Calculus, Hybrid

ISBN-10: 1133103855
ISBN-13: 9781133103851
Edition: 9th 2012
List price: $176.95
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Book details

List price: $176.95
Edition: 9th
Copyright year: 2012
Publisher: Brooks/Cole
Publication date: 3/17/2011
Binding: Paperback
Pages: 896
Size: 8.25" wide x 10.25" long x 1.25" tall
Weight: 3.696
Language: English

Ron Larson received his PhD. in mathematics from the University of Colorado and has been a professor of mathematics at The Pennsylvania State University since 1970. He has pioneered the use of multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson has also conducted numerous seminars and in-service workshops for math teachers around the country about using computer technology as a teaching tool and motivational aid. His Interactive Calculus (a complete text on CD-ROM) received the 1996 Texty Award for the most innovative mathematics instructional material at the college level, and it was the first mainstream college textbook to be offered on the Internet.

Bruce Edwards has been a mathematics professor at the University of Florida since 1976. Dr. Edwards majored in mathematics at Stanford University, graduating in 1968. He then joined the Peace Corps and spent four years teaching math in Colombia, South America. He returned to the United States and Dartmouth in 1972, and he received his PhD. in mathematics in 1976. Dr. Edwards' research interests include the area of numerical analysis, with a particular interest in the so-called CORDIC algorithms used by computers and graphing calculators to compute function values. His hobbies include jogging, reading, chess, simulation baseball games, and travel.

Preliminaries
Real Numbers and the Real Line
Lines, Circles, and Parabolas
Functions and Their Graphs
Identifying Functions; Mathematical Models
Combining Functions; Shifting and Scaling Graphs
Trigonometric Functions
Graphing with Calculators and Computers
Limits and Derivatives
Rates of Change and Limits
Calculating Limits Using the Limit Laws
Precise Definition of a Limit
One-Sided Limits and Limits at Infinity
Infinite Limits and Vertical Asymptotes
Continuity
Tangents and Derivatives
Differentiation
The Derivative as a Function
Differentiation Rules
The Derivative as a Rate of Change
Derivatives of Trigonometric Functions
The Chain Rule and Parametric Equations
Implicit Differentiation
Related Rates
Linearization and Differentials
Applications of Derivatives
Extreme Values of Functions
The Mean Value Theorem
Monotonic Functions and the First Derivative Test
Concavity and Curve Sketching
Applied Optimization Problems
Indeterminate Forms and L'Hopital's Rule
Newton's Method
Antiderivatives
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
Applications of Definite Integrals
Volumes by Slicing and Rotation About an Axis
Volumes by Cylindrical Shells
Lengths of Plane Curves
Moments and Centers of Mass
Areas of Surfaces of Revolution and The Theorems of Pappus
Work
Fluid Pressures and Forces
Transcendental Functions
Inverse Functions and their Derivatives
Natural Logarithms
The Exponential Function
ax and loga x
Exponential Growth and Decay
Relative Rates of Growth
Inverse Trigonometric Functions
Hyperbolic Functions
Techniques Of Integration
Basic Integration Formulas
Integration by Parts
Integration of Rational Functions by Partial Fractions
Trigonometric Integrals
Trigonometric Substitutions
Integral Tables and Computer Algebra Systems
Numerical Integration
Improper Integrals
Further Applications of Integration
Slope Fields and Separable Differential Equations
First-Order Linear Differential Equations
Euler's Method
Graphical Solutions of Autonomous Equations
Applications of First-Order Differential Equations
Conic Sections and Polar Coordinates
Conic Sections and Quadratic Equations
Classifying Conic Sections by Eccentricity
Quadratic Equations and Rotations
Conics and Parametric Equations; The Cycloid
Polar Coordinates
Graphing in Polar Coordinates
Area and Lengths in Polar Coordinates
Conic Sections in Polar Coordinates
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; Error Estimates
Applications of Power Series
Fourier Series
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
Modeling Projectile Motion
Arc Length and the Unit Tangent Vector T
Curvature and the Unit Normal Vector N
Torsion and the Unit Binormal Vector B
Planetary Motion and Satellites
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
Partial Derivatives with Constrained Variables
Taylor's Formula for Two Variables
Multiple Integrals
Double Integrals
Areas, Moments and Centers of Mass
Double Integrals in Polar Form
Triple Integrals in Rectangular Coordinates
Masses and Moments in Three Dimensions
Triple Integrals in Cylindrical and Spherical Coordinates
Substitutions in Multiple Integrals
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' Theorem
The Divergence Theorem and a Unified Theory
Appendices
Mathematical Induction
Proofs of Limit Theorems
Commonly Occurring Limits
Theory of the Real Numbers
Complex Numbers
The Distributive Law for Vector Cross Products
Determinants and Cramer's Rule
The Mixed Derivative Theorem and the Increment Theorem
The Area of a Parallelogram's Projection on a Plane

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