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 Comprehensiveness rating: 4 see less. 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.
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. 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. 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.
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. In many places, the words are poorly spaced on the lines.
For example, page , 2nd column, third line: there are three words, "of" "semicircular" and "arch" and much whitespace in between. Nothing struck me as being culturally insensitive, but nothing struck me as culturally inclusive, either. For example, one of their examples mentions a company producing golf balls, not a person at the company producing golf balls. 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. The first 6 chapters of 7 cover what I currently cover in a Multivariable Calculus course.
Well, actually a good deal more than I cover! I would go lightly on the conic sections material and several of the sections on physics applications Comprehensiveness rating: 5 see less. I would go lightly on the conic sections material and several of the sections on physics applications e.
For this physicist, I was happy to see somewhat more mathematical rigor available than what I usually present to my students. The 7th chapter is on differential equations. The index on the PDF version is thoroughly hyperlinked—a joy to use.
I would say this book leans most heavily on the symbolic and to a lesser extent graphic and numeric modes. It does take into account visualization technology explicitly with some exercises designated to be done with tech. The prose is clear and definitions and theorems are carefully and precisely worded.
Despite the great number of figures and illustrations throughout the whole text, I felt like there were some sections which could have used still more. I was puzzled that in section 3. Yes, highly consistent. I have one quibble: Up through the first five chapters there is no typographic distinction between vectors and unit vectors. But In the section on vector calculus Chapter 6 a caret over a vector is introduced to indicate a unit vector in the radial direction.
I would love to see this notation with the caret used throughout the text even including the Cartesian unit vectors i, j, and k. I thought about re-arranging things to group in another order--such as waiting to cover integration in polar coordinates occurs very early in the book until building up a more general expression for the differential of area--and it seems that would be need some re-working. But, to be fair, since mathematics builds one concept on top of another, I can't imagine any textbook that can be effortlessly modular!
Good within current tech limits. Happy to see a lot of hyperlinks within the document and external links. Some of the simulations link to Mathematica files - proprietary but sometimes available via the CDF player.
I would love to see open source visualizations in, say, GeoGebra instead The book has an absolutely lavish number of exercises with answers to many in the back , checkpoint exercises, and examples.
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. His Ph. Content Accuracy rating: 5 The text is very accurate. Clarity rating: 4 There are times when incorrect references are made and instructions are unclear.
Consistency rating: 4 There are times when the authors may become a bit too fast and loose with their terminology. Modularity rating: 2 Not fairly modular, since each section will make reference to material developed in the text. Interface rating: 4 There are some issues with links to entries in the text, e. Grammatical Errors rating: 5 Great grammar, even by non-mathematician standards!
Very clear and concise wording. Cultural Relevance rating: 3 Nothing struck me as being culturally insensitive, but nothing struck me as culturally inclusive, either. Comments I think this book would benefit from a thorough and complete read-through by a copy editor who is also teaching the course.
PDF - MIT Professor Gilbert Strang has created a series of videos to show ways in which calculus is important in our lives. The videos, which include real-life examples to illustrate the concepts, are ideal for high school students, college students, and anyone interested in learning the basics of calculus.
Chapter 1 - complete PDF - 2. Chapter 2 - complete PDF - 3. Chapter 3 - complete PDF - 3. Chapter 4 - complete PDF - 1. Chapter 5 - complete PDF - 3. Chapter 6 - complete PDF - 3. Chapter 7 - complete PDF - 1. Chapter 8 - complete PDF - 2. Chapter 9 - complete PDF. Chapter 10 - complete PDF - 2. Chapter 11 - complete PDF - 3. Chapter 12 - complete PDF - 1.
Chapter 13 - complete PDF - 3. Chapter 14 - complete PDF - 1. Chapter 15 - complete PDF - 3. Chapter 16 - complete PDF. Don't show me this again.
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