{"product_id":"calculus-isbn-9781119778189","title":"Calculus","description":"In the newly revised Twelfth Edition of Calculus: Early Transcendentals, an expert team of mathematicians delivers a rigorous and intuitive exploration of calculus, introducing polynomials, rational functions, exponentials, logarithms, and trigonometric functions early in the text. Using the Rule of Four, the authors present mathematical concepts from verbal, algebraic, visual, and numerical points of view. The book includes numerous exercises, applications, and examples that help readers learn and retain the concepts discussed within. \u003cp\u003ePREFACE vii\u003c\/p\u003e \u003cp\u003eSUPPLEMENTS ix\u003c\/p\u003e \u003cp\u003eACKNOWLEDGMENTS xi\u003c\/p\u003e \u003cp\u003eTHE ROOTS OF CALCULUS xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Limits and Continuity 1 \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Limits (An Intuitive Approach) 1\u003c\/p\u003e \u003cp\u003e1.2 Computing Limits 13\u003c\/p\u003e \u003cp\u003e1.3 Limits at Infinity; End Behavior of a Function 21\u003c\/p\u003e \u003cp\u003e1.4 Limits (Discussed More Rigorously) 30\u003c\/p\u003e \u003cp\u003e1.5 Continuity 39\u003c\/p\u003e \u003cp\u003e1.6 Continuity of Trigonometric Functions 50\u003c\/p\u003e \u003cp\u003e1.7 Inverse Trigonometric Functions 55\u003c\/p\u003e \u003cp\u003e1.8 Exponential and Logarithmic Functions 62\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 The Derivative 77 \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Tangent Lines and Rates of Change 77\u003c\/p\u003e \u003cp\u003e2.2 The Derivative Function 87\u003c\/p\u003e \u003cp\u003e2.3 Introduction to Techniques of Differentiation 98\u003c\/p\u003e \u003cp\u003e2.4 The Product and Quotient Rules 105\u003c\/p\u003e \u003cp\u003e2.5 Derivatives of Trigonometric Functions 110\u003c\/p\u003e \u003cp\u003e2.6 The Chain Rule 114\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Topics in Differentiation 124 \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Implicit Differentiation 124\u003c\/p\u003e \u003cp\u003e3.2 Derivatives of Logarithmic Functions 131\u003c\/p\u003e \u003cp\u003e3.3 Derivatives of Exponential and Inverse Trigonometric Functions 136\u003c\/p\u003e \u003cp\u003e3.4 Related Rates 142\u003c\/p\u003e \u003cp\u003e3.5 Local Linear Approximation; Differentials 149\u003c\/p\u003e \u003cp\u003e3.6 L’Hoˆ pital’s Rule; Indeterminate Forms 157\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 The Derivative in Graphing \u003c\/b\u003e\u003cb\u003eand Applications 169 \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Analysis of Functions I: Increase, Decrease, and Concavity 169\u003c\/p\u003e \u003cp\u003e4.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials 180\u003c\/p\u003e \u003cp\u003e4.3 Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents 189\u003c\/p\u003e \u003cp\u003e4.4 Absolute Maxima and Minima 200\u003c\/p\u003e \u003cp\u003e4.5 Applied Maximum and Minimum Problems 208\u003c\/p\u003e \u003cp\u003e4.6 Rectilinear Motion 222\u003c\/p\u003e \u003cp\u003e4.7 Newton’s Method 230\u003c\/p\u003e \u003cp\u003e4.8 Rolle’s Theorem; Mean-Value Theorem 235\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Integration 249 \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 An Overview of the Area Problem 249\u003c\/p\u003e \u003cp\u003e5.2 The Indefinite Integral 254\u003c\/p\u003e \u003cp\u003e5.3 Integration by Substitution 264\u003c\/p\u003e \u003cp\u003e5.4 The Definition of Area as a Limit; Sigma Notation 271\u003c\/p\u003e \u003cp\u003e5.5 The Definite Integral 281\u003c\/p\u003e \u003cp\u003e5.6 The Fundamental Theorem of Calculus 290\u003c\/p\u003e \u003cp\u003e5.7 Rectilinear Motion Revisited Using Integration 302\u003c\/p\u003e \u003cp\u003e5.8 Average Value of a Function and its Applications 310\u003c\/p\u003e \u003cp\u003e5.9 Evaluating Definite Integrals by Substitution 315\u003c\/p\u003e \u003cp\u003e5.10 Logarithmic and Other Functions Defined by Integrals 320\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Applications of the Definite \u003c\/b\u003e\u003cb\u003eIntegral in Geometry, Science, and Engineering 336 \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Area Between Two Curves 336\u003c\/p\u003e \u003cp\u003e6.2 Volumes by Slicing; Disks and Washers 344\u003c\/p\u003e \u003cp\u003e6.3 Volumes by Cylindrical Shells 354\u003c\/p\u003e \u003cp\u003e6.4 Length of a Plane Curve 360\u003c\/p\u003e \u003cp\u003e6.5 Area of a Surface of Revolution 365\u003c\/p\u003e \u003cp\u003e6.6 Work 370\u003c\/p\u003e \u003cp\u003e6.7 Moments, Centers of Gravity, and Centroids 378\u003c\/p\u003e \u003cp\u003e6.8 Fluid Pressure and Force 387\u003c\/p\u003e \u003cp\u003e6.9 Hyperbolic Functions and Hanging Cables 392\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Principles of Integral \u003c\/b\u003e\u003cb\u003eEvaluation 406 \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 An Overview of Integration Methods 406\u003c\/p\u003e \u003cp\u003e7.2 Integration by Parts 409\u003c\/p\u003e \u003cp\u003e7.3 Integrating Trigonometric Functions 417\u003c\/p\u003e \u003cp\u003e7.4 Trigonometric Substitutions 424\u003c\/p\u003e \u003cp\u003e7.5 Integrating Rational Functions by Partial Fractions 430\u003c\/p\u003e \u003cp\u003e7.6 Using Computer Algebra Systems and Tables of Integrals 437\u003c\/p\u003e \u003cp\u003e7.7 Numerical Integration; Simpson’s Rule 446\u003c\/p\u003e \u003cp\u003e7.8 Improper Integrals 458\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Mathematical Modeling \u003c\/b\u003e\u003cb\u003ewith Differential Equations 471 \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Modeling with Differential Equations 471\u003c\/p\u003e \u003cp\u003e8.2 Separation of Variables 477\u003c\/p\u003e \u003cp\u003e8.3 Slope Fields; Euler’s Method 488\u003c\/p\u003e \u003cp\u003e8.4 First-Order Differential Equations and Applications 494\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Infinite Series 504 \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Sequences 504\u003c\/p\u003e \u003cp\u003e9.2 Monotone Sequences 513\u003c\/p\u003e \u003cp\u003e9.3 Infinite Series 520\u003c\/p\u003e \u003cp\u003e9.4 Convergence Tests 528\u003c\/p\u003e \u003cp\u003e9.5 The Comparison, Ratio, and Root Tests 534\u003c\/p\u003e \u003cp\u003e9.6 Alternating Series; Absolute and Conditional Convergence 539\u003c\/p\u003e \u003cp\u003e9.7 Maclaurin and Taylor Polynomials 549\u003c\/p\u003e \u003cp\u003e9.8 Maclaurin and Taylor Series; Power Series 559\u003c\/p\u003e \u003cp\u003e9.9 Convergence of Taylor Series 567\u003c\/p\u003e \u003cp\u003e9.10 Differentiating and Integrating Power Series; Modeling with Taylor Series 575\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Parametric and Polar Curves; \u003c\/b\u003e\u003cb\u003eConic Sections 588 \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Parametric Equations; Tangent Lines and Arc Length for Parametric Curves 588\u003c\/p\u003e \u003cp\u003e10.2 Polar Coordinates 600\u003c\/p\u003e \u003cp\u003e10.3 Tangent Lines, Arc Length, and Area for Polar Curves 613\u003c\/p\u003e \u003cp\u003e10.4 Conic Sections 622\u003c\/p\u003e \u003cp\u003e10.5 Rotation of Axes; Second-Degree Equations 639\u003c\/p\u003e \u003cp\u003e10.6 Conic Sections in Polar Coordinates 644\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 \u003c\/b\u003e\u003cb\u003eThree-dimensional Space; Vector \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces 657\u003c\/p\u003e \u003cp\u003e11.2 Vectors 663\u003c\/p\u003e \u003cp\u003e11.3 Dot Product; Projections 673\u003c\/p\u003e \u003cp\u003e11.4 Cross Product 682\u003c\/p\u003e \u003cp\u003e11.5 Parametric Equations of Lines 692\u003c\/p\u003e \u003cp\u003e11.6 Planes in 3-Space 698\u003c\/p\u003e \u003cp\u003e11.7 Quadric Surfaces 705\u003c\/p\u003e \u003cp\u003e11.7 Cylindrical and Spherical Coordinates 715\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 \u003c\/b\u003e\u003cb\u003eVector-Valued Functions 723 \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction to Vector-Valued Functions 723\u003c\/p\u003e \u003cp\u003e12.2 Calculus of Vector-Valued Functions 729\u003c\/p\u003e \u003cp\u003e12.3 Change of Parameter; Arc Length 738\u003c\/p\u003e \u003cp\u003e12.4 Unit Tangent, Normal, and Binormal Vectors 746\u003c\/p\u003e \u003cp\u003e12.5 Curvature 751\u003c\/p\u003e \u003cp\u003e12.6 Motion Along a Curve 759\u003c\/p\u003e \u003cp\u003e12.7 Kepler’s Laws of Planetary Motion 771\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Partial Derivatives 781 \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Functions of Two or More Variables 781\u003c\/p\u003e \u003cp\u003e13.2 Limits and Continuity 791\u003c\/p\u003e \u003cp\u003e13.3 Partial Derivatives 800\u003c\/p\u003e \u003cp\u003e13.4 Differentiability, Differentials, and Local Linearity 812\u003c\/p\u003e \u003cp\u003e13.5 The Chain Rule 820\u003c\/p\u003e \u003cp\u003e13.6 Directional Derivatives and Gradients 830\u003c\/p\u003e \u003cp\u003e13.7 Tangent Planes and Normal Vectors 840\u003c\/p\u003e \u003cp\u003e13.8 Maxima and Minima of Functions of Two Variables 845\u003c\/p\u003e \u003cp\u003e13.9 Lagrange Multipliers 856\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Multiple Integrals 925 \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Double Integrals 925\u003c\/p\u003e \u003cp\u003e14.2 Double Integrals Over Nonrectangular Regions 932\u003c\/p\u003e \u003cp\u003e14.3 Double Integrals in Polar Coordinates 941\u003c\/p\u003e \u003cp\u003e14.4 Surface Area; Parametric Surfaces 948\u003c\/p\u003e \u003cp\u003e14.5 Triple Integrals 961\u003c\/p\u003e \u003cp\u003e14.6 Triple Integrals in Cylindrical and Spherical Coordinates 968\u003c\/p\u003e \u003cp\u003e14.7 Change of Variables in Multiple Integrals; Jacobians 977\u003c\/p\u003e \u003cp\u003e14.8 Centers of Gravity Using Multiple Integrals 989\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Topics in Vector Calculus 1001 \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Vector Fields 1001\u003c\/p\u003e \u003cp\u003e15.2 Line Integrals 1010\u003c\/p\u003e \u003cp\u003e15.3 Independence of Path; Conservative Vector Fields 1025\u003c\/p\u003e \u003cp\u003e15.4 Green’s Theorem 1035\u003c\/p\u003e \u003cp\u003e15.5 Surface Integrals 1042\u003c\/p\u003e \u003cp\u003e15.6 Applications of Surface Integrals; Flux 1049\u003c\/p\u003e \u003cp\u003e15.7 The Divergence Theorem 1058\u003c\/p\u003e \u003cp\u003e15.8 Stokes’ Theorem 1067\u003c\/p\u003e \u003cp\u003eAPPENDIX A A1\u003c\/p\u003e \u003cp\u003eAPPENDIX B 00\u003c\/p\u003e \u003cp\u003eAPPENDIX C 00\u003c\/p\u003e \u003cp\u003eAPPENDIX D 00\u003c\/p\u003e \u003cp\u003eAPPENDIX E 00\u003c\/p\u003e \u003cp\u003eANSWERS 00\u003c\/p\u003e \u003cp\u003eINDEX I1\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988877623525,"sku":"NP9781119778189","price":111.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119778189.jpg?v=1761781883","url":"https:\/\/k12savings.com\/products\/calculus-isbn-9781119778189","provider":"K12savings","version":"1.0","type":"link"}