9780321471963

Key Message:University Calculus: Alternate Editionanswers the demand for a more streamlined, less expensive version of the highly acclaimedThomas'Calculus, Eleventh Edition. The text retains the same quality and quantity of exercises as the eleventh edition while using a faster-paced presentation. This text focuses on the thinking behind calculus and uses the same precise, accurate exposition for which the Thomas series is well known. The elegant art program helps todayrs"s readers visualize important concepts. Key Topics: Functions; Limits and Continuity; Differentiation; Applications of Derivatives; Integration; Applications of Definite Integrals; Transcendental Functions; Techniques of Integration; Infinite Sequences and Series; Polar Coordinates and Conics; Vectors and the Geometry of Space; Vector-Valued Functions and Motion in Space; Partial Derivatives; Multiple Integrals; Integration in Vector Fields; First-Order Differential Equations; Second-Order Differential Equations Market: For all readers interested in Calculus.

Joel Hass received his PhD from the University of California—Berkeley. He is currently a professor of mathematics at the University of California—Davis. He has coauthored six widely used calculus texts as well as two calculus study guides. He is currently on the editorial board of Geometriae Dedicata and Media-Enhanced Mathematics. He has been a member of the Institute for Advanced Study at Princeton University and of the Mathematical Sciences Research Institute, and he was a Sloan Research Fellow. Hass’s current areas of research include the geometry of proteins, three dimensional manifolds, applied math, and computational complexity. In his free time, Hass enjoys kayaking.

Maurice D. Weir holds a DA and MS from Carnegie-Mellon University and received his BS at Whitman College. He is a Professor Emeritus of the Department of Applied Mathematics at the Naval Postgraduate School in Monterey, California. Weir enjoys teaching Mathematical Modeling and Differential Equations. His current areas of research include modeling and simulation as well as mathematics education. Weir has been awarded the Outstanding Civilian Service Medal, the Superior Civilian Service Award, and the Schieffelin Award for Excellence in Teaching. He has coauthored eight books, including the University Calculus series and the twelfth edition of Thomas’ Calculus.

George B. Thomas, Jr. (late) of the Massachusetts Institute of Technology, was a professor of mathematics for thirty-eight years; he served as the executive officer of the department for ten years and as graduate registration officer for five years. Thomas held a spot on the board of governors of the Mathematical Association of America and on the executive committee of the mathematics division of the American Society for Engineering Education. His book, Calculus and Analytic Geometry, was first published in 1951 and has since gone through multiple revisions. The text is now in its twelfth edition and continues to guide students through their calculus courses. He also co-authored monographs on mathematics, including the text Probability and Statistics.

Functions
Functions and Their Graphs
Combining Functions; Shifting and Scaling Graphs
Trigonometric Functions
Graphing with Calculators and Computers
Limits and Continuity
Rates of Change and Tangents to Curves
Limit of a Function and Limit Laws
The Precise Definition of a Limit
One-Sided Limits and Limits at Infinity
Infinite Limits and Vertical Asymptotes
Continuity
Tangents and Derivatives at a Point
Differentiation
The Derivative as a Function
Differentiation Rules
The Derivative as a Rate of Change
Derivatives of Trigonometric Functions
The Chain Rule
Implicit Differentiation
Related Rates
Linearization and Differentials
Parametrizations of Plane Curves
Applications of Derivatives
Extreme Values of Functions
The Mean Value Theorem
Monotonic Functions and the First Derivative Test
Concavity and Curve Sketching
Applied Optimization
Newton's Method
Antiderivatives
Integration
Area and Estimating with Finite Sums
Sigma Notation and Limits of Finite Sums
The Definite Integral
The Fundamental Theorem of Calculus
Indefinite Integrals and the Substitution Rule
Substitution and Area Between Curves
Applications of Definite Integrals
Volumes by Slicing and Rotation About an Axis
Volumes by Cylindrical Shells
Lengths of Plane Curves
Areas of Surfaces of Revolution
Work
Moments and Centers of Mass
Fluid Pressures and Forces
Transcendental Functions
Inverse Functions and Their Derivatives
Natural Logarithms
Exponential Functions
Inverse Trigonometric Functions
Exponential Change and Separable Differential Equations
Indeterminate Forms and L'Hopital's Rule
Hyperbolic Functions
Techniques of Integration
Integration by Parts
Trigonometric Integrals
Trigonometric Substitutions
Integration of Rational Functions by Partial Fractions
Integral Tables and Computer Algebra Systems
Numerical Integration
Improper Integrals
Infinite Sequences and Series
Sequences
Infinite Series
The Integral Test
Comparison Tests
The Ratio and Root Tests
Alternating Series, Absolute and Conditional Convergence
Power Series
Taylor and Maclaurin Series
Convergence of Taylor Series
The Binomial Series
Polar Coordinates and Conics
Polar Coordinates
Graphing in Polar Coordinates
Areas and Lengths in Polar Coordinates
Conic Sections
Conics in Polar Coordinates
Conics and Parametric Equations; The Cycloid
Vectors and the Geometry of Space
Three-Dimensional Coordinate Systems
Vectors
The Dot Product
The Cross Product
Lines and Planes in Space
Cylinders and Quadric Surfaces
Vector-Valued Functions and Motion in Space
Vector Functions and Their Derivatives
Integrals of Vector Functions
Arc Length in Space
Curvature of a Curve
Tangential and Normal Components of Acceleration
Velocity and Acceleration in Polar Coordinates
Partial Derivatives
Functions of Several Variables
Limits and Continuity in Higher Dimensions
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University Calculus Alternate Edition

University Calculus Alternate Edition

0321471962

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