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Calculus Calculus: An Intuitive and Physical Approach by Kline

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  1. Feb 4, 2013 #1

    micromass

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    Table of Contents:
    Code (Text):

    [LIST]
    [*] Why Calculus?
    [LIST]
    [*] The Historical Motivations for the Calculus
    [*] The Creators of the Calculus
    [*] The Nature of the Calculus
    [/LIST]
    [*] The Derivative
    [LIST]
    [*] The Concept of Function
    [*] The Graph or Curve of a Function
    [*] Average and Instantaneous Speed
    [*] The Method of Increments
    [*] A Matter of Notation
    [*] The Method of Increments Applied to y=ax^2
    [*] The Derived Function
    [*] The Differentiation of Simple Monomials
    [*] The Differentiation of Simple Polynomials
    [*] The Second Derivative
    [/LIST]
    [*] The Antiderived Function or the Integral
    [LIST]
    [*] The Integral
    [*] Straight Line Motion in One Direction
    [*] Up and Down Motion
    [*] Motion Along an Inclined Plane
    [*] Appendix: The Coordinate Geometry of Straight Lines
    [LIST]
    [*] The Need for Geometrical Interpretation
    [*] The Distance Formula
    [*] The Slope of a Straight Line
    [*] The Inclination of a Line
    [*] Slopes of Parallel and Perpendicular Lines
    [*] The Angle Between Two Lines
    [*] The Equation of a Straight Lines
    [*] The Distance from a Point to a Line
    [*] Equation and Curve
    [/LIST]
    [/LIST]
    [*] The Geometrical Significance of the Derivative
    [LIST]
    [*] The Derivative as Slope
    [*] The Concept of Tangent to a Curve
    [*] Applications of the Derivative as the Slope
    [*] The Equation of the Paraboa
    [*] Physical Applications of the Derivative as Slope
    [*] Further Discussion of the Derivative as the Slope
    [/LIST]
    [*] The Differentiation and Integration of Powers of x
    [LIST]
    [*] Introduction
    [*] The Functions x^n for Positive Integral n
    [*] A Calculus Method of Finding Roots
    [*] Differentiation and Integration of x^n for Fractional Values of n
    [/LIST]
    [*] Some Theorems on Differentiation and Antidifferentiation
    [LIST]
    [*] Introduction
    [*] Some Remarks about Functions
    [*] The Differentiation of Sums and Differences of Functions
    [*] The Differentiation of Products and Quotients of Functions
    [*] The Integration of Combinations of Functions
    [*] All Integrals Differ by a Constant
    [*] The Power Rule for Negative Exponents
    [*] The Concept of Work and an Application
    [/LIST]
    [*] The Chain Rule
    [LIST]
    [*] Introduction
    [*] The Chain Rule
    [*] Application of the Chain Rule to Differentiation
    [*] The Differentiation of Implicit Functions
    [*] Equations of the Ellipse and Hyperbola
    [*] Differentiation of the Equations of Ellipse and Hyperbola
    [*] Integration Employing the Chain Rule
    [*] The Problem of Escape Velocity
    [*] Appendix: Transformation of Coordinates
    [LIST]
    [*] Introduction
    [*] Rotation of Axes
    [*] Translation of Axes
    [*] Invariants
    [/LIST]
    [/LIST]
    [*] Maxima and Minima
    [LIST]
    [*] Introduction
    [*] The Geometrical Approach to Maxima and Minima
    [*] Analytical Treatment of Maxima and Minima
    [*] An Alternative Method of Determining Relative Maxima and Minima
    [*] Some Applications of the Method of Maxima and Minima
    [*] Some Applications to Economics
    [*] Curve Tracing
    [/LIST]
    [*] The Definite Integral
    [LIST]
    [*] Introduction
    [*] Area as the Limit of a Sum
    [*] The Definite Integral
    [*] The Evaluation of Definite Integrals
    [*] Area Below the x-Axis
    [*] Areas Between Curves
    [*] Some Additional Properties of the Definite Integrals
    [*] Numerical Methods for Evaluating Definite Integrals
    [*] Appendix: The Sum of the Squares of the First n Integers
    [/LIST]
    [*] The Trigonometric Functions
    [LIST]
    [*] Introduction
    [*] The Sinusoidal Function
    [*] Some Preliminaries on Limits
    [*] Differentiation of the Trigonometric Functions
    [*] Integration of the Trigonometric Functions
    [*] Application of the Trigonometric Functions to Periodic Phenomena
    [/LIST]
    [*] The Inverse Trigonometric Functions
    [LIST]
    [*] The Notion of an Inverse Function
    [*] The Inverse Trigonometric Functions
    [*] The Differentiation of the Inverse Trigonometric Functions
    [*] Integration Involving the Inverse Trigonometric Functions
    [*] Change of Variable in Integration
    [*] Time of Motion Under Gravitational Attraction
    [/LIST]
    [*] Logarithmic and Exponential Functions
    [LIST]
    [*] Introduction
    [*] A Review of Logarithms
    [*] The Derived Functions of Logarithmic Functions
    [*] Exponential Functions and Their Derived Functions
    [*] Problems of Growth and Decay
    [*] Motion in One Direction in a Resisting Medium
    [*] Up and Down Motion in Resisting Media
    [*] Hyperbolic Functions
    [*] Logarithmic Differentiation
    [/LIST]
