{"product_id":"calculus-9781119770671","title":"Calculus","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eChapter 1. Precalculus Review. \u003cp\u003e1.1       What is Calculus?\u003c\/p\u003e \u003cp\u003e1.2       Review of Elementary Mathematics.\u003c\/p\u003e \u003cp\u003e1.3       Review of Inequalities.\u003c\/p\u003e \u003cp\u003e1.4       Coordinate Plane; Analytic Geometry.\u003c\/p\u003e \u003cp\u003e1.5       Functions.\u003c\/p\u003e \u003cp\u003e1.6       The Elementary Functions.\u003c\/p\u003e \u003cp\u003e1.7       Combinations of Functions.\u003c\/p\u003e \u003cp\u003e1.8       A Note on Mathematical Proof; Mathematical Induction.\u003c\/p\u003e \u003cp\u003eChapter 2. Limits and Continuity.\u003c\/p\u003e \u003cp\u003e2.1       The Limit Process (An Intuitive Introduction).\u003c\/p\u003e \u003cp\u003e2.2       Definition of Limit.\u003c\/p\u003e \u003cp\u003e2.3       Some Limit Theorems.\u003c\/p\u003e \u003cp\u003e2.4       Continuity.\u003c\/p\u003e \u003cp\u003e2.5       The Pinching Theorem; Trigonometric Limits.\u003c\/p\u003e \u003cp\u003e2.6       Two Basic Theorems.\u003c\/p\u003e \u003cp\u003eChapter 3. The Derivative; The Process of Differentiation.\u003c\/p\u003e \u003cp\u003e3.1       The Derivative.\u003c\/p\u003e \u003cp\u003e3.2       Some Differentiation Formulas.\u003c\/p\u003e \u003cp\u003e3.3       The \u003ci\u003ed\/dx\u003c\/i\u003e Notation; Derivatives of Higher Order.\u003c\/p\u003e \u003cp\u003e3.4       The Derivative as a Rate of Change.\u003c\/p\u003e \u003cp\u003e3.5       The Chain Rule.\u003c\/p\u003e \u003cp\u003e3.6       Differentiating the Trigonometric Functions.\u003c\/p\u003e \u003cp\u003e3.7       Implicit Differentiation; Rational Powers.\u003c\/p\u003e \u003cp\u003eChapter 4. The Mean-Value Theorem; Applications of the First and Second Derivatives.\u003c\/p\u003e \u003cp\u003e4.1       The Mean-Value Theorem.\u003c\/p\u003e \u003cp\u003e4.2       Increasing and Decreasing Functions.\u003c\/p\u003e \u003cp\u003e4.3       Local Extreme Values.\u003c\/p\u003e \u003cp\u003e4.4       Endpoint Extreme Values; Absolute Extreme Values.\u003c\/p\u003e \u003cp\u003e4.5       Some Max-Min Problems.\u003c\/p\u003e \u003cp\u003e4.6       Concavity and Points of Inflection.\u003c\/p\u003e \u003cp\u003e4.7       Vertical and Horizontal Asymptotes; Vertical Tangents and Cusps.\u003c\/p\u003e \u003cp\u003e4.8       Some Curve Sketching.\u003c\/p\u003e \u003cp\u003e4.9       Velocity and Acceleration; Speed.\u003c\/p\u003e \u003cp\u003e4.10     Related Rates of Change Per Unit Time.\u003c\/p\u003e \u003cp\u003e4.11     Differentials.\u003c\/p\u003e \u003cp\u003e4.12     Newton-Raphson Approximations.\u003c\/p\u003e \u003cp\u003eChapter 5.  Integration.\u003c\/p\u003e \u003cp\u003e5.1       An Area Problem; A Speed-Distance Problem.\u003c\/p\u003e \u003cp\u003e5.2       The Definite Integral of a Continuous Function.\u003c\/p\u003e \u003cp\u003e\u003cbr\u003e5.3       The Function f(x) = Integral from a to x of f(t) dt.\u003c\/p\u003e \u003cp\u003e5.4      The Fundamental Theorem of Integral Calculus.\u003c\/p\u003e \u003cp\u003e5.5       Some Area Problems.\u003c\/p\u003e \u003cp\u003e5.6       Indefinite Integrals.\u003c\/p\u003e \u003cp\u003e5.7       Working Back from the Chain Rule; the \u003ci\u003eu\u003c\/i\u003e-Substitution.