Calculus: Early Transcendental Functions [Smith Minton]

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ISBN-10: 0071107517
ISBN-13: 9780071107518
Author: Smith Minton (Robert T. Smith Roland B. Minton)
Publisher: McGraw Hill Higher Education

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Table of Content

Chapter 0: Preliminaries
0.1 Polynomials and Rational Functions
0.2 Graphing Calculators and Computer Algebra Systems
0.3 Inverse Functions
0.4 Trigonometric and 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 First Look at Calculus
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
1.6 Formal Definition of the Limit Exploring the Definition of Limit Graphically
1.7 Limits and Loss-of-Significance Errors Computer Representation of Real Numbers

Chapter 2: Differentiation
2.1 Tangent Lines and Velocity
2.2 The Derivative Numerical Differentiation
2.3 Computation of Derivatives: The Power Rule Higher Order Derivatives Acceleration
2.4 The Product and Quotient Rules
2.5 The Chain Rule
2.6 Derivatives of the Trigonometric Functions
2.7 Derivatives of the Exponential and Logarithmic Functions
2.8 Implicit Differentiation and Inverse Trigonometric Functions
2.9 The Mean Value Theorem

Chapter 3: Applications of Differentiation
3.1 Linear Approximations and Newton's Method
3.2 Indeterminate Forms and L'Hopital's Rule
3.3 Maximum and Minimum Values
3.4 Increasing and Decreasing Functions
3.5 Concavity and the Second Derivative Test
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
4.7 Numerical Integration 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
5.3 Volumes by Cylindrical Shells
5.4 Arc Length and Surface Area
5.5 Projectile Motion
5.6 Applications of Integration to Economics and the Sciences
5.7 Probability

Chapter 6: Integration Techniques
6.1 Review of Formulas and Techniques
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 General Strategies for Integration Techniques
6.5 Integration Tables and Computer Algebra Systems
6.6 Improper Integrals A Comparison Test
Chapter 7: First Order Differential Equations
7.1 Growth and Decay Problems Compound Interest Modeling with Differential Equations
7.2 Separable Differential Equations Logistic Growth
7.3 Direction Fields and Euler's Method
7.4 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
8.4 Alternating Series Estimating the Sum of an Alternating Series
8.5 Absolute Convergence and the Ratio Test The Root Test Summary of Convergence Tests
8.6 Power Series
8.7 Taylor Series Representations of Functions as Series Proof of Taylor?s Theorem
8.8 Applications of Taylor Series The Binomial Series
8.9 Fourier Series

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
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
10.3 The Dot Product Components and Projections
10.4 The Cross Product
10.5 Lines and Planes in Space
10.6 Surfaces in Space

Chapter 11: Vector-Valued Functions
11.1 Vector-Valued Functions
11.2 The Calculus of Vector-Valued Functions
11.3 Motion in Space
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 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
12.6 The Gradient and Directional Derivatives
12.7 Extrema of Functions of Several Variables
12.8 Constrained Optimization and Lagrange Multipliers

Chapter 13: Multiple Integrals
13.1 Double Integrals
13.2 Area, Volume, 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
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
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

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