{"product_id":"calculus-isbn-9781119696551","title":"Calculus","description":"\u003cp\u003eThe Calculus Consortium's focus on the “Rule of Four” (viewing problems graphically, numerically, symbolically, and verbally) has become an integral part of teaching calculus in a way that promotes critical thinking to reveal solutions to mathematical problems. Their approach reinforces the conceptual understanding necessary to reduce complicated problems to simple procedures without losing sight of the practical value of mathematics. In this edition, the authors continue their focus on introducing different perspectives for students with an increased emphasis on active learning in a ‘flipped’ classroom. \u003c\/p\u003e\u003cp\u003eThe 8th edition of \u003ci\u003eCalculus: Single and Multivariable\u003c\/i\u003e features a variety of problems with applications from the physical sciences, health, biology, engineering, and economics, allowing for engagement across multiple majors. The Consortium brings Calculus to (real) life with current, relevant examples and a focus on active learning. \u003c\/p\u003e\u003cp\u003e\u003cb\u003e1 Foundation For Calculus: Functions and Limits 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Functions and Change 2\u003c\/p\u003e \u003cp\u003e1.2 Exponential Functions 14\u003c\/p\u003e \u003cp\u003e1.3 New Functions From Old 26\u003c\/p\u003e \u003cp\u003e1.4 Logarithmic Functions 34\u003c\/p\u003e \u003cp\u003e1.5 Trigonometric Functions 42\u003c\/p\u003e \u003cp\u003e1.6 Powers, Polynomials, and Rational Functions 53\u003c\/p\u003e \u003cp\u003e1.7 Introduction To Limits and Continuity 62\u003c\/p\u003e \u003cp\u003e1.8 Extending The Idea of A Limit 71\u003c\/p\u003e \u003cp\u003e1.9 Further Limit Calculations Using Algebra 80\u003c\/p\u003e \u003cp\u003e1.10 Preview of The Formal Definition of A Limit \u003ci\u003eOnline\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Key Concept: The Derivative 87\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 How Do We Measure Speed? 88\u003c\/p\u003e \u003cp\u003e2.2 The Derivative At A Point 96\u003c\/p\u003e \u003cp\u003e2.3 The Derivative Function 105\u003c\/p\u003e \u003cp\u003e2.4 Interpretations of The Derivative 113\u003c\/p\u003e \u003cp\u003e2.5 The Second Derivative 121\u003c\/p\u003e \u003cp\u003e2.6 Differentiability 130\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Short-Cuts To Differentiation 135\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Powers and Polynomials 136\u003c\/p\u003e \u003cp\u003e3.2 The Exponential Function 146\u003c\/p\u003e \u003cp\u003e3.3 The Product and Quotient Rules 151\u003c\/p\u003e \u003cp\u003e3.4 The Chain Rule 158\u003c\/p\u003e \u003cp\u003e3.5 The Trigonometric Functions 165\u003c\/p\u003e \u003cp\u003e3.6 The Chain Rule and Inverse Functions 171\u003c\/p\u003e \u003cp\u003e3.7 Implicit Functions 178\u003c\/p\u003e \u003cp\u003e3.8 Hyperbolic Functions 181\u003c\/p\u003e \u003cp\u003e3.9 Linear Approximation and The Derivative 185\u003c\/p\u003e \u003cp\u003e3.10 Theorems About Differentiable Functions 193\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Using The Derivative 199\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Using First and Second Derivatives 200\u003c\/p\u003e \u003cp\u003e4.2 Optimization 211\u003c\/p\u003e \u003cp\u003e4.3 Optimization and Modeling 220\u003c\/p\u003e \u003cp\u003e4.4 Families of Functions and Modeling 234\u003c\/p\u003e \u003cp\u003e4.5 Applications To Marginality 244\u003c\/p\u003e \u003cp\u003e4.6 Rates and Related Rates 253\u003c\/p\u003e \u003cp\u003e4.7 L’hopital’s Rule, Growth, and Dominance 264\u003c\/p\u003e \u003cp\u003e4.8 Parametric Equations 271\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Key Concept: The Definite Integral 285\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 How Do We Measure Distance Traveled? 286\u003c\/p\u003e \u003cp\u003e5.2 The Definite Integral 298\u003c\/p\u003e \u003cp\u003e5.3 The Fundamental Theorem and Interpretations 308\u003c\/p\u003e \u003cp\u003e5.4 Theorems About Definite Integrals 319\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Constructing Antiderivatives 333\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Antiderivatives Graphically and Numerically 334\u003c\/p\u003e \u003cp\u003e6.2 Constructing Antiderivatives Analytically 341\u003c\/p\u003e \u003cp\u003e6.3 Differential Equations and Motion 348\u003c\/p\u003e \u003cp\u003e6.4 Second Fundamental Theorem of Calculus 355\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Integration 361\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Integration By Substitution 362\u003c\/p\u003e \u003cp\u003e7.2 Integration By Parts 373\u003c\/p\u003e \u003cp\u003e7.3 Tables of Integrals 380\u003c\/p\u003e \u003cp\u003e7.4 Algebraic Identities and Trigonometric Substitutions 386\u003c\/p\u003e \u003cp\u003e7.5 Numerical Methods For Definite Integrals 398\u003c\/p\u003e \u003cp\u003e7.6 Improper Integrals 408\u003c\/p\u003e \u003cp\u003e7.7 Comparison of Improper Integrals 417\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Using The Definite Integral 425\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Areas and Volumes 426\u003c\/p\u003e \u003cp\u003e8.2 Applications To Geometry 436\u003c\/p\u003e \u003cp\u003e8.3 Area and Arc Length In Polar Coordinates 447\u003c\/p\u003e \u003cp\u003e8.4 Density and Center of Mass 456\u003c\/p\u003e \u003cp\u003e8.5 Applications To Physics 467\u003c\/p\u003e \u003cp\u003e8.6 Applications To Economics 478\u003c\/p\u003e \u003cp\u003e8.7 Distribution Functions 489\u003c\/p\u003e \u003cp\u003e8.8 Probability, Mean, and Median 497\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Sequences and Series 507\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Sequences 508\u003c\/p\u003e \u003cp\u003e9.2 Geometric Series 514\u003c\/p\u003e \u003cp\u003e9.3 Convergence of Series 522\u003c\/p\u003e \u003cp\u003e9.4 Tests For Convergence 529\u003c\/p\u003e \u003cp\u003e9.5 Power Series and Interval of Convergence 539\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Approximating Functions Using Series 549\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Taylor Polynomials 550\u003c\/p\u003e \u003cp\u003e10.2 Taylor Series 560\u003c\/p\u003e \u003cp\u003e10.3 Finding and Using Taylor Series 567\u003c\/p\u003e \u003cp\u003e10.4 The Error In Taylor Polynomial Approximations 577\u003c\/p\u003e \u003cp\u003e10.5 Fourier Series 584\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Differential Equations 599\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 What is a Differential Equation? 600\u003c\/p\u003e \u003cp\u003e11.2 Slope Fields 605\u003c\/p\u003e \u003cp\u003e11.3 Euler’s Method 614\u003c\/p\u003e \u003cp\u003e11.4 Separation of Variables 619\u003c\/p\u003e \u003cp\u003e11.5 Growth and Decay 625\u003c\/p\u003e \u003cp\u003e11.6 Applications and Modeling 637\u003c\/p\u003e \u003cp\u003e11.7 The Logistic Model 647\u003c\/p\u003e \u003cp\u003e11.8 Systems of Differential Equations 657\u003c\/p\u003e \u003cp\u003e11.9 Analyzing The Phase Plane 667\u003c\/p\u003e \u003cp\u003e11.10 Second-Order Differential Equations: Oscillations 674\u003c\/p\u003e \u003cp\u003e11.11 Linear Second-Order Differential Equations 682\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Functions of Several Variables 693\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Functions of Two Variables 694\u003c\/p\u003e \u003cp\u003e12.2 Graphs and Surfaces 702\u003c\/p\u003e \u003cp\u003e12.3 Contour Diagrams 711\u003c\/p\u003e \u003cp\u003e12.4 Linear Functions 725\u003c\/p\u003e \u003cp\u003e12.5 Functions of Three Variables 732\u003c\/p\u003e \u003cp\u003e12.6 Limits and Continuity 739\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 A Fundamental Tool: Vectors 745\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Displacement Vectors 746\u003c\/p\u003e \u003cp\u003e13.2 Vectors In General 755\u003c\/p\u003e \u003cp\u003e13.3 The Dot Product 763\u003c\/p\u003e \u003cp\u003e13.4 The Cross Product 774\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Differentiating Functions of Several Variables 785\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 The Partial Derivative 786\u003c\/p\u003e \u003cp\u003e14.2 Computing Partial Derivatives Algebraically 795\u003c\/p\u003e \u003cp\u003e14.3 Local Linearity and The Differential 800\u003c\/p\u003e \u003cp\u003e14.4 Gradients and Directional Derivatives In The Plane 809\u003c\/p\u003e \u003cp\u003e14.5 Gradients and Directional Derivatives In Space 819\u003c\/p\u003e \u003cp\u003e14.6 The Chain Rule 827\u003c\/p\u003e \u003cp\u003e14.7 Second-Order Partial Derivatives 838\u003c\/p\u003e \u003cp\u003e14.8 Differentiability 847\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Optimization: Local and Global Extrema 855\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Critical Points: Local Extrema and Saddle Points 856\u003c\/p\u003e \u003cp\u003e15.2 Optimization 866\u003c\/p\u003e \u003cp\u003e15.3 Constrained Optimization: Lagrange Multipliers 876\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Integrating Functions of Several Variables 889\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 The Definite Integral of A Function of Two Variables 890\u003c\/p\u003e \u003cp\u003e16.2 