{"product_id":"calculus-isbn-9781119777915","title":"Calculus","description":"\u003cp\u003eThe ideal resource for promoting active learning in flipped classroom environments, Calculus: Multivariable, 8th Edition brings calculus to real life with relevant examples and a variety of problems with applications from the physical sciences, economics, health, biology, engineering, and economics. Emphasizing the Rule of Four—viewing problems graphically, numerically, symbolically, and verbally—this popular textbook provides students with numerous opportunities to master key mathematical concepts and apply critical thinking skills to reveal solutions to mathematical problems.\u003c\/p\u003e \u003cp\u003eDeveloped by Calculus Consortium based at Harvard University, \u003ci\u003eCalculus: Multivariable\u003c\/i\u003e uses a student-friendly approach that highlights the practical value of mathematics while reinforcing both the conceptual understanding and computational skills required to reduce complicated problems to simple procedures. The new eighth edition further reinforces the Rule of Four, offers additional problem sets and updated examples, and supports complex, multi-part questions through new visualizations and graphing questions powered by GeoGebra.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Functions to Several Variables 693\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Functions to 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 to 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 to 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 to Several Variables 889\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 The Definite Integral to a Function to 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 to 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 to 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 to 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 to 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 to 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 to 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 to 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 1107\u003c\/p\u003e \u003cp\u003eIndex 1129\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988877361381,"sku":"NP9781119777915","price":111.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119777915.jpg?v=1761781882","url":"https:\/\/k12savings.com\/es\/products\/calculus-isbn-9781119777915","provider":"K12savings","version":"1.0","type":"link"}