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What is included with this book?
Introduction to Analytic Geometry | |
The Cartesian Coordinate System | |
The Slope | |
The Straight Line | |
Curve Sketching | |
Discussion of Curves with Graphing Utilities | |
The Conics | |
The Circle | |
The Parabola | |
The Ellipse | |
The Hyperbola | |
Translation of Axes | |
Standard Equations of the Conics | |
Review Exercises | |
Introduction to Calculus: The Derivative | |
Functions and Intervals | |
Limits | |
The Derivative | |
The Derivative by the Four-Step Process | |
Derivatives of Polynomials | |
Instantaneous Rates of Change | |
Differentiation Formulas | |
Implicit Differentiation | |
Higher Derivatives | |
Review Exercises | |
Applications of the Derivative | |
The First-Derivative Test | |
The Second-Derivative Test | |
Exploring with Graphing Utilities | |
Applications of Minima and Maxima | |
Related rates | |
Differentials | |
Review Exercises | |
The Integral | |
Antiderivatives | |
The Area Problem | |
The Fundamental Theorem of Calculus | |
The Integral: Notation and General Definition | |
Basic Integration Formulas | |
Area Between Curves | |
Improper Integrals | |
The Constant of Integration | |
Numerical Integration | |
Review Exercises | |
Application of the Integral | |
Means of Root Mean Squares | |
Volumes of Revolution: Disk and Washer Methods | |
Volumes of Revolution: Shell Method | |
Centroids | |
Moments of Inertia | |
Work and Fluid Pressure | |
Review Exercises | |
Derivatives of Transcendental Functions | |
Review of Trigonometry | |
Derivatives of Sine and Cosine Functions | |
Other Trigonometric Functions | |
Inverse Trigonometric Functions | |
Derivatives of Inverse Trigonometric Functions | |
Exponential and Logarithmic Functions | |
Derivative of the Logarithmic Function | |
Derivative of the Exponential Function | |
L'Hospital's rule | |
Applications | |
Newton's Method | |
Review Exercises | |
Integration Techniques | |
The Power Formula Again | |
The Logarithmic and Exponentials Forms | |
Trigonometric Forms | |
Further Trigonometric Forms | |
Inverse Trigonometric Forms | |
Integration by Trigonometric Substitution | |
Integration by Parts | |
Integration of Rational Functions | |
Integration by Use of Tables | |
Additional Remarks | |
Review Exercises | |
Parametic Equations, Vectors, and Polar Coordinates | |
Vectors and Parametric Equations | |
Arc Length | |
Polar Coordinates | |
Curves in Polar Coordinates | |
Areas in Polar Coordinates | |
Review Exercises | |
Three-Dimensional Space; Partial Derivatives; Multiple Integrals | |
Surfaces in Three Dimensions | |
Partial Derivatives | |
Applications of Partial Derivatives | |
Curve Fitting | |
Integrated Integrals | |
Volumes by Double Integration | |
Mass, Centroids, and Moments of Inertia | |
Volumes in Cylindrical Coordinates | |
Review Exercises | |
Infinite Series | |
Introduction to Infinite Series | |
Tests for Convergence | |
Maclaurin Series | |
Operations with Series | |
Computations with Series | |
Applications | |
Fourier Series | |
Review Exercises | |
First-Order Differetial Equations | |
What is Differential Equation? Separation of Variables | |
First-Order Linear Differential Equations | |
Applications of First-Order Differential Equations | |
Numerical Solutions | |
Review Exercises | |
Higher Order Linear Differential Equations | |
Higher-Order Homogeneous Differential Equations | |
Auxiliary Equations with Repeating or Complex Roots | |
Nonhomogeneous Equations | |
Applications of Second-Order Equations | |
Review Exercises | |
The Laplace Transform | |
Introduction and Basic Properties | |
Inverse Laplace Transforms | |
Partial Fractions | |
Solutions of Linear Equations by Laplace Transforms | |
Review Exercises | |
Tables | |
Common Units of Measure | |
A Short Table of Integrals | |
Answers to Selected Exercises | |
Index | |
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