Calculus volume 3 answers

Calculus volume 3 answers DEFAULT

Contents

Book Information

Book Description

This OpenStax book was imported into Pressbooks on August 7, 2019, to make it easier for instructors to edit, build upon, and remix the content. Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.

Please note that this title is published under a CC BY-NC-SA 4.0 license, which means that you are free to use and adapt, but not for commercial purposes. Changes you make need to be shared using this license.

Authors

Gilbert Strang and Edwin “Jed” Herman

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Metadata

Title
Calculus Volume 3

Authors
Gilbert Strang and Edwin “Jed” Herman

Publisher
OpenStax

Publication Date
March 30, 2016

Click for more information

Sours: https://opentextbc.ca/calculusv3openstax/

OpenStax Calculus Volume 3

NEW: A peer-reviewed edition of this course with instructional content (videos, applets) is now available.

OpenStax Calculus Volume 3

 This is an online homework companion to OpenStax Calculus Volume 3. It comprises over 400 interactive problems that are designed to develop conceptual understanding and reinforce problem-solving skills. It comprises problems carefully organized into problem sets mapped to textbook sections. Use this course as-is, or customize at any level. You can mix-and-match problems from other catalog courses, add problems from the Edfinity problem repository, or write your own.

How to use this course

  1. Homework: Assign high quality problems with hints and personalized feedback to develop problem-solving skills.
  2. Testing: Create summative secure online quizzes and tests in minutes. 
  3. Supplementary resources: Embed videos, class notes, and applets alongside assignments.
  4. Intervention: Use rich analytics to identify and monitor at-risk students for timely intervention.
  5. Analytics: Drill down into student performance and identify problematic or difficult topics.
  6. Flipped classroom: Assign pre-class assignments. Save precious class time for discussions.
  7. Emporium classes: Use Edfinity for individual/group work for large enrollment sections in labs.

Edfinity is a full-featured homework system that supports mathematically-aware problems with algebraic input, evaluation of mathematical expressions, randomized variants, prerequisite pathways for personalized learning, collaboration, coordinated courses, flexible configuration of students’ experience, and complete customization of assignments. Edfinity is WeBWorK-compatible - existing WeBWorK courses can be automatically imported, and you can author new WeBWorK problems using our problem authoring tool.

Interactive, algorithmic problems
Algebraic, graphing, open response; randomized variants, hints, and tips

Adaptive learning and personalization
Each student receives personalized support
to fill learning gaps.

Corequisite course structures
Use pre-built corequisite content,
or create your own.

LMS integration and accessibility
Connect to your LMS in minutes. VPAT here.

WeBWorK-compatible
Import and author WeBWorK problems.

Problem Sets

  1. Edfinity Demo
  2. 1.1 Parametric Equations
  3. 1.2 Calculus of Parametric Curves
  4. 1.3 Introduction to Polar Coordinates
  5. 1.4 Area and Arc Length in Polar Coordinates
  6. 1.5 Conic Sections
  7. 2.1 Vectors in the Plane
  8. 2.2 Vectors in Three Dimensions
  9. 2.3 The Dot Product
  10. 2.4 The Cross Product
  11. 2.5 Equations of Lines and Planes in Space
  12. 2.6 A Survey of Quadric Surfaces
  13. 2.7 Cylindrical and Spherical Coordinates
  14. 3.1 Vector-Valued Functions and Space Curves
  15. 3.2 Calculus of Vector-Valued Functions
  16. 3.3 Arc Length and Curvature
  17. 3.4 Motion in Space
  18. 4.1 Introduction to Multivariable Functions
  19. 4.2 Limits and Continuity
  20. 4.3 Partial Derivatives
  21. 4.4 Tangent Planes and Linear Approximations
  22. 4.5 The Multivariable Chain Rule
  23. 4.6 Directional Derivatives and the Gradient
  24. 4.7 Maxima/Minima Problems
  25. 4.8 Lagrange Multipliers
  26. 5.1 Double Integrals over Rectangular Regions
  27. 5.2 Double Integrals over General Regions
  28. 5.3 Double Integration in Polar Coordinates
  29. 5.4 Triple Integrals
  30. 5.5 Triple Integrals in Cylindrical and Spherical Coordinates
  31. 5.6 Calculating Centers of Mass and Moments of Inertia
  32. 5.7 Change of Variables in Multiple Integrals
  33. 6.1 Vector Fields
  34. 6.2 Line Integrals
  35. 6.3 Conservative Vector Fields
  36. 6.4 Flow, Flux, Green's Theorem
  37. 6.5 Divergence and Curl
  38. 6.6 Surface Integrals
  39. 6.7 Stokes' Theorem
  40. 6.8 The Divergence Theorem
  41. 7.1 Second-Order Linear Equations
  42. 7.2 Nonhomogeneous Linear Equations
  43. 7.3 Applications
  44. 7.4 Series Solutions of Differential Equations

FAQ

  1. How much does this course cost?

    Educator access is free. Student access costs \$14 to \$29 per term (depending on the choice of course, level of support, scale of adoption, features included, and commitment to affordability), and may be paid by students or institutions. Bookstores may purchase access codes as described here. Schedule a call to discuss pricing for your institution.

  2. How is this course licensed?

    This is a multi-student license intended for use during instruction. You will be able to manage a section of students and monitor their progress. Student access is valid for the duration of the 5 month term.

  3. Tell me more about Edfinity.

    Edfinity is a full-featured homework system that supports mathematically-aware problems with algebraic input, evaluation of mathematical expressions, randomized variants, prerequisite pathways for personalized learning, collaboration, coordinated courses, flexible configuration of students’ experience, and complete customization of assignments. Edfinity is WeBWorK-compatible - existing WeBWorK courses can be automatically imported, and you can author new WeBWorK problems using our problem authoring tool.

