Other Functions Defined by Integrals
Chapter 6 Applications of the Definite Integral in Geometry, Science, and Engineering
6.1 Area Between Two Curves
6.2 Volumes by Slicing; Disks and Washers
6.3 Volumes by Cylindrical Shells
6.4 Length of a Plane Curve
6.5 Area of a Surface of Revolution
6.7 Moments, Centers of Gravity, and Centroids
6.8 Fluid Pressure and Force
6.9 Hyperbolic Functions and Hanging Cables
Ch 7 Principles of Integral Evaluation
7.1 An Overview of Integration Methods
7.2 Integration by Parts
7.3 Integrating Trigonometric Functions
7.4 Trigonometric Substitutions
7.5 Integrating Rational Functions by Partial Fractions
7.6 Using Computer Algebra Systems and Tables of Integrals
7.7 Numerical Integration; Simpson's Rule
7.8 Improper Integrals
Ch 8 Mathematical Modeling with Differential Equations
8.1 Modeling with Differential Equations
8,2 Separation of Variables
8.3 Slope Fields; Euler's Method
8.4 First-Order Differential Equations and Applications
Ch 9 Infinite Series
9.2 Monotone Sequences
9.3 Infinite Series
9.4 Convergence Tests
9.5 The Comparison, Ratio, and Root Tests
9.6 Alternating Series; Absolute and Conditional Convergence
9.7 Maclaurin and Taylor Polynomials
9.8 Maclaurin and Taylor Series; Power Series
9.9 Convergence of Taylor Series
9.10 Differentiating and Integrating Power Series; Modeling with Taylor Series
Ch 10 Parametric and Polar Curves; Conic Sections
10.1 Parametric Equations; Tangent Lines and Arc Length for Parametric Curves
10.2 Polar Coordinates
10.3 Tangent Lines, Arc Length, and Area for Polar Curves
10.4 Conic Sections
10.5 Rotation of Axes; Second-Degree Equations
10.6 Conic Sections in Polar Coordinates
Ch 11 Three-Dimensional Space; Vectors
11.1 Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces
11.3 Dot Product; Projections
11.4 Cross Product
11.5 Parametric Equations of Lines
11.6 Planes in 3-Space
11.7 Quadric Surfaces
11.8 Cylindrical and Spherical Coordinates
Ch 12 Vector-Valued Functions
12.1 Introduction to Vector-Valued Functions
12.2 Calculus of Vector-Valued Functions
12.3 Change of Parameter; Arc Length
12.4 Unit Tangent, Normal, and Binormal Vectors
12.6 Motion Along a Curve
12.7 Kepler's Laws of Planetary Motion
Ch 13 Partial Derivatives
13.1 Functions of Two or More Variables
13.2 Limits and Continuity
13.3 Partial Derivatives
13.4 Differentiability, Differentials, and Local Linearity
13.5 The Chain Rule
13.6 Directional Derivatives and Gradients
13.7 Tangent Planes and Normal Vectors
13.8 Maxima and Minima of Functions of Two Variables
13.9 Lagrange Multipliers
Ch 14 Multiple Integrals
14.1 Double Integrals
14.2 Double Integrals over Nonrectangular Regions
14.3 Double Integrals in Polar Coordinates
14.4 Surface Area; Parametric Surfaces}
14.5 Triple Integrals
14.6 Triple Integrals in Cylindrical and Spherical Coordinates
14.7 Change of Variable in Multiple Integrals; Jacobians
14.8 Centers of Gravity Using Multiple Integrals
Ch 15 Topics in Vector Calculus
15.1 Vector Fields
15.2 Line Integrals
15.3 Independence of Path; Conservative Vector Fields
15.4 Green's Theorem
15.5 Surface Integrals
15.6 Applications of Surface Integrals; Flux
15.7 The Divergence Theorem
15.8 Stokes' Theorem
Appendix [order of sections TBD]
A Graphing Functions Using Calculators and Computer Algebra Systems
B Trigonometry Review
C Solving Polynomial Equations
D Mathematical Models
E Selected Proofs
F Real Numbers, Intervals, and Inequalities
G Absolute Value
H Coordinate Planes, Lines, and Linear Functions
I Distance, Circles, and Quadratic Functions
J Second-Order Linear Homogeneous Differential Equations; The Vibrating String
K The Discriminant
Exercise Sets: New true/false exercises and new expository writing exercises have been added.
