Multivariable Calculus,
12th Edition

Ron Larson, Bruce H. Edwards

ISBN-13: 9780357749159
Copyright 2023 | Published
480 pages | List Price: USD $312.95

Discover the clear approach and digital support you need to truly understand calculus with MULTIVARIABLE CALCULUS, 12th Edition by award-winning authors Larson and Edwards. This edition effectively presents and demonstrates the concepts and rules of calculus using a thoroughly updated learning experience specifically designed to remove any typical barriers to learning. New "Big Ideas of Calculus" notes present the overarching ideas behind chapter topics, while annotated examples and "Concept Checks" further reinforce your understanding. Step-by-step solution videos, exercise solutions and other tutorial support are available at no cost from, and In addition, new automatically graded Proof Problems with instant feedback, Expanded Problems and "Explore It" interactive learning modules within WebAssign digital resources help you develop a deeper conceptual understanding of calculus to succeed in this course and beyond.


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.
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.
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.
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.
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.
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.
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).

  • Ron Larson

    Dr. Ron Larson is a professor of mathematics at the Pennsylvania State University, where he has taught since 1970. He is considered the pioneer of using multimedia to enhance the learning of mathematics, having authored more than 30 software titles since 1990. Dr. Larson has also written numerous acclaimed textbooks, including the best-selling Calculus Series published by Cengage. He is the recipient of the 2017 William Holmes McGuffey Longevity Award for PRECALCULUS, the 2018 Text and Academic Authors Association TEXTY Award for CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS and the 2017 William Holmes McGuffey Longevity Award for CALCULUS. He also received the 1996 Text and Academic Authors Association TEXTY Award for INTERACTIVE CALCULUS -- a complete text on CD-ROM that was the first mainstream college textbook to be offered on the internet.

  • Bruce H. Edwards

    Dr. Bruce H. Edwards is professor of mathematics at the University of Florida. Dr. Edwards received his B.S. in mathematics from Stanford University and his Ph.D. in mathematics from Dartmouth College. He taught mathematics at a university near Bogotá, Colombia, as a Peace Corps volunteer. While teaching at the University of Florida, Dr. Edwards has received many teaching awards, including Teacher of the Year in the College of Liberal Arts and Sciences, Liberal Arts and Sciences Student Council Teacher of the Year and the University of Florida Honors Program Teacher of the Year. He was recognized by the Office of Alumni Affairs as the Distinguished Alumni Professor for 1991-1993. Dr. Edwards has taught a variety of mathematics courses at the University of Florida, from first-year calculus to graduate-level classes in algebra and numerical analysis. He is also a frequent speaker at research conferences and meetings of the National Council of Teachers of Mathematics. He has co-authored a wide range of award-winning mathematics textbooks with Dr. Ron Larson.

  • 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.

  • 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 provides online reinforcement with tutorial videos that offer stepped-out solutions for selected exercises. In addition, 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.

  • [[[Team: Dan would like you to verify this is still accurate]]]] Graded Homework Exercises - Online homework and tests are evaluated using powerful Maple software to ensure mathematical accuracy. Instructors control point values, weighting grades, and whether or not an item is graded. An electronic gradebook helps instructors manage course information easily and can be exported to other files, such as Excel.

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Cengage eBook: Multivariable Calculus 12 Months