Sours: https://edfinity.com/products/5c6cb0717758b325775b77fe
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Calculus Volume 3

The text is very comprehensive. All of the important topics are covered and the examples are very thorough. That said, I would have liked to see something on the higher-order derivative test. The reason for the '4' in this category is that there could be many more figures, especially in the later sections on minimizing and maximizing functions and multivariable functions (viewing the level curves in conjunction with the surface). Additionally, some figures are not entirely accurate and are misleading, e.g., the figure on continuity (the image of the open disk should not then again be an open disk on the surface, rather the image of such).

The text is very accurate.

The content is up to date. The mathematics at this level is on a firm footing and will not be changing for the foreseeable future. That said, if what one considers 'calculus 3' changes as a result of students being less prepared, then this text will need to be updated to account for students with weaker foundations. What I appreciated was the book beginning with 'parametric equations and polar coordinates.' Of course, this is suppose to be standard material in a Calculus II course, but perhaps this is evidence of "Calculus 3"-creep into "Calculus 2". I find that students are weak in this area (parametric equations) and the review would be helpful.

There are times when incorrect references are made and instructions are unclear. For example, in the minimizing/maximizing section, the 'partial derivatives test' is referenced, but never defined. Such questions in the HW will leave the students wondering what exactly is being asked. Moreover, the text makes reference to Fermat's Theorem, when they in fact meant the 2nd derivative test. Overall, the text is fairly clear, but I think it could be edited for precision in links and wording.

There are times when the authors may become a bit too fast and loose with their terminology. Such casual use of terms is okay in conversation with the student, but is best avoided in a text.

Not fairly modular, since each section will make reference to material developed in the text. While I did not notice explicit references to Volumes 1 and 2, I would imagine those are there, as well, since it helps to make reference to earlier material developed in Calculus I and II to explain some of the concepts in Calculus III. But, as a text for Calculus III, it is as self-contained as it can be without becoming a text for all three courses, Calculus I, II and III.

The text is very well organized and some of the application examples come at exactly the right time and at a level that is accessible to most students.

There are some issues with links to entries in the text, e.g., references to theorems are not correct. In many places, the words are poorly spaced on the lines. For example, page 710, 2nd column, third line: there are three words, "of" "semicircular" and "arch" and much whitespace in between.

Great grammar, even by non-mathematician standards! Very clear and concise wording.

Nothing struck me as being culturally insensitive, but nothing struck me as culturally inclusive, either. Really, for those that I read, the examples seem fairly neutral, as far as race/ethnicity are concerned, and focus more on the example, rather than the person behind it. For example, one of their examples mentions a company producing golf balls, not a person at the company producing golf balls. On the contrary, there are three uses of the word 'she' in the text, one use of 'woman', one use of 'man' and 27 uses of the word 'he' (32 in total, minus 5 that are in reference to the authors and donors/supporters). I would like to see more gender balance, or completely gender neutral examples.

I think this book would benefit from a thorough and complete read-through by a copy editor who is also teaching the course. Those two professions may not overlap, so I would recommend someone actually use this in teaching and detail the minor and major issues so they can be fixed in later versions.

Sours: https://open.umn.edu/opentextbooks/textbooks/371

Calculus Volume 3 - Textbook and Exercise

Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.

✨Contents of the Application✨
1 Parametric Equations and Polar Coordinates
Introduction
1.1 Parametric Equations
1.2 Calculus of Parametric Curves
1.3 Polar Coordinates
1.4 Area and Arc Length in Polar Coordinates
1.5 Conic Sections


2 Vectors in Space
Introduction
2.1 Vectors in the Plane
2.2 Vectors in Three Dimensions
2.3 The Dot Product
2.4 The Cross Product
2.5 Equations of Lines and Planes in Space
2.6 Quadric Surfaces
2.7 Cylindrical and Spherical Coordinates


3 Vector-Valued Functions
Introduction
3.1 Vector-Valued Functions and Space Curves
3.2 Calculus of Vector-Valued Functions
3.3 Arc Length and Curvature
3.4 Motion in Space


4 Differentiation of Functions of Several Variables
Introduction
4.1 Functions of Several Variables
4.2 Limits and Continuity
4.3 Partial Derivatives
4.4 Tangent Planes and Linear Approximations
4.5 The Chain Rule
4.6 Directional Derivatives and the Gradient
4.7 Maxima/Minima Problems
4.8 Lagrange Multipliers


5 Multiple Integration
Introduction
5.1 Double Integrals over Rectangular Regions
5.2 Double Integrals over General Regions
5.3 Double Integrals in Polar Coordinates
5.4 Triple Integrals
5.5 Triple Integrals in Cylindrical and Spherical Coordinates
5.6 Calculating Centers of Mass and Moments of Inertia
5.7 Change of Variables in Multiple Integrals


6 Vector Calculus
Introduction
6.1 Vector Fields
6.2 Line Integrals
6.3 Conservative Vector Fields
6.4 Green’s Theorem
6.5 Divergence and Curl
6.6 Surface Integrals
6.7 Stokes’ Theorem
6.8 The Divergence Theorem


7 Second-Order Differential Equations
Introduction
7.1 Second-Order Linear Equations
7.2 Non-homogeneous Linear Equations
7.3 Applications
7.4 Series Solutions of Differential Equations

👉Each Chapter Include:
✔Key Terms
✔Key Equations
✔Key Concepts
✔Chapter Review Exercises

👉Appendix
A | Table of Integrals
B | Table of Derivatives
C | Review of Pre-Calculus

Sours: https://play.google.com/

3 answers volume calculus

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Disk \u0026 Washer Method - Calculus

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