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kline m calculus intuitive physical approach 2ed 1998

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Textbook in PDF format Application-oriented introduction relates the subject as closely as possible to science. In-depth explorations of the derivative, the differentiation and integration of the powers of x, and theorems on differentiation and antidifferentiation lead to a definition of the chain rule and examinations of trigonometric functions, logarithmic and exponential functions, techniques of integration, polar coordinates, much more. Clear-cut explanations, numerous drills, illustrative examples. 1967 edition. Solution guide available upon request. Why calculus? The Historical Motivations for the Calculus The Creators of the Calculus The Nature of the Calculus The derivative 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 = ax2 The Derived Function The Differentiation of Simple Monomials The Differentiation of Simple Polynomials The Second Derivative The antiderived function or the integral The Integral Straight Line Motion in One Direction Up and Down Motion Motion Along an Inclined Plane Appendix The Coordinate Geometry of Straight Lines A1. The Need for Geometrical Interpretation A2. The Distance Formula A3. The Slope of a Straight Line A4. The Inclination of a Line A5. Slopes of Parallel and Perpendicular Lines A6. The Angle Between Two Lines A7. The Equation of a Straight Line A8. The Distance from a Point to a Line A9. Equation and Curve The geometrical significance of the derivative The Derivative as Slope The Concept of Tangent to a Curve Applications of the Derivative as the Slope The Equation of the Parabola Physical Applications of the Derivative as Slope Further Discussion of the Derivative as the Slope The differentiation and integration of powers of x The Functions xn for Positive Integral n A Calculus Method of Finding Roots Differentiation and Integration of xn for Fractional Values of n Some theorems on differentiation and antidifferentiation 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 The Chain rule 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 Related Rates Appendix Transformation of Coordinates A1. Introduction A2. Rotation of Axes A3. Translation of Axes A4. Invariants Maxima and Minima 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 9 The definite integral Area as the Limit of a Sum The Definite Integral The Evaluation of Definite Integrals Areas Below the x-Axis Areas Between Curves Some Additional Properties of the Definite Integral Numerical Methods for Evaluating Definite Integrals Appendix The Sum of the Squares of the First n Integers The trigonometric functions The Sinusoidal Functions Some Preliminaries on Limits Differentiation of the Trigonometric Functions Integration of the Trigonometric Functions Application of the Trigonometric Functions to Periodic Phenomena The inverse trigonometric functions 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 Logarithmic and exponential functions 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 Differentials and the law of the mean Differentials The Mean Value Theorem of the Differential Calculus Indeterminate Forms Further techniques of integration Integration by Parts Reduction Formulas Integration by Partial Fractions Integration by Substitution and Change of Variable The Use of Tables Some geometric uses of the definite integral 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 Some physical applications of the definite integral The Calculation of Work Applications to Economics The Hanging Chain Gravitational Attraction of Rods Gravitational Attraction of Disks Gravitational Attraction of Spheres Polar coordinates 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 Rectangular parametric equations and curvilinear motion The Parametric Equations of a Curve Some Additional Examples of Parametric Equations Projectile 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 Polar parametric equations and curvilinear motion Polar Parametric Equations Velocity and Acceleration in the Polar Parametric Representation Kepler’s Laws Satellites and Projectiles Taylor’s theorem and infinite series 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 Functions of two or more variables and their geometric representation 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 Partial differentiation 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 Multiple integrals 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 24 An introduction to differential equations First-Order Ordinary Differential Equations Second-Order Linear Homogeneous Differential Equations Second-Order Linear Non-Homogeneous Differential Equations A reconsideration of the foundations The Concept of a Function The Concept of the 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 Tables

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kline m calculus intuitive physical approach 2ed 1998

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