\u003c\/p\u003e \u003cp\u003e5.8       Additional Properties of the Definite Integral.\u003c\/p\u003e \u003cp\u003e5.9       Mean-Value Theorems for Integrals; Average Value of a Function.\u003c\/p\u003e \u003cp\u003eChapter 6.  Some Applications of the Integral.\u003c\/p\u003e \u003cp\u003e6.1       More on Area.\u003c\/p\u003e \u003cp\u003e6.2       Volume by Parallel Cross-Sections; Discs and Washers.\u003c\/p\u003e \u003cp\u003e6.3       Volume by the Shell Method.\u003c\/p\u003e \u003cp\u003e6.4       The Centroid of a Region; Pappus’s Theorem on Volumes.\u003c\/p\u003e \u003cp\u003e6.5       The Notion of Work.\u003c\/p\u003e \u003cp\u003e6.6       Fluid Force.\u003c\/p\u003e \u003cp\u003eChapter 7.  The Transcendental Functions.\u003c\/p\u003e \u003cp\u003e7.1       One-to-One Functions; Inverse Functions.\u003c\/p\u003e \u003cp\u003e7.2       The Logarithm Function, Part I.\u003c\/p\u003e \u003cp\u003e7.3       The Logarithm Function, Part II.\u003c\/p\u003e \u003cp\u003e7.4       The Exponential Function.\u003c\/p\u003e \u003cp\u003e7.5       Arbitrary Powers; Other Bases.\u003c\/p\u003e \u003cp\u003e7.6       Exponential Growth and Decay.\u003c\/p\u003e \u003cp\u003e7.7       The Inverse Trigonometric Functions.\u003c\/p\u003e \u003cp\u003e7.8       The Hyperbolic Sine and Cosine.\u003c\/p\u003e \u003cp\u003e7.9       The Other Hyperbolic Functions.\u003c\/p\u003e \u003cp\u003eChapter 8.  Techniques of Integration.\u003c\/p\u003e \u003cp\u003e8.1       Integral Tables and Review.\u003c\/p\u003e \u003cp\u003e8.2       Integration by Parts.\u003c\/p\u003e \u003cp\u003e8.3       Powers and Products of Trigonometric Functions.\u003c\/p\u003e \u003cp\u003e\u003cbr\u003e8.4       Integrals Featuring Square Root of (a^2 – x^2),  Square Root of (a^2 + x^2), and Square Root of (x^2 – a^2).\u003c\/p\u003e \u003cp\u003e8.5       Rational Functions; Partial Functions.\u003c\/p\u003e \u003cp\u003e8.6       Some Rationalizing Substitutions.\u003c\/p\u003e \u003cp\u003e8.7       Numerical Integration.\u003c\/p\u003e \u003cp\u003eChapter 9.  Differential Equations.\u003c\/p\u003e \u003cp\u003e9.1       First-Order Linear Equations.\u003c\/p\u003e \u003cp\u003e9.2       Integral Curves; Separable Equations.\u003c\/p\u003e \u003cp\u003e9.3       The Equation \u003ci\u003ey\u003c\/i\u003e′′ + \u003ci\u003eay\u003c\/i\u003e′+ \u003ci\u003eby\u003c\/i\u003e = 0.\u003c\/p\u003e \u003cp\u003eChapter 10.  The Conic Sections; Polar Coordinates; Parametric Equations.\u003c\/p\u003e \u003cp\u003e10.1     Geometry of Parabola, Ellipse, Hyperbola.\u003c\/p\u003e \u003cp\u003e10.2     Polar Coordinates.\u003c\/p\u003e \u003cp\u003e10.3     Graphing in Polar Coordinates.\u003c\/p\u003e \u003cp\u003e10.4     Area in Polar Coordinates.\u003c\/p\u003e \u003cp\u003e10.5     Curves Given Parametrically.\u003c\/p\u003e \u003cp\u003e10.6     Tangents to Curves Given Parametrically.\u003c\/p\u003e \u003cp\u003e10.7     Arc Length and Speed.\u003c\/p\u003e \u003cp\u003e10.8     The Area of a Surface of Revolution; Pappus’s Theorem on Surface Area.\u003c\/p\u003e \u003cp\u003eChapter 11.  Sequences; Indeterminate Forms; Improper Integrals.\u003c\/p\u003e \u003cp\u003e11.1     The Least Upper Bound Axiom.