Vector Calculus, 5th edition
- Susan J. Colley
- , Santiago Cañez
Learn more, spend less
- Find it fast
Quickly navigate your eTextbook with search
- Stay organized
Access all your eTextbooks in one place
- Easily continue access
Keep learning with auto-renew
Vector Calculus uses the language and notation of vectors and matrices to help you start the transition from first-year calculus to more advanced technical math. Its readable narrative, numerous figures, strong examples and exercise sets help foster a solid grasp of the concepts. An appropriate level of rigor collects most of the technical derivations at the ends of sections; many proofs are available for reference but are positioned in a way that does not disrupt the flow of main ideas. The 5th Edition offers clarifications, new examples and new exercises throughout. For the first time, this book is now available as a Pearson eText that includes interactive GeoGebra applets. Background in single-variable calculus is assumed.
Published by Pearson (August 15th 2022) - Copyright © 2022
ISBN-13: 9780136800101
Subject: Calculus
Category: Vector Calculus
1. Vectors
- 1.1 Vectors in Two and Three Dimensions
- 1.2 More About Vectors
- 1.3 The Dot Product
- 1.4 The Cross Product
- 1.5 Equations for Planes; Distance Problems
- 1.6 Some n-dimensional Geometry
- 1.7 New Coordinate Systems
- True/False Exercises for Chapter 1
- Miscellaneous Exercises for Chapter 1
2. Differentiation in Several Variables
- 2.1 Functions of Several Variables; Graphing Surfaces
- 2.2 Limits
- 2.3 The Derivative
- 2.4 Properties; Higher-order Partial Derivatives
- 2.5 The Chain Rule
- 2.6 Directional Derivatives and the Gradient
- 2.7 Newton's Method (optional)
- True/False Exercises for Chapter 2
- Miscellaneous Exercises for Chapter 2
3. Vector-Valued Functions
- 3.1 Parametrized Curves and Kepler's Laws
- 3.2 Arclength and Differential Geometry
- 3.3 Vector Fields: An Introduction
- 3.4 Gradient, Divergence, Curl, and the Del Operator
- True/False Exercises for Chapter 3
- Miscellaneous Exercises for Chapter 3
4. Maxima and Minima in Several Variables
- 4.1 Differentials and Taylor's Theorem
- 4.2 Extrema of Functions
- 4.3 Lagrange Multipliers
- 4.4 Some Applications of Extrema
- True/False Exercises for Chapter 4
- Miscellaneous Exercises for Chapter 4
5. Multiple Integration
- 5.1 Introduction: Areas and Volumes
- 5.2 Double Integrals
- 5.3 Changing the Order of Integration
- 5.4 Triple Integrals
- 5.5 Change of Variables
- 5.6 Applications of Integration
- 5.7 Numerical Approximations of Multiple Integrals (optional)
- True/False Exercises for Chapter 5
- Miscellaneous Exercises for Chapter 5
6. Line Integrals
- 6.1 Scalar and Vector Line Integrals
- 6.2 Green's Theorem
- 6.3 Conservative Vector Fields
- True/False Exercises for Chapter 6
- Miscellaneous Exercises for Chapter 6
7. Surface Integrals and Vector Analysis
- 7.1 Parametrized Surfaces
- 7.2 Surface Integrals
- 7.3 Stokes's and Gauss's Theorems
- 7.4 Further Vector Analysis; Maxwell's Equations
- True/False Exercises for Chapter 7
- Miscellaneous Exercises for Chapter 7
8. Vector Analysis in Higher Dimensions
- 8.1 An Introduction to Differential Forms
- 8.2 Manifolds and Integrals of k-forms
- 8.3 The Generalized Stokes's Theorem
- True/False Exercises for Chapter 8
- Miscellaneous Exercises for Chapter 8
Suggestions for Further Reading
Answers to Selected Exercises
Index
Your questions answered
Pearson+ is a one-stop shop for eTextbooks and Study & Exam Prep (also referred to as Channels), both designed to help students get better grades in college. eTextbooks and Study & Exam Prep can be purchased separately or together. eTextbooks have built-in tools that simplify studying, like flashcards, audiobook and search. Study & Exam Prep includes video lessons, practice problems, study guides, Q&A with experts and more, to help you understand tricky topics and get you prepared for test time — all in one place.
A Pearson eTextbook is an easy-to-use digital version of your assigned textbook. eTextbooks, available in Pearson+, give you access to upgraded study tools, including enhanced search, highlights and notes, customizable flashcards, and audio options for hand-free studying. Plus, you can learn on the go with the Pearson+ app.
Pearson+ offers an eTextbook rental, billed as a 6-month subscription. A subscription includes instant access to your eTextbook, including study tools such as the ability to create custom flash cards, take notes, and the option to search and highlight important info in your eTextbook. You can also bundle your eTextbook with Study & Exam Prep. When you check out, you can make a one-time, up-front payment for your eTextbook, or you can choose to pay monthly. If you opt for monthly payments, we will charge your payment method each month until your 6-month subscription ends. If something happens and you need your eTextbook for longer than 6 months, select Extend subscription on the Manage subscription page in My account at any time to continue your subscription before it ends.
A Study & Exam Prep subscription includes video lessons, practice problems and other study tools. With a subscription, you'll get unlimited access to the full range of subjects:
When you purchase an eTextbook subscription, it will last 6 months. You can renew your subscription by selecting Extend subscription on the Manage subscription page in My account before your initial term ends. If you extend your subscription, we'll automatically charge you every month. If you made a one-time payment for your initial 6-month term, you'll now pay monthly. To make sure your learning is uninterrupted, please check your card details. To avoid the next payment charge, select Cancel subscription on the Manage subscription page in My account before the renewal date. You can subscribe again in the future by purchasing another eTextbook subscription.
Channels, also referred to as Study & Exam Prep, is a video platform with thousands of explanations, solutions, and practice problems in 19 subjects to help you do homework and prep for exams. Videos are personalized to your course, and tutors walk you through solutions. Plus, interactive AI-powered summaries and a social community help you understand lessons from your class.
Channels doesn't replace traditional textbooks or eTextbooks. It's an additional tool to help you with your studies, and it can be used with Pearson textbooks or non-Pearson textbooks.
When you choose a Channels subscription, you're signing up for a 1-month, 3-month or 12-month term and you make an upfront payment for your subscription. By default, these subscriptions auto-renew at the frequency you select during checkout. You'll have access to the full video library across all 19 subjects once you've subscribed. You can bundle Channels (also referred to as Study & Exam Prep) with your eTextbook at the time of purchase. Bundle subscription terms vary. You can choose your subscription term and payment frequency at checkout.
When you purchase a Channels subscription, it will last 1 month, 3 months or 12 months, depending on the plan you chose. Your subscription will automatically renew at the end of your term unless you cancel it. We use your credit card to renew your subscription automatically. To make sure your learning is uninterrupted, please check your card details. If your payment method fails, we'll send you an email with instructions for how to update it.