Calculus with analytic geometry /

Calculus with analytic geometry /

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Bibliographic Details
Author / Creator:Simmons, George F. (George Finlay), 1925-
Imprint:New York : McGraw-Hill, c1985.
Description:xxi, 950 p. : ill. (some col.) ; 26 cm.
Language:English
Subject:Calculus
Geometry, Analytic.
Calculus.
Geometry, Analytic.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/864151
Hidden Bibliographic Details
ISBN:0070574197 : $39.95 (est.)
Notes:Includes bibliographical references and index.
Table of Contents:
  • Chapter 1. Numbers, Functions, and Graphs
  • 1-1. Introduction
  • 1-2. The Real Line and Coordinate Plane: Pythagoras
  • 1-3. Slopes and Equations of Straight Lines
  • 1-4. Circles and Parabolas: Descartes and Fermat
  • 1-5. The Concept of a Function
  • 1-6. Graphs of Functions
  • 1-7. Introductory Trigonometry
  • 1-8. The Functions Sin O and Cos O
  • Chapter 2. The Derivative of a Function
  • 2-0. What is Calculus ?
  • 2-1. The Problems of Tangents
  • 2-2. How to Calculate the Slope of the Tangent
  • 2-3. The Definition of the Derivative
  • 2-4. Velocity and Rates of Change: Newton and Leibriz
  • 2-5. The Concept of a Limit: Two Trigonometric Limits
  • 2-6. Continuous Functions: The Mean Value Theorem and Other Theorem
  • Chapter 3. The Computation of Derivatives
  • 3-1. Derivatives of Polynomials
  • 3-2. The Product and Quotient Rules
  • 3-3. Composite Functions and the Chain Rule
  • 3-4. Some Trigonometric Derivatives
  • 3-5. Implicit Functions and Fractional Exponents
  • 3-6. Derivatives of Higher Order
  • Chapter 4. Applications of Derivatives
  • 4-1. Increasing and Decreasing Functions: Maxima and Minima
  • 4-2. Concavity and Points of Inflection
  • 4-3. Applied Maximum and Minimum Problems
  • 4-4. More Maximum-Minimum Problems
  • 4-5. Related Rates
  • 4-6. Newtons Method for Solving Equations
  • 4-7. Applications to Economics: Marginal Analysis
  • Chapter 5. Indefinite Integrals and Differential Equations
  • 5-1. Introduction
  • 5-2. Differentials and Tangent Line Approximations
  • 5-3. Indefinite Integrals: Integration by Substitution
  • 5-4. Differential Equations: Separation of Variables
  • 5-5. Motion Under Gravity: Escape Velocity and Black Holes
  • Chapter 6. Definite Integrals
  • 6-1. Introduction
  • 6-2. The Problem of Areas
  • 6-3. The Sigma Notation and Certain Special Sums
  • 6-4. The Area Under a Curve: Definite Integrals
  • 6-5. The Computation of Areas as Limits
  • 6-6. The Fundamental Theorem of Calculus
  • 6-7. Properties of Definite Integrals
  • Chapter 7. Applications of Integration
  • 7-1. Introduction: The Intuitive Meaning of Integration
  • 7-2. The Area between Two Curves
  • 7-3. Volumes: The Disk Method
  • 7-4. Volumes: The Method of Cylindrical Shells
  • 7-5. Arc Length
  • 7-6. The Area of a Surface of Revolution
  • 7-7. Work and Energy
  • 7-8. Hydrostatic Force PART II
  • Chapter 8. Exponential and Logarithm Functions
  • 8-1. Introduction
  • 8-2. Review of Exponents and Logarithms
  • 8-3. The Number e and the Function y = e x
  • 8-4. The Natural Logarithm Function y = ln x
  • 8-5. Applications Population Growth and Radioactive Decay
  • 8-6. More Applications
  • Chapter 9. Trigonometric Functions
  • 9-1. Review of Trigonometry
  • 9-2. The Derivatives of the Sine and Cosine
  • 9-3. The Integrals of the Sine and Cosine
  • 9-4. The Derivatives of the Other Four Functions
  • 9-5. The Inverse Trigonometric Functions
  • 9-6. Simple Harmonic Motion
  • 9-7. Hyperbolic Functions
  • Chapter 10. Methods of Integration
  • 10-1. Introduction
  • 10-2. The Method of Substitution
  • 10-3. Certain Trigonometric Integrals
  • 10-4. Trigonometric Substitutions
  • 10-5. Completing the Square
  • 10-6. The Method of Partial Fractions
  • 10-7. Integration by Parts
  • 10-8. A Mixed Bag
  • 10-9. Numerical Integration
  • Chapter 11. Further Applications of Integration
  • 11-1. The Center of Mass of a Discrete System
  • 11-2. Centroids
  • 11-3. The Theorems of Pappus
  • 11-4. Moment of Inertia
  • Chapter 12. Indeterminate Forms and Improper Integrals
  • 12-1. Introduction. The Mean Value Theorem Revisited
  • 12-2. The Interminate Form 0/0. L'Hospital's Rule
  • 12-3. Other Interminate Forms
  • 12-4. Improper Integrals
  • 12-5. The Normal Distribution
  • Chapter 13. Infinite Series of Constants
  • 13-1. What is an Infinite Series ?
  • 13-2. Convergent Sequences
  • 13-3. Convergent and Divergent Series
  • 13-4. General Properties of Convergent Series
  • 13-5. Series on Non-negative Terms: Comparison Test

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