\u003c\/p\u003e \u003cp\u003e11.2     Sequences of Real Numbers.\u003c\/p\u003e \u003cp\u003e11.3     The Limit of a Sequence.\u003c\/p\u003e \u003cp\u003e11.4     Some Important Limits.\u003c\/p\u003e \u003cp\u003e11.5     The Indeterminate Forms (0\/0).\u003c\/p\u003e \u003cp\u003e11.6     The Indeterminate Form (∞\/∞); Other Indeterminate Forms.\u003c\/p\u003e \u003cp\u003e11.7     Improper Integrals.\u003c\/p\u003e \u003cp\u003eChapter 12.  Infinite Series.\u003c\/p\u003e \u003cp\u003e12.1     Sigma Notation.\u003c\/p\u003e \u003cp\u003e12.2     Infinite Series.\u003c\/p\u003e \u003cp\u003e12.3     The Integral Test; Basic Comparison, Limit Comparison.\u003c\/p\u003e \u003cp\u003e12.4     The Root Test; The Ratio Test.\u003c\/p\u003e \u003cp\u003e12.5     Absolute and Conditional Convergence; Alternating Series.\u003c\/p\u003e \u003cp\u003e12.6     Taylor Polynomials in \u003ci\u003ex\u003c\/i\u003e; Taylor Series in \u003ci\u003ex.\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e12.7     Taylor Polynomials and Taylor Series in \u003ci\u003ex\u003c\/i\u003e – \u003ci\u003ea.\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e12.8     Power Series.\u003c\/p\u003e \u003cp\u003e12.9     Differentiation and Integration of Power Series.\u003c\/p\u003e \u003cp\u003eChapter 13.  Vectors.\u003c\/p\u003e \u003cp\u003e13.1     Rectangular Space Coordinates.\u003c\/p\u003e \u003cp\u003e13.2     Vectors in Three-Dimensional Space.\u003c\/p\u003e \u003cp\u003e13.3     The Dot Product.\u003c\/p\u003e \u003cp\u003e13.4     The Cross Product.\u003c\/p\u003e \u003cp\u003e13.5     Lines.\u003c\/p\u003e \u003cp\u003e13.6     Planes.\u003c\/p\u003e \u003cp\u003e13.7     Higher Dimensions.\u003c\/p\u003e \u003cp\u003eChapter 14.  Vector Calculus.\u003c\/p\u003e \u003cp\u003e14.1     Limit, Continuity, Vector Derivative.\u003c\/p\u003e \u003cp\u003e14.2     The Rules of Differentiation.\u003c\/p\u003e \u003cp\u003e14.3     Curves.\u003c\/p\u003e \u003cp\u003e14.4     Arc Length.\u003c\/p\u003e \u003cp\u003e14.5     Curvilinear Motion; Curvature.\u003c\/p\u003e \u003cp\u003e14.6     Vector Calculus in Mechanics.\u003c\/p\u003e \u003cp\u003e14.7     Planetary Motion.\u003c\/p\u003e \u003cp\u003eChapter 15.  Functions of Several Variables.\u003c\/p\u003e \u003cp\u003e15.1     Elementary Examples.\u003c\/p\u003e \u003cp\u003e15.2     A Brief Catalogue of Quadric Surfaces; Projections.\u003c\/p\u003e \u003cp\u003e15.3     Graphs; Level Curves and Level Surfaces.\u003c\/p\u003e \u003cp\u003e15.4     Partial Derivatives.\u003c\/p\u003e \u003cp\u003e15.5     Open Sets and Closed Sets.\u003c\/p\u003e \u003cp\u003e15.6     Limits and Continuity; Equality of Mixed Partials.\u003c\/p\u003e \u003cp\u003eChapter 16.  Gradients; Extreme Values; Differentials.\u003c\/p\u003e \u003cp\u003e16.1     Differentiability and Gradient.\u003c\/p\u003e \u003cp\u003e16.2     Gradients and Directional Derivatives.\u003c\/p\u003e \u003cp\u003e16.3     The Mean-Value Theorem; the Chain Rule.\u003c\/p\u003e \u003cp\u003e16.4     The Gradient as a Normal; Tangent Lines and Tangent Planes.\u003c\/p\u003e \u003cp\u003e16.5     Local Extreme Values.\u003c\/p\u003e \u003cp\u003e16.6     Absolute Extreme Values.\u003c\/p\u003e \u003cp\u003e16.7     Maxima and Minima with Side Conditions.