University Calculus

ISBN-10: 0321350146
ISBN-13: 9780321350145
Edition: 2007
List price: $140.00 Buy it from $0.01
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Description: This streamlined version of 'Thomas' Calculus' provides a faster-paced, precise and accurate presentation of calculus for a college-level calculus course. 'University Calculus' covers both single variable and multivariable calculus and is  More...

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Book details

List price: $140.00
Copyright year: 2007
Publisher: Addison Wesley
Publication date: 2/9/2006
Binding: Hardcover
Pages: 930
Size: 8.75" wide x 10.00" long x 1.25" tall
Weight: 4.840
Language: English

This streamlined version of 'Thomas' Calculus' provides a faster-paced, precise and accurate presentation of calculus for a college-level calculus course. 'University Calculus' covers both single variable and multivariable calculus and is appropriate for a three semester or four quarter course.

Preface
Functions
Functions and Their Graphs
Combining Functions; Shifting and Scaling Graphs
Trigonometric Functions
Exponential Functions
Inverse Functions and Logarithms
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
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Differentiation
The Derivative as a Function
Differentiation Rules for Polynomials, Exponentials, Products, and Quotients
The Derivative as a Rate of Change
Derivatives of Trigonometric Functions
The Chain Rule and Parametric Equations
Implicit Differentiation
Derivatives of Inverse Functions and Logarithms
Inverse Trigonometric Functions
Related Rates
Linearization and Differentials
Hyperbolic Functions
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Applications of Derivatives
Extreme Values of Functions
The Mean Value Theorem
Monotonic Functions and the First Derivative Test
Concavity and Curve Sketching
Applied Optimization
Indeterminate Forms and L'Hopital's Rule
Newton's Method
Antiderivatives
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Integration
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
The Logarithm Defined as an Integral
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
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
Exponential Change and Separable Differential Equations
Work
Moments and Centers of Mass
Questions to Guide Your Review
Practice Exercises
Additional and Advanced 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 Exercises
Additional and Advanced 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 Exercises
Additional and Advanced Exercises
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
Questions to Guide Your Review
Practice Exercises
Additional and Advanced 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 Exercises
Additional and Advanced Exercises
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
Questions to Guide Your Review
Practice Exercises
Additional and Advanced 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
Taylor's Formula for Two Variables
Questions to Guide Your Review
Practice Exercises
Additional and Advanced 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 Exercises
Additional and Advanced 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
Surfaces and Area
Surface Integrals and Flux
Stokes' Theorem
The Divergence Theorem and a Unified Theory
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
First-Order Differential Equations (online)
Solutions, Slope Fields, and Picard's Theorem
First-order Linear Equations
Applications
Euler's Method
Graphical Solutions of Autonomous Equations
Systems of Equations and Phase Planes
Second-Order Differential Equations (online)
Second-Order Linear Equations
Nonhomogeneous Linear Equations
Applications
Euler Equations
Power Series Solutions
Appendices
Real Numbers and the Real Line
Mathematical Induction
Lines, Circles, and Parabolas
Trigonometry Formulas
Proofs of Limit Theorems
Commonly Occurring Limits
Theory of the Real Numbers
The Distributive Law for Vector Cross Products
The Mixed Derivative Theorem and the Increment Theorem
Answers
Index
A Brief Table of Integrals
Credits

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