Making Connections: Contains a select group of exercises that draw on ideas developed in the entire chapter rather than focusing on a single section as with the regular exercise sets.
Centroids and Center of Gravity: A new section on centroids and center of gravity in two dimensions is now included. (Chapter 6)
Visualization: Illustrations make extensive use of modern computer graphics to clarify concepts and to develop the student's ability to visualize mathematical objects, particularly those in 3-space. For students working with graphing technology, many exercises develop the ability to generate and analyze mathematical curves and surfaces.
New Chapter 0: The precalculus review material from Chapter 1 is now in Chapter 0, a chapter which focuses exclusively on the preliminary topics that students need to start the calculus course.
Parametric equations reorganized: This edition returns to the traditional organization: the material on parametric equations is now first introduced and then discussed in detail in Section 10.1 (Parametric Curves). However, to support those instructors who want to continue the 8th edition path of giving an early exposure to parametric curves, web materials and self-contained exercise sets on the topic in Section 6.4 are available.
Differntial equations reorganized: The chapter on differential equations has been reordered and revised so that instructors who cover only separable equations can do so without a forced diversion into general first-order equations and other unrelated topics. This chapter can be skipped entirely by those who do not cover differential equations at all in calculus.
Related Rates and Local Linearity: The sections on related rates and local linearity now follow the sections on implicit differentiation and logarithmic, exponential, and inverse trigonometric functions, making a richer variety of techniques and functions available to study related rates and local linearity.
Rectilinear Motion Reorganized: Aspects of rectilinear motion that were discussed in the introductory discussion of derivatives in the 8th edition have been deferred so as to not distract from the primary task of developing the notion of the derivative. This also provides a less fragmented development of rectilinear motion.
Additional Student-Friendly Reorganization The sections "Graphing Functions Using Calculators and Computer Algebra Systems" and "Mathematical Models" are now text appendices; and the section "Second-Order Linear Homogeneous Differential Equations; The Vibrating String" is now posted on the web site that supports this text.
- Readability Balanced with Rigor: The authors' goal is to present precise mathematics to the fullest extent possible in an introductory treatment.
- Commitment to Student Success: Clear writing, effective pedagogy--including special exercises designed for self-assessment--and visual representations of the mathematics help students from a variety of backgrounds to learn. Recognizing variations in learning styles, the authors take a "rule of four" approach, presenting concepts from the verbal, algebraic, visual, and numerical points of view to foster deeper understanding whenever appropriate.
- Dependability: Anton provides thorough topic coverage organized to fit standard curricula and carefully-constructed exercise sets that users of previous editions have come to depend upon.
- Flexibility: This edition is designed to serve a broad spectrum of calculus philosophies-from traditional to "reform." Technology can be emphasized or not, and the order of many topics can be adapted to accommodate each instructor's specific needs.
- Quick Check Exercises: Each exercise set begins with approximately five exercises (answers included) that are designed to provide the student with an immediate assessment of whether he or she has mastered key ideas from the section. They require a minimum of computation and can usually be answered by filling in the blanks.
- Focus on Concepts Exercises: Each exercise set contains a clearly-identified group of problems that focus on the main ideas of the section.
- Technology Exercises: Most sections include exercises that are designed to be solve using either a graphing calculator or a computer algebra system such as Mathematica, Maple, or Derive. These exercises are marked with an icon for easy identification.
- Expository Excellence: Clear explanations allow students to build confidence and provide flexibility for the instructor to use class time for problem solving, applications and explanation of difficult concepts.
- Mathematical Level: The book is written at a mathematical level that is suitable for students planning on careers in engineering or science.
- Applicability of Calculus: One of the primary goals of this text is to link calculus to the real world and the student s own experience. This theme is carried through in the examples and exercises.
- Historical Notes: The biographies and historical notes have been a hallmark of this text from its first edition and have been maintained in this edition. All of the biographical materials have been distilled from standard sources with the goal of capturing the personalities of the great mathematicians and bringing them to life for the student.
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