\u003c\/p\u003e \u003cp\u003e16.8     Differentials.\u003c\/p\u003e \u003cp\u003e16.9     Reconstructing a Function from Its Gradient.\u003c\/p\u003e \u003cp\u003eChapter 17.  Multiple Integrals.\u003c\/p\u003e \u003cp\u003e17.1     Multiple-Sigma Notation.\u003c\/p\u003e \u003cp\u003e17.2     Double Integrals.\u003c\/p\u003e \u003cp\u003e17.3     The Evaluation of Double Integrals by Repeated Integrals.\u003c\/p\u003e \u003cp\u003e17.4     The Double Integral as the Limit or Riemann Sums; Polar Coordinates.\u003c\/p\u003e \u003cp\u003e17.5     Further Applications of Double Integration.\u003c\/p\u003e \u003cp\u003e17.6     Triple Integrals.\u003c\/p\u003e \u003cp\u003e17.7     Reduction to Repeated Integrals.\u003c\/p\u003e \u003cp\u003e17.8     Cylindrical Coordinates.\u003c\/p\u003e \u003cp\u003e17.9     The Triple Integral as the Limit of Riemann Sums; Spherical Coordinates.\u003c\/p\u003e \u003cp\u003e17.10   Jacobians; Changing Variables in Multiple Integration.\u003c\/p\u003e \u003cp\u003eChapter 18.  Line Integrals and Surface Integrals.\u003c\/p\u003e \u003cp\u003e18.1     Line Integrals.\u003c\/p\u003e \u003cp\u003e18.2     The Fundamental Theorem for Line Integrals.\u003c\/p\u003e \u003cp\u003e18.3     Work-Energy Formula; Conservation of Mechanical Energy.\u003c\/p\u003e \u003cp\u003e18.4     Another Notation for Line Integrals; Line Integrals with Respect to Arc Length.\u003c\/p\u003e \u003cp\u003e18.5     Green’s Theorem.\u003c\/p\u003e \u003cp\u003e18.6     Parametrized Surfaces; Surface Area.\u003c\/p\u003e \u003cp\u003e18.7     Surface Integrals.\u003c\/p\u003e \u003cp\u003e18.8     The Vector Differential Operator Ñ.\u003c\/p\u003e \u003cp\u003e18.9     The Divergence Theorem.\u003c\/p\u003e \u003cp\u003e18.10   Stokes’s Theorem.\u003c\/p\u003e \u003cp\u003eChapter 19.  Additional Differential Equations.\u003c\/p\u003e \u003cp\u003e19.1     Bernoulli Equations; Homogeneous Equations.\u003c\/p\u003e \u003cp\u003e19.2     Exact Differential Equations; Integrating Factors.\u003c\/p\u003e \u003cp\u003e19.3     Numerical Methods.\u003c\/p\u003e \u003cp\u003e19.4     The Equation \u003ci\u003ey\u003c\/i\u003e′′ + \u003ci\u003eay\u003c\/i\u003e′+ \u003ci\u003eby\u003c\/i\u003e = ø(\u003ci\u003ex\u003c\/i\u003e).\u003c\/p\u003e \u003cp\u003e19.5     Mechanical Vibrations.\u003c\/p\u003e \u003cp\u003eAppendix A.  Some Additional Topics.\u003c\/p\u003e \u003cp\u003eA.1      Rotation of Axes; Eliminating the \u003ci\u003exy\u003c\/i\u003e-Term.\u003c\/p\u003e \u003cp\u003eA.2      Determinants.\u003c\/p\u003e \u003cp\u003eAppendix B.  Some Additional Proofs.\u003c\/p\u003e \u003cp\u003eB.1       The Intermediate-Value Theorem.\u003c\/p\u003e \u003cp\u003eB.2       Boundedness; Extreme-Value Theorem.\u003c\/p\u003e \u003cp\u003eB.3       Inverses.\u003c\/p\u003e \u003cp\u003eB.4       The Integrability of Continuous Functions.\u003c\/p\u003e \u003cp\u003eB.5       The Integral as the Limit of Riemann Sums.\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49407146328407,"sku":"9781119770671","price":53.19,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119770671.jpg?v=1730498331","url":"https:\/\/bookcurl.com\/products\/calculus-9781119770671","provider":"Book Curl","version":"1.0","type":"link"}