    [*] Differentials and the Law of the Mean
    [LIST]
    [*] Differentiation
    [*] The Mean Value Theorem of the Differential Calculus
    [*] Indeterminate Forms
    [/LIST]
    [*] Further Techniques of Integration
    [LIST]
    [*] Introduction
    [*] Integration by Parts
    [*] Reduction Formulas
    [*] Integration by Partial Fractions
    [*] Integration by Substitution and Change of Variable
    [*] The Use of Tables
    [/LIST]
    [*] Some Geometric Uses of the Definite Integral
    [LIST]
    [*] Introduction
    [*] Volumes of Solids: The Cylindrical Element
    [*] Volumes of solids: The Shell Game
    [*] Lengths of Arcs of Curves
    [*] Curvature
    [*] Areas of Surfaces of Revolution
    [*] Remarks on Approximating Figures
    [/LIST]
    [*] Some Physical Applications of the Definite Integral
    [LIST]
    [*] Introduction
    [*] The calculation of Work
    [*] Applications to Economics
    [*] The Hanging Chain
    [*] Gravitational Attraction of Rods
    [*] Gravitational Attraction of Disks
    [*] Gravitational Attraction of Spheres
    [/LIST]
    [*] Polar Coordinates
    [LIST]
    [*] The Polar Coordinate System
    [*] The Polar Coordinate Equations of Curves
    [*] The Polar Coordinate Equations of the Conic Sections
    [*] The Relation Between Rectangular and Polar Coordinates
    [*] The Derivative of a Polar Coordinate Function
    [*] Areas in Polar Coordinates
    [*] Arc Length in Polar Coordinates
    [*] Curvature in Polar Coordinates
    [/LIST]
    [*] Rectangular Parametric Equations and Curvilinear Motion
    [LIST]
    [*] Introduction
    [*] The Parametric Equations of a Curve
    [*] Some Additional Examples of Parametric Equations
    [*] Projective Motion in a Vacuum
    [*] Slope, Area, Arc Length, and Curvature Derived from Parametric Equations
    [*] An Application of Arc Length
    [*] Velocity and Acceleration in Curvilinear Motion
    [*] Tangential and Normal Acceleration in Curvilinear Motion
    [/LIST]
    [*] Polar Parametric Equations and Curvilinear Motion
    [LIST]
    [*] Polar Parametric Equations
    [*] Velocity and Acceleration in the Polar Parametric Representation
    [*] Kepler's Laws
    [*] Statellites and Projectiles
    [/LIST]
    [*] Taylor's Theorem and Infinite Series
    [LIST]
    [*] The Need to Approximate Functions
    [*] The Approximation of Functions by Polynomials
    [*] Taylor's Formula
    [*] Some Applications of Taylor's Theorem
    [*] The Taylor Series
    [*] Infinite Series of Constant Terms
    [*] Tests for Convergence and Divergence
    [*] Absolute and Conditional Convergence
    [*] The Ratio Test
    [*] Power Series
    [*] Return to Taylor's Series
    [*] Some Applications of Taylor's Series
    [*] Series as Functions
    [/LIST]
    [*] Functions of Two or More Variables and Their Geometric Representation
    [LIST]
    [*] Functions of Two or More Variables
    [*] Basic Facts on Three-Dimensional Cartesian Coordinates
    [*] Equations of Planes
    [*] Equations of Straight Lines
    [*] Quadric or Second Degree Surfaces
    [*] Remarks on Further Work in Solid Analytic Geometry
    [/LIST]
    [*] Partial Differentiation
    [LIST]
    [*] Functions of Two or More Variables
    [*] Partial Differentiation
    [*] The Geometrical Meaning of the Partial Derivatives
    [*] The Directional Derivative
    [*] The Chain Rule
    [*] Implicit Functions
    [*] Differentials
    [*] Maxima and Minima
    [*] Envelopes
    [/LIST]
    [*] Multiple Integrals
    [LIST]
    [*] Introduction
    [*] Volume Under a Surface
    [*] Some Physical Applications of the Double Integral
    [*] The Double Integral
    [*] The Double Integral in Cylindrical Coordinates
    [*] Triple Integrals in Rectangular Coordinates
    [*] Triple Integrals in Cylindrical Coordinates
    [*] Triple Integrals in Spherical Coordinates
    [*] The Moment of Inertia of a Body
    [/LIST]
    [*] An Introduction to Differential Equations
    [LIST]
    [*] Introduction
    [*] First-Order Ordinary Differential Equations
    [*] Second-Order Linear Homogeneous Differential Equations
    [*] Second-Order Linear Non-Homogeneous Differential Equations
    [/LIST]
    [*] A Reconsideration of the Foundations
    [LIST]
    [*] Introduction
    [*] The Concept of a Function
    [*] The Concept of a Limit of a Function
    [*] Some Theorems on Limits of Functions
    [*] Continuity and Differentiability
    [*] The Limit of a Sequence
    [*] Some Theorems on Limits of Sequences
    [*] The Definite Integral
    [*] Improper Integrals
    [*] The Fundamental Theorem of the Calculus
    [*] The Directions of Future Work
    [/LIST]
    [*] Tables
    [*] Index
    [/LIST]
     
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Feb 14, 2013 #2
    The thing that I like about this book is that it doesn't just briefly mention applications, it actually does them. So in the chapter on polar coordinates he has a complete section on Kepler's laws, in the max/min sections he has Fermat's principle of least time, etc.
     
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