Iterated Integrals 898\u003c\/p\u003e \u003cp\u003e16.3 Triple Integrals 908\u003c\/p\u003e \u003cp\u003e16.4 Double Integrals In Polar Coordinates 916\u003c\/p\u003e \u003cp\u003e16.5 Integrals In Cylindrical and Spherical Coordinates 921\u003c\/p\u003e \u003cp\u003e16.6 Applications of Integration To Probability 931\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Parameterization and Vector Fields 937\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Parameterized Curves 938\u003c\/p\u003e \u003cp\u003e17.2 Motion, Velocity, and Acceleration 948\u003c\/p\u003e \u003cp\u003e17.3 Vector Fields 958\u003c\/p\u003e \u003cp\u003e17.4 The Flow of A Vector Field 966\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Line Integrals 973\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 The Idea of A Line Integral 974\u003c\/p\u003e \u003cp\u003e18.2 Computing Line Integrals Over Parameterized Curves 984\u003c\/p\u003e \u003cp\u003e18.3 Gradient Fields and Path-Independent Fields 992\u003c\/p\u003e \u003cp\u003e18.4 Path-Dependent Vector Fields and Green’s Theorem 1003\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Flux Integrals and Divergence 1017\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e19.1 The Idea of A Flux Integral 1018\u003c\/p\u003e \u003cp\u003e19.2 Flux Integrals For Graphs, Cylinders, and Spheres 1029\u003c\/p\u003e \u003cp\u003e19.3 The Divergence of A Vector Field 1039\u003c\/p\u003e \u003cp\u003e19.4 The Divergence Theorem 1048\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 The Curl and Stokes’ Theorem 1055\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e20.1 The Curl of A Vector Field 1056\u003c\/p\u003e \u003cp\u003e20.2 Stokes’ Theorem 1064\u003c\/p\u003e \u003cp\u003e20.3 The Three Fundamental Theorems 1071\u003c\/p\u003e \u003cp\u003e\u003cb\u003e21 Parameters, Coordinates, and Integrals 1077\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e21.1 Coordinates and Parameterized Surfaces 1078\u003c\/p\u003e \u003cp\u003e21.2 Change of Coordinates In A Multiple Integral 1089\u003c\/p\u003e \u003cp\u003e21.3 Flux Integrals Over Parameterized Surfaces 1094\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendices \u003c\/b\u003e\u003cb\u003e\u003ci\u003eOnline\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA Roots, Accuracy, and Bounds \u003ci\u003eOnline\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003eB Complex Numbers \u003ci\u003eOnline\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003eC Newton’s Method \u003ci\u003eOnline\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003eD Vectors In The Plane \u003ci\u003eOnline\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003eE Determinants \u003ci\u003eOnline\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003eReady Reference 1099\u003c\/p\u003e \u003cp\u003eAnswers To Odd Numbered Problems 1117\u003c\/p\u003e \u003cp\u003eIndex 1177\u003c\/p\u003e \u003cp\u003e\u003cb\u003eDeborah Hughes Hallett\u003c\/b\u003e is Professor of Mathematics at the University of Arizona and Adjunct Professor of Public Policy at the Harvard Kennedy School. With Andrew M. Gleason at Harvard, she organized the Calculus Consortium based at Harvard, which brought together faculty from a wide variety of schools to work on undergraduate curricular issues. She is regularly consulted on the design of curricula and pedagogy for undergraduate mathematics at the national and international level and she is an author of several college level mathematics texts. In 1998 and 2002 and 2006, she was co-chair of the International Conference on the Teaching of Mathematics in Greece and Turkey, attended by several hundred faculty from about 50 countries. She has designed courses in Brunei, Colombia and Niger. She was awarded the Louise Hay Prize and elected a fellow of the American Association for the Advancement of Science for contributions to mathematics education. Her work has been recognized by prizes from Harvard, the University of Arizona, and as national winner MAA Award for Distinguished Teaching. Deb was also recently awarded with the \u003cb\u003e2022 AMS Award for Impact on the Teaching and Learning of Mathematics\u003c\/b\u003e. This award is given annually to a mathematician (or group of mathematicians) who has made significant contributions of lasting value to mathematics education.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988877328613,"sku":"NP9781119696551","price":111.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119696551.jpg?v=1761781882","url":"https:\/\/k12savings.com\/products\/calculus-isbn-9781119696551","provider":"K12savings","version":"1.0","type":"link"}