University Calculus Elements with Early

KEY BENEFIT: The popular and respectedThomasrs" Calculus Serieshas been expanded to include a concise alternative.University Calculus: Elementsis the ideal text for instructors who prefer the flexibility of a text that is streamlined without compromising the necessary coverage for a typical three-semester course. As with all of Thomasrs" texts, this book delivers the highest quality writing, trusted exercises, and an exceptional art program. Providing the shortest, lightest, and least-expensive early transcendentals presentation of calculus,University Calculus: Elementsis the text that students will carry and use! KEY TOPICS: Functions and Limits ; Differentiation; Applications of Derivatives ; Integration; Techniques of Integration; Applications of Definite Integrals; 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. 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 and Limits
Functions and Their Graphs
Combining Functions
Shifting and Scaling Graphs
Rates of Change and Tangents to Curves
Limit of a Function and Limit Laws
Precise Definition of a Limit
One-Sided Limits
Continuity
Limits Involving Infinity
Questions to Guide Your Review
Practice and Additional Exercises
Differentiation
Tangents and Derivatives at a Point
The Derivative as a Function
Differentiation Rules
The Derivative as a Rate of Change
Derivatives of Trigonometric Functions
Exponential Functions
The Chain Rule
Implicit Differentiation
Inverse Functions and Their Derivatives
Logarithmic Functions
Inverse Trigonometric Functions
Related Rates
Linearization and Differentials
Questions to Guide Your Review
Practice and Additional Exercises
Applications of Derivatives
Extreme Values of Functions
The Mean Value Theorem
Monotonic Functions and the First Derivative Test
Concavity and Curve Sketching
Parametrizations of Plane Curves
Applied Optimization
Indeterminate Forms and L'Hopital's Rule
Newton's Method
Hyperbolic Functions
Questions to Guide Your Review
Practice and Additional Exercises
Integration
Antiderivatives
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
Questions to Guide Your Review
Practice and Additional Exercises
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
Questions to Guide Your Review
Practice and Additional Exercises
Applications of Definite Integrals
Volumes by Slicing and Rotation About an Axis
Volumes by Cylindrical Shells
Lengths of Plane Curves
Exponential Change and Separable Differential Equations
Work and Fluid Forces
Moments and Centers of Mass
Questions to Guide Your Review
Practice and Additional Exercises
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
Questions to Guide Your Review
Practice and Additional Exercises
Polar Coordinates and Conics
Polar Coordinates
Graphing in Polar Coordinates
Areas and Lengths in Polar Coordinates
Conics in Polar Coordinates
Conics and Parametric Equations
The Cycloid
Questions to Guide Your Review
Practice and Additional Exercises
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
Questions to Guide Your Review
Practice and Additional Exercises
Vector-Valued Functions and Motion in Space
Vector Functions and Their Derivatives
Integrals of Vector Functions
Arc Length and the Unit Tangent Vector T
Curvature and the Unit Normal Vector N
Torsion and the Unit Binormal Vector B
Planetary Motion
Questions to Guide Your Review
Practice and Additional Exercises
Partial Derivatives
Functions of Several Variables
Limits and Continuity in Higher Dimensions
Partial Derivatives
The Chain Rule
Directional Derivatives and Gradient Vectors
Tangent Planes and Differentials
Extreme Values and Saddle Points
Lagrange Multipliers
Questions to Guide Your Review
Practice and Additional Exercises
Multiple Integrals
Double and Iterated Integrals over Rectangles
Double Integrals over General Regions
Area by Double Integration
Double Integrals in Polar Form
Triple Integrals in Rectangular Coordinates
Moments and Centers of Mass
Triple Integrals in Cylindrical and Spherical Coordinates
Substitutions in Multiple Integrals
Questions to Guide Your Review
Practice and Additional Exercises
Integration in Vector Fields
Line Integrals
Vector Fields, Work, Circulation, and Flux
Path Independence, Potential Functions, and Conservative Fields
Green's Theorem in the Plane
Surface Area and Surface Integrals
Parametrized Surfaces
Stokes'
The Divergence Theorem and a Unified Theory
Questions to Guide Your Review
Practice and Additional Exercises
Appendices
Real Numbers and the Real Line
Mathematical Induction
Lines, Circles, and Parabolas
Trigonometric Functions
Basic Algebra and Geometry Formulas
Proofs of Limit Theorems and L'Hopital's Rule
Commonly Occurring Limits
Theory of the Real Numbers
Convergence of Power Series and Taylor's Theorem
The Distributive Law for Vector Cross Products
The Mixed Derivative Theorem and the Increment Theorem
Taylor's Formula for Two Variables
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University Calculus Elements with Early Transcendentals

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