Technical Calculus with Analytic Geometry

ISBN-10: 0495018767
ISBN-13: 9780495018766
Edition: 4th 2006
Authors: Peter Kuhfittig
List price: $379.95 Buy it from $3.00
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Description: This text is written for today's technology student, with an accessible, intuitive approach and an emphasis on applications of calculus to technology. The text's presentation of concepts is clear and concise, with examples worked in great detail,  More...

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Book details

List price: $379.95
Edition: 4th
Copyright year: 2006
Publisher: Brooks/Cole
Publication date: 8/29/2005
Binding: Hardcover
Pages: 544
Size: 8.50" wide x 9.50" long x 0.75" tall
Weight: 2.618
Language: English

This text is written for today's technology student, with an accessible, intuitive approach and an emphasis on applications of calculus to technology. The text's presentation of concepts is clear and concise, with examples worked in great detail, enhanced by marginal annotations, and supported with step-by-step procedures whenever possible. Another powerful enhancement is the use of a functional second color to help explain steps. Differential and integral calculus are introduced in the first five chapters, while more advanced topics, such as differential equations and LaPlace transforms, are covered in later chapters. This organization allows the text to be used in a variety of technology programs.

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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