Calculus: Early Transcendental Functions

Name: Calculus: Early Transcendental Functions
Price: 6990 ISK
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Author: Robert Smith
ISBN: 9780077166656

Höfundur: Robert Smith (Útgáfa: 5)

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Útgefandi: McGraw-Hill UK

ISBN: 9780077166656

Print ISBN: 9780077166472

Format: ePub

Útgáfa: 5

Höfundar: Robert Smith

Tungumál: English

Útgefið: 01/2018

Prent takmörkun á líftíma: 100

Prent takmörkun: 2

Afritunar takmörkun: 2

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Cover
Title
Copyright
Dedication
About the Authors
Brief Table of Contents
Table of Contents
Seeing the Beauty and Power of Mathematics
Applications Index
Chapter 0: Preliminaries
0.1 Polynomials and Rational Functions
The Real Number System and Inequalities
Equations of Lines
Functions
0.2 Graphing Calculators and Computer Algebra Systems
0.3 Inverse Functions
0.4 Trigonometric and Inverse Trigonometric Functions
The Inverse Trigonometric Functions
0.5 Exponential and Logarithmic Functions
Hyperbolic Functions
Fitting a Curve to Data
0.6 Transformations of Functions
Chapter 1: Limits and Continuity
1.1 A Brief Preview of Calculus: Tangent Lines and the Length of a Curve
1.2 The Concept of Limit
1.3 Computation of Limits
1.4 Continuity and its Consequences
The Method of Bisections
1.5 Limits Involving Infinity; Asymptotes
Limits at Infinity
1.6 Formal Definition of the Limit
Exploring the Definition of Limit Graphically
Limits Involving Infinity
1.7 Limits and Loss-of-Significance Errors
Computer Representation of Real Numbers
Chapter 2: Differentiation
2.1 Tangent Lines and Velocity
The General Case
Velocity
2.2 The Derivative
Alternative Derivative Notations
Numerical Differentiation
2.3 Computation of Derivatives: The Power Rule
The Power Rule
General Derivative Rules
Higher Order Derivatives
Acceleration
2.4 The Product and Quotient Rules
Product Rule
Quotient Rule
Applications
2.5 The Chain Rule
Concept Mapping
2.6 Derivatives of Trigonometric Functions
Applications
2.7 Derivatives of Exponential and Logarithmic Functions
Derivatives of the Exponential Functions
Derivative of the Natural Logarithm
Logarithmic Differentiation
2.8 Implicit Differentiation and Inverse Trigonometric Functions
Derivatives of the Inverse Trigonometric Functions
2.9 The Hyperbolic Functions
The Inverse Hyperbolic Functions
2.10 The Mean Value Theorem
Chapter 3: Applications of Differentiation
3.1 Linear Approximations and Newton’s Method
Linear Approximations
Newton’s Method
3.2 Indeterminate Forms and L’Hôpital’s Rule
Other Indeterminate Forms
3.3 Maximum and Minimum Values
3.4 Increasing and Decreasing Functions
What You See May Not Be What You Get
3.5 Concavity and the Second Derivative Test
Concept Mapping
3.6 Overview of Curve Sketching
3.7 Optimization
3.8 Related Rates
3.9 Rates of Change in Economics and the Sciences
Chapter 4: Integration
4.1 Antiderivatives
4.2 Sums and Sigma Notation
Principle of Mathematical Induction
4.3 Area
4.4 The Definite Integral
Average Value of a Function
4.5 The Fundamental Theorem of Calculus
4.6 Integration by Substitution
Substitution in Definite Integrals
4.7 Numerical Integration
Simpson’s Rule
Error Bounds for Numerical Integration
4.8 The Natural Logarithm as an Integral
The Exponential Function as the Inverse of the Natural Logarithm
Chapter 5: Applications of the Definite Integral
5.1 Area Between Curves
5.2 Volume: Slicing, Disks and Washers
Volumes by Slicing
The Method of Disks
The Method of Washers
5.3 Volumes by Cylindrical Shells
5.4 Arc Length and Surface Area
Arc Length
Surface Area
5.5 Projectile Motion
5.6 Applications of Integration to Physics and Engineering
5.7 Probability
Chapter 6: Integration Techniques
6.1 Review of Formulas and Techniques
Concept Mapping
6.2 Integration by Parts
6.3 Trigonometric Techniques of Integration
Integrals Involving Powers of Trigonometric Functions
