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Overview
Clearly present and effectively demonstrate the concepts and rules of calculus with the student-focused approach in MULTIVARIABLE CALCULUS, 12th Edition by award-winning authors Larson and Edwards. This edition offers a wealth of learning support and digital resources -- all thoroughly updated and refined using proven learning design principles that remove typical barriers to learning to create a carefully planned, inclusive experience for all students. New "Big Ideas of Calculus" notes highlight overarching ideas behind chapter topics, while annotated examples, "Concept Checks" and visually driven exercises help students master key concepts. New automatically graded Proof Problems, Expanded Problems and "Explore It" interactive learning modules within WebAssign digital resources help students develop a deeper conceptual understanding as they apply concepts. In addition, CalcView.com, CalcChat.com and LarsonCalculus.com offer tutorial support to further your students' understanding.
What's New
Show More- NEW "BIG IDEAS OF CALCULUS" NOTES FOCUS ON A DEEPER UNDERSTANDING OF CORE CONCEPTS. Each chapter introduces the overarching or primary ideas behind the chapter's topics and includes a clear summary of key concepts. Conceptual exercises further solidify students' understanding while follow-up exercises demonstrate how to apply the concepts students are learning.
- NEW AUTOMATICALLY GRADED PROOF PROBLEMS IN WEBASSIGN BUILD STUDENT CONFIDENCE. These online Proof Problems help students develop an understanding of the entire process of writing proofs with carefully crafted practice opportunities and immediate feedback.
- NEW EXPANDED PROBLEMS IN WEBASSIGN INCLUDE MULTIPLE PARTS TO ENSURE UNDERSTANDING. These online Expanded Problems go beyond the basic exercises to ask students to show the specific steps of their work or to explain the reasoning behind the answers they've provided.
Features
Show More- STUDENT-FOCUSED APPROACH PROVIDES CLEAR GUIDANCE AND LEARNING FEATURES. This edition offers section-level objectives and clearly stated theorems and definitions as well as engaging exploration features and helpful remarks.
- CAREFULLY DESIGNED EXERCISE SETS OFFER RELEVANT AND RIGOROUS PRACTICE. The exercise sets have been extensively examined to ensure they offer an appropriate level of difficulty and relevant content. Conceptual and multi-step questions and real-life exercises reinforce problem-solving skills and mastery of concepts by giving students the opportunity to apply the concepts in real-life situations.
- UNIQUE "HOW DO YOU SEE IT?" EXERCISES PROVIDE VISUALLY DRIVEN PRACTICE WITH CONCEPTS. These "How Do You See It?" exercises for each section present a problem that your students solve through visual inspection -- using the concepts learned in the lesson they've just completed.
- WEBASSIGN PROVIDES ONLINE TOOLS TO BUILD STUDENTS’ CONFIDENCE AND ELEVATE PERFORMANCE. WebAssign digital resources provide instant access to expertly designed support for you and your students, including additional practice and instructional videos. This high-quality, affordable content offers you both built-in flexibility and control.
- HELPFUL TUTORIAL VIDEOS PROVIDE STEP-BY-STEP EXPLANATIONS AND WORKED-OUT SOLUTIONS. For additional support, Larson’s CalcView.com provides online reinforcement with tutorial videos that offer stepped-out solutions for selected exercises. In addition, LarsonCalculus.com provides videos explaining concepts and proofs.
- LARSON’S CALCCHAT.COM OFFERS ADDITIONAL ONLINE LEARNING SUPPORT. This no-cost invaluable website provides students with online tutoring and solutions to all odd-numbered problems.
Table of Contents
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11. VECTORS AND THE GEOMETRY OF SPACE.
Vectors in the Plane. Space Coordinates and Vectors in Space. The Dot Product of Two Vectors. The Cross Product of Two Vectors in Space. Lines and Planes in Space. Section Project: Distances in Space. Surfaces in Space. Cylindrical and Spherical Coordinates. Review Exercises. P.S. Problem Solving.
12. VECTOR-VALUED FUNCTIONS.
Vector-Valued Functions. Section Project: Witch of Agnesi. Differentiation and Integration of Vector-Valued Functions. Velocity and Acceleration. Tangent Vectors and Normal Vectors. Arc Length and Curvature. Review Exercises. P.S. Problem Solving.
13. FUNCTIONS OF SEVERAL VARIABLES.
Introduction to Functions of Several Variables. Limits and Continuity. Partial Derivatives. Differentials. Chain Rules for Functions of Several Variables. Directional Derivatives and Gradients. Tangent Planes and Normal Lines. Section Project: Wildflowers. Extrema of Functions of Two Variables. Applications of Extrema of Functions of Two Variables. Section Project: Building a Pipeline. Lagrange Multipliers. Review Exercises. P.S. Problem Solving.
