Calculus Multivariable 9th Edition
March 2009, ©2009
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.
New Chapter 0: The review material from Chapter 1 is now in Chapter 0.
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.
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.