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Calculus Concepts and Connections

ISBN-10: 007330929X

ISBN-13: 9780073309293

Edition: 2006

Authors: Robert T. Smith, Roland B. Minton

List price: $219.38
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Book details

List price: $219.38
Copyright year: 2006
Publisher: McGraw-Hill Higher Education
Publication date: 5/23/2007
Binding: Mixed Media
Size: 8.75" wide x 10.50" long x 2.00" tall
Weight: 5.610
Language: English

Preliminaries
Polynomial and Rational Functions
Graphing Calculators and Computer Algebra
Inverse Functions
Trigonometric and Inverse Trigonometric Functions
Exponential and Logarithmic Functions
Transformations of Functions
Parametric Equations and Polar Coordinates
Limits and Continuity
A Brief Preview of
The Concept of Limit
Computation of Limits
Continuity and its Consequences
Limits Involving Infinity
Limits and Loss-of-Significance Errors
Differentiation
Tangent Lines and Velocity
The Derivative
Computation of Derivatives: The Power Rule
The Product and Quotient Rules
The Chain Rule
Derivatives of Trigonometric and Inverse Trigonometric Functions
Derivatives of Exponential and Logarithmic Functions
Implicit Differentiation
The Mean Value Theorem
Applications of Differentiation
Linear Approximations and Newton’s Method
Indeterminate Forms and L'Hopital's Rule
Maximum and Minimum Values
Increasing and Decreasing Functions
Concavity and Overview of Curve Sketching
Optimization
Rates of Change in Economics and the Sciences
Related Rates and Parametric Equations
Integration
Area Under a Curve
The Definite Integral
Antiderivatives
The Fundamental Theorem of Calculus
Integration by Substitution
Integration by Parts
Other Techniques of Integration
Integration Tables and Computer Algebra Systems
Numerical Integration
Improper Integrals
Applications of the Definite Integral
Area Between Curves
Volume
Arc Length and Surface Area
Projectile Motion
Applications of Integration to Physics and Engineering
Probability
Differential Equations
Growth and Decay Problems
Separable Differential Equations
Euler's
Second Order Equations with Constant Coefficients
Nonhomogeneous Equations: Undetermined Coefficients
Applications of Differential Equations
Infinite Series
Sequences of Real
Infinite Series
The Integral Test and Comparison Tests
Alternating Series
Absolute Convergence and the Ratio Test
Power Series
Taylor Series
Applications of Taylor Series
Fourier Series
Power Series Solutions of Differential Equations
Vectors and the Geometry of Space
Vectors in the Plane
Vectors in Space
The Dot
The Cross Product
Lines and Planes in Space
Surfaces in Space
Vector-Valued Functions
Vector-Valued
Parametric Surfaces
The Calculus of Vector-Valued Functions
Motion in Space
Curvature
Tangent and Normal Vectors
Functions of Several Variables and Differentiation
Functions of Several Variables
Limits and Continuity
Partial Derivatives
Tangent Planes and Linear Approximations
The Chain Rule
The Gradient and Directional Derivatives
Extrema of Functions of Several Variables
Constrained Optimization and Lagrange Multipliers
Multiple Integrals
Double Integrals
Area, Volume and Center of Mass
Double Integrals in Polar Coordinates
Surface Area
Triple Integrals
Cylindrical Coordinates
Spherical Coordinates
Change of Variables in Multiple Integrals
Vector Calculus
Vector Fields
Curl and Divergence
12.3
Independence of Path and Conservative Vector Fields
Green's Theorem
Surface Integrals
The Divergence Theorem
Stokes' Theorem
Applications of Vector Calculus
Graphs of Additional Polar Equations
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