14. MULTIPLE INTEGRATION.
Iterated Integrals and Area in the Plane. Double Integrals and Volume. Change of Variables: Polar Coordinates. Center of Mass and Moments of Inertia. Section Project: Center of Pressure on a Sail. Surface Area. Section Project: Surface Area in Polar Coordinates. Triple Integrals and Applications. Triple Integrals in Cylindrical and Spherical Coordinates. Section Project: Wrinkled and Bumpy Spheres. Change of Variables: Jacobians. Review Exercises. P.S. Problem Solving.
15. VECTOR ANALYSIS.
Vector Fields. Line Integrals. Conservative Vector Fields and Independence of Path. Green's Theorem. Section Project: Hyperbolic and Trigonometric Functions. Parametric Surfaces. Surface Integrals. Section Project: Hyperboloid of One Sheet. Divergence Theorem. Stokes' Theorem. Review Exercises. Section Project: The Planimeter. P.S. Problem Solving.
16. SECOND ORDER DIFFERENTIAL EQUATIONS* ONLINE.
Exact First-Order Equations. Second-Order Homogeneous Linear Equations. Second-Order Nonhomogeneous Linear Equations. Section Project: Parachute Jump. Series Solutions of Differential Equations. Review Exercises. P.S. Problem Solving.
APPENDIX.
A. Proofs of Selected Theorems.
B. Integration Tables.
C. Precalculus Review (Web).
C.1. Real Numbers and the Real Number Line.
C.2. The Cartesian Plane.
D. Rotation and the General Second-Degree Equation (Web).
E. Complex Numbers (Web).
F. Business and Economic Applications (Web).
G. Fitting Models to Data (Web).
Vectors in the Plane. Space Coordinates and Vectors in Space. The Dot Product of Two Vectors. The Cross Product of Two Vectors in Space. Lines and Planes in Space. Section Project: Distances in Space. Surfaces in Space. Cylindrical and Spherical Coordinates. Review Exercises. P.S. Problem Solving.
12. VECTOR-VALUED FUNCTIONS.
Vector-Valued Functions. Section Project: Witch of Agnesi. Differentiation and Integration of Vector-Valued Functions. Velocity and Acceleration. Tangent Vectors and Normal Vectors. Arc Length and Curvature. Review Exercises. P.S. Problem Solving.
13. FUNCTIONS OF SEVERAL VARIABLES.
Introduction to Functions of Several Variables. Limits and Continuity. Partial Derivatives. Differentials. Chain Rules for Functions of Several Variables. Directional Derivatives and Gradients. Tangent Planes and Normal Lines. Section Project: Wildflowers. Extrema of Functions of Two Variables. Applications of Extrema of Functions of Two Variables. Section Project: Building a Pipeline. Lagrange Multipliers. Review Exercises. P.S. Problem Solving.
14. MULTIPLE INTEGRATION.
Iterated Integrals and Area in the Plane. Double Integrals and Volume. Change of Variables: Polar Coordinates. Center of Mass and Moments of Inertia. Section Project: Center of Pressure on a Sail. Surface Area. Section Project: Surface Area in Polar Coordinates. Triple Integrals and Applications. Triple Integrals in Cylindrical and Spherical Coordinates. Section Project: Wrinkled and Bumpy Spheres. Change of Variables: Jacobians. Review Exercises. P.S. Problem Solving.
15. VECTOR ANALYSIS.
Vector Fields. Line Integrals. Conservative Vector Fields and Independence of Path. Green's Theorem. Section Project: Hyperbolic and Trigonometric Functions. Parametric Surfaces. Surface Integrals. Section Project: Hyperboloid of One Sheet. Divergence Theorem. Stokes' Theorem. Review Exercises. Section Project: The Planimeter. P.S. Problem Solving.
16. SECOND ORDER DIFFERENTIAL EQUATIONS* ONLINE.
Exact First-Order Equations. Second-Order Homogeneous Linear Equations. Second-Order Nonhomogeneous Linear Equations. Section Project: Parachute Jump. Series Solutions of Differential Equations. Review Exercises. P.S. Problem Solving.
APPENDIX.
A. Proofs of Selected Theorems.
B. Integration Tables.
C. Precalculus Review (Web).
C.1. Real Numbers and the Real Number Line.
C.2. The Cartesian Plane.
D. Rotation and the General Second-Degree Equation (Web).
E. Complex Numbers (Web).
F. Business and Economic Applications (Web).
G. Fitting Models to Data (Web).
