Calculus: From Graphical, Numerical, and Symbolic Points of View,9780030526596

Calculus: From Graphical, Numerical, and Symbolic Points of View

by ;
ISBN13: 9780030526596
ISBN10: 0030526590
Format: Hardcover
Pub. Date: 1997-07-01
Publisher(s): Brooks Cole
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Table of Contents

Functions in Calculus
1(92)
Functions, Calculus Style
1(11)
Graphs
12(13)
Machine Graphics
25(10)
What Is a Function?
35(14)
A Field Guide to Elementary Functions
49(19)
New Functions from Old
68(13)
Modeling with Elementary Functions
81(10)
Chapter Summary
91(2)
The Derivative
93(86)
Amount Functions and Rate Functions: The Idea of the Derivative
93(15)
Estimating Derivatives: A Closer Look
108(10)
The Geometry of Derivatives
118(12)
The Geometry of Higher-Order Derivatives
130(8)
Average and Instantaneous Rates: Defining the Derivative
138(11)
Limits and Continuity
149(13)
Limits Involving Infinity; New Limits from Old
162(14)
Chapter Summary
176(3)
Derivatives of Elementary Functions
179(69)
Derivatives of Power Functions and Polynomials
179(15)
Using Derivative and Antiderivative Formulas
194(4)
Derivatives of Exponential and Logarithm Functions
198(11)
Derivatives of Trigonometric Functions
209(7)
New Derivatives from Old: The Product and Quotient Rules
216(8)
New Derivatives from Old: The Chain Rule
224(9)
Implicit Differentiation
233(4)
Inverse Trigonometric Functions and Their Derivatives
237(10)
Chapter Summary
247(1)
Applications of the Derivative
248(93)
Differential Equations and their Solutions
248(8)
More Differential Equations: Modeling Growth
256(9)
Linear and Quadratic Approximation; Taylor Polynomials
265(14)
Newton's Method: Finding Roots
279(8)
Splines: Connecting the Dots
287(10)
Optimization
297(8)
Calculus for Money: Derivatives in Economics
305(6)
Related Rates
311(4)
Parametric Equations, Parametric Curves
315(11)
Why Continuity Matters
326(5)
Why Differentiability Matters; The Mean Value Theorem
331(8)
Chapter Summary
339(2)
The Integral
341(56)
Areas and Integrals
341(16)
The Area Function
357(8)
The Fundamental Theorem of Calculus
365(12)
Approximating Sums: The Integral as a Limit
377(9)
Approximating Sums: Interpretations and Applications
386(9)
Chapter Summary
395(2)
Finding Antiderivatives
397(24)
Antiderivatives: The Idea
397(8)
Antidifferentiation by Substitution
405(8)
Integral Aids: Tables and Computers
413(8)
Numerical Integration
421(32)
The Idea of Approximation
421(9)
More on Error: Left and Right Sums and the First Derivative
430(8)
Trapezoid Sums, Midpoint Sums, and the Second Derivative
438(7)
Simpson's Rule
445(7)
Chapter Summary
452(1)
Using the Definite Integral
453(39)
Introduction
453(6)
Finding Volumes by Integration
459(7)
Arclength
466(4)
Work
470(7)
Present Value
477(7)
Fourier Polynomials
484(5)
Chapter Summary
489(3)
More Antidifferentiation Techniques
492(27)
Integration by Parts
492(8)
Partial Fractions
500(10)
Trigonometric Antiderivatives
510(7)
Miscellaneous Exercises
517(2)
Improper Integrals
519(33)
When Is an Integral Improper?
519(7)
Detecting Convergence, Estimating Limits
526(10)
Improper Integrals and Probability
536(8)
l'Hopital's Rule: Comparing Rates
544(7)
Chapter Summary
551(1)
Infinite Series
552(66)
Sequences and Their Limits
552(9)
Infinite Series, Convergence, and Divergence
561(14)
Testing for Convergence; Estimating Limits
575(11)
Absolute Convergence; Alternating Series
586(8)
Power Series
594(8)
Power Series as Functions
602(8)
Maclaurin and Taylor Series
610(7)
Chapter Summary
617(1)
Differential Equations
618(35)
Differential Equations: The Basics
618(5)
Slope Fields: Solving DEs Graphically
623(9)
Euler's Method: Solving DEs Numerically
632(9)
Separating Variables: Solving DEs Symbolically
641(10)
Chapter Summary
651(2)
Polar Coordinates
653(19)
Polar Coordinates and Polar Curves
653(10)
Calculus in Polar Coordinates
663(9)
Multivariable Calculus: A First Look
672(53)
Three-Dimensional Space
672(10)
Functions of Several Variables
682(7)
Partial Derivatives
689(12)
Optimization and Partial Derivatives: A First Look
701(6)
Multiple Integrals and Approximating Sums
707(9)
Calculating Integrals by Iteration
716(9)
Double Integrals in Polar Coordinates
725
Real Numbers and the Coordinate Plane A-1
Lines and Linear Functions A-13
Polynomial Algebra: A Brisk Review A-21
Real-World Calculus: From Words to Mathematics A-30
Algebra of Exponentials A-40
Algebra of Logarithms A-45
Trigonometric Functions A-50
Selected Proofs A-57
A Graphical Glossary of Functions A-61
Index I-1

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