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Calculator Calculus

How THIS BOOK DIFFERS This book is about the calculus. What distinguishes it, however, from other books is that it uses the pocket calculator to illustrate the theory. A computation that requires hours of labor when done by hand with tables is quite inappropriate as an example or exercise in a begin...

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Bibliographic Details
Main Author: Mccarty, G.
Format: eBook
Language:English
Published: New York, NY Springer US 1982, 1982
Edition:1st ed. 1982
Subjects:
Humanities And Social Sciences
Humanities
Mathematical Analysis
Social Sciences
Analysis
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • Exercises
  • Problems
  • 6 Trigonometric Functions
  • Angles
  • Trig Functions
  • Triangles
  • Example: The Derivative for sin x
  • Derivatives for Trig Functions
  • Example: ƒ(x)=x sin x-1
  • Inverse Trig Functions
  • Example: ƒ(x)=2 arcsin x-3
  • Exercises
  • Problems
  • 7 Definite Integrals
  • Example: ? and the Area of a Disc
  • Riemann Sums and the Integral
  • Example: The Area under ƒ(x)=x sin x
  • Average Values
  • Fundamental Theorems
  • Trapezoidal Sums
  • Example: The Sine Integral
  • Exercises
  • Problems
  • 8 Logarithms and Exponentials
  • The Definition of Logarithm
  • Example: In 2
  • The Graph of In x
  • Exponentials
  • Example: A Calculation of e
  • Example: Compound Interest and Growth
  • Example: Carbon Dating and Decay
  • Exercises
  • Problems
  • 9 Volumes
  • Example: The Slab Method for a Cone
  • Example: The Slab Method for a Ball.-Example: The Shell Method for a Cone
  • Exercises
  • Problems
  • 10 Curves and Polar Coordinates
  • Example: ƒ(x)=2?x
  • Example: g(x)=x2/4
  • Example: Parametric Equations and the Exponential Spiral
  • Polar Coordinates
  • Example: The Spiral of Archimedes
  • Exercises
  • Problems
  • 11 Sequences and Series
  • The Definitions
  • Example: The Harmonic Series
  • Example: p-Series
  • Geometric Series
  • Example: An Alternating Series
  • Example: Estimation of Remainders by Integrals
  • Example: Estimation of Remainders for Alternating Series
  • Example: Remainders Compared to Geometric Series
  • Round-off
  • Exercises
  • Problems
  • 12 Power Series
  • The Theorems
  • Example: ex
  • Taylor Polynomials
  • The Remainder Function
  • Example: The Calculation of ex
  • Example: Alternative Methods for ex
  • Exercises
  • Problems
  • 13 Taylor Series
  • Taylor’s Theorem
  • Example: In x
  • Newton’s Method
  • Example: 2x+1= eX
  • Example: ƒ(x)=(x-l)/x2
  • Example: Integrating the Sine Integral with Series
  • Example: The Fresnel Integral
  • The Error in Series Integration
  • Example: l/(l-x2)
  • Exercises
  • Exponential and Logarithmic Functions
  • Differentiation
  • Integration Formulas
  • Indefinite Integrals
  • Problems
  • 14 Differential Equations
  • Example: y’=ky and Exponential Growth
  • Some Definitions
  • Separable Variables
  • Example: The Rumor DE
  • Example: Series Solution by Computed Coefficients for y’ = 2xy
  • Example: Series Solution by Undetermined Coefficients for y’-x-y
  • Example: A Stepwise Process
  • Exercises
  • Problems
  • Appendix: Some Calculation Techniques and Machine Tricks
  • Invisible Registers
  • Program Records
  • Rewriting Formulas
  • Constant Arithmetic
  • Factoring Integers
  • Integer Parts and Conversion of Decimals
  • Polynomial Evaluation and Synthetic Division
  • Taylor Series Evaluation
  • Artificial Scientific Notation
  • Round-off, Overflow, and Underflow
  • Handling Large Exponents
  • MachineDamage and Error
  • Reference data and Formulas
  • Greek Alphabet
  • Mathematical Constants
  • Conversion of Units
  • Algebra
  • Geometry
  • Ellipse; Center at Origin
  • Hyperbola; Center at Origin
  • Trigonometric Functions
  • 1 Squares, Square Roots, and the Quadratic Formula
  • The Definition
  • Example: ?67.89
  • The Algorithm
  • Example: ?100
  • Exercises
  • Problems
  • 2 More Functions and Graphs
  • Definition: Limits of Sequences
  • Example: x3-3x-1=0
  • Finding z3 with another Algorithm
  • Finding z3 with Synthetic Division
  • Example: 4x3+3x2-2x-1=0
  • Exercises
  • Problems
  • 3 Limits and Continuity
  • Example: ƒ(x)=3x+4
  • Examples: Theorems for Sums and Products
  • Examples: Limits of Quotients
  • Exercises
  • Problems
  • 4 Differentiation, Derivatives, and Differentials
  • Example: ƒ(x)=x2
  • Example: ƒ(x)=1/x
  • Rules for Differentiation
  • Derivatives for Polynomials
  • Example: The Derivative of ?x
  • Differentials
  • Example: ?103, Example: ?142.3
  • Example: Painting a Cube
  • Composites and Inverses
  • Exercises
  • Problems
  • 5 Maxima, Minima, and the Mean Value Theorem
  • Example: A Minimal Fence
  • The Mean Value Theorem
  • Example: Car Speed
  • Example: Painting a Cube

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