Trigonometric Substitution
6.4 Integration of Rational Functions Using Partial Fractions
Brief Summary of Integration Techniques
6.5 Integration Tables and Computer Algebra Systems
Using Tables of Integrals
Integration Using a Computer Algebra System
6.6 Improper Integrals
Improper Integrals with a Discontinuous Integrand
Improper Integrals with an Infinite Limit of Integration
A Comparison Test
Chapter 7: First-Order Differential Equations
7.1 Modeling with Differential Equations
Growth and Decay Problems
Compound Interest
7.2 Separable Differential Equations
Logistic Growth
7.3 First-Order Linear Differential Equations
General Solution of Linear Differential Equations of the First Order
7.4 Direction Fields and Euler’s Method
7.5 Systems of First-Order Differential Equations
Predator–Prey Systems
Chapter 8: Infinite Series
8.1 Sequences of Real Numbers
8.2 Infinite Series
8.3 The Integral Test and Comparison Tests
Comparison Tests
8.4 Alternating Series
Estimating the Sum of an Alternating Series
8.5 Absolute Convergence and the Ratio Test
The Ratio Test
The Root Test
Summary of Convergence Tests
Concept Mapping
8.6 Power Series
8.7 Taylor Series
Representation of Functions as Power Series
Proof of Taylor’s Theorem
8.8 Applications of Taylor Series
The Binomial Series
8.9 Fourier Series
Functions of Period Other Than 2π
Fourier Series and Music Synthesizers
Chapter 9: Parametric Equations and Polar Coordinates
9.1 Plane Curves and Parametric Equations
9.2 Calculus and Parametric Equations
9.3 Arc Length and Surface Area in Parametric Equations
9.4 Polar Coordinates
9.5 Calculus and Polar Coordinates
9.6 Conic Sections
Parabolas
Ellipses
Hyperbolas
9.7 Conic Sections in Polar Coordinates
Chapter 10: Vectors and the Geometry of Space
10.1 Vectors in the Plane
10.2 Vectors in Space
Vectors in ℝ3
10.3 The Dot Product
Components and Projections
10.4 The Cross Product
10.5 Lines and Planes in Space
Planes in ℝ3
10.6 Surfaces in Space
Cylindrical Surfaces
Quadric Surfaces
An Application
Chapter 11: Vector-Valued Functions
11.1 Vector-Valued Functions
Arc Length in ℝ3
11.2 The Calculus of Vector-Valued Functions
11.3 Motion in Space
Equations of Motion
11.4 Curvature
11.5 Tangent and Normal Vectors
Tangential and Normal Components of Acceleration
Kepler’s Laws
11.6 Parametric Surfaces
Chapter 12: Functions of Several Variables and Partial Differentiation
12.1 Functions of Several Variables
12.2 Limits and Continuity
12.3 Partial Derivatives
12.4 Tangent Planes and Linear Approximations
Increments and Differentials
12.5 The Chain Rule
Implicit Differentiation
12.6 The Gradient and Directional Derivatives
12.7 Extrema of Functions of Several Variables
Proof of the Second Derivatives Test
12.8 Constrained Optimization and Lagrange Multipliers
Chapter 13: Multiple Integrals
13.1 Double Integrals
Double Integrals over a Rectangle
Double Integrals over General Regions
13.2 Area, Volume and Center of Mass
Moments and Center of Mass
13.3 Double Integrals in Polar Coordinates
13.4 Surface Area
13.5 Triple Integrals
Mass and Center of Mass
13.6 Cylindrical Coordinates
13.7 Spherical Coordinates
Triple Integrals in Spherical Coordinates
13.8 Change of Variables in Multiple Integrals
Chapter 14: Vector Calculus
14.1 Vector Fields
14.2 Line Integrals
14.3 Independence of Path and Conservative Vector Fields
14.4 Green’s Theorem
14.5 Curl and Divergence
14.6 Surface Integrals
Parametric Representation of Surfaces
14.7 The Divergence Theorem
14.8 Stokes’ Theorem
14.9 Applications of Vector Calculus
Chapter 15: Second-Order Differential Equations
15.1 Second-Order Equations with Constant Coefficients
15.2 Nonhomogeneous Equations: Undetermined Coefficients
15.3 Applications of Second-Order Equations
15.4 Power Series Solutions of Differential Equations
15.5 Laplace Transforms
15.6 Solving Differential Equations Using Laplace Transforms
Appendix A: Proofs of Selected Theorems
Credits
Subject Index
Derivative Formulas
Table of Integrals