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Calculus: Late Transcendentals, International Student Version, Combined 9th Edition

Calculus: Late Transcendentals, International Student Version, Combined 9th Edition


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0. Before Calculus
0.1 Functions
0.2New Functions from Old
0.3Families of Functions
0.4Inverse Functions

1. Limits and Continuity
1.1Limits (An Intuitive Approach)
1.2Computing Limits
1.3Limits at Infinity; End Behavior of a Function
1.4Limits (Discussed More Rigorously)
1.6Continuity of Trigonometric Functions

2. The Derivative
2.1Tangent Lines and Rates of Change
2.2The Derivative Function
2.3Introduction to Techniques of Differentiation
2.4The Product and Quotient Rules
2.5Derivatives of Trigonometric Functions
2.6The Chain Rule
2.7Implicit Differentiation
2.8Related Rates
2.9Local Linear Approximation; Differentials

3. The Derivative in Graphing and Applications
3.1Analysis of Functions I: Increase, Decrease, and Concavity
3.2Analysis of Functions II: Relative Extrema; Graphing Polynomials
3.3Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents
3.4Absolute Maxima and Minima
3.5Applied Maximum and Minimum Problems
3.6Rectilinear Motion
3.7Newton's Method
3.8Rolle's Theorem; Mean-Value Theorem

4. Integration
4.1An Overview of the Area Problem
4.2The Indefinite Integral
4.3Integration by Substitution
4.4 The Definition of Area as a Limit; Sigma Notation
4.5The Definite Integral
4.6The Fundamental Theorem of Calculus
4.7Rectilinear Motion Revisited: Using Integration
4.8Average Value of a Function and Its Applications
4.9Evaluating Definite Integrals by Substitution

5. Applications of the Definite Integral in Geometry, Science and Engineering
5.1Area Between Two Curves
5.2Volumes by Slicing; Disks and Washers
5.3Volumes by Cylindrical Shells
5.4Length of a Plane Curve
5.5Area of a Surface Revolution
5.7Moments, Centers of Gravity, and Centroids
5.8Fluid Pressure and Force

6. Exponential, Logarithmic, and Inverse Trigonometric Functions
6.1Exponential and Logarithmic Functions
6.2Derivatives and Integrals Involving Logarithmic Functions
6.3Derivatives of Inverse Functions; Derivatives and Integrals Involving Exponential Functions
6.4Graphs and Applications Involving Logarithmic and Exponential Functions
6.5L'Hˆopital's Rule; Indeterminate Forms
6.6Logarithmic and Other Functions Defined by Integrals
6.7Derivatives and Integrals Involving Inverse Trigonometric Functions
6.8Hyperbolic Functions and Hanging Cubes

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
9.1 Sequences
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
11.2 Vectors
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
12.5 Curvature
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

Web Appendices
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
  • Differential Equations: This chapter has been reordered and revised so that instructors who cover only separable differential equations can do so without having to cover general first-order equations and other unrelated topics
  • 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.
  • Centroids and Center of Gravity: A new section on centroids and center of gravity in two dimensions is included
  • Chapter 0: The precalculus review material from Chapter 1 is now in Chapter 0
  • Parametric equations reorganized: returns to the traditional organization: the material on parametric equations is now first introduced and then discussed in detail in the Parametric Curves section.  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.
  • 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
  • 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
  • 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 specifc 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.
  • 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.
  • 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.