Technical Calculus With Analytic Geometry

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  • Edition: 4th
  • Format: Hardcover
  • Copyright: 2005-08-29
  • Publisher: Brooks Cole
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Written for today's technology student, TECHNICAL CALCULUS WITH ANALYTIC GEOMETRY prepares you for your future courses! With an emphasis on applications, this mathematics text helps you learn calculus skills that are particular to technology. Clear presentation of concepts, detailed examples, marginal annotations, and step-by-step procedures enhance your understanding of difficult concepts. Notations that are frequently encountered in technology are used throughout to help you prepare for further courses in your career.

Table of Contents

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
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
Review Exercises
The Integral
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
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
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
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
Common Units of Measure
A Short Table of Integrals
Answers to Selected Exercises
Table of Contents provided by Publisher. All Rights Reserved.

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