PDF Basic Differentiation (Calculus Revision Book 2)

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Questions, with answers, explanations and proofs, on derivatives of even and odd functions are presented. Calculus Questions with Answers 1. The uses of the first and second derivative to determine the intervals of increase and decrease of a function, the maximum and minimum points, the interval s of concavity and points of inflections are discussed. Calculus Questions with Answers 2. The behaviors and properties of functions, first derivatives and second derivatives are studied graphically.

Calculus Questions with Answers 3. Approximate graphically the first derivative of a function from its graph.

Outline of calculus

Questions are presented along with solutions. Calculus Questions with Answers 4. Calculus questions, on differentiable functions, with detailed solutions are presented. We first present two important theorems on differentiable functions that are used to discuss the solutions to the questions. Calculus Questions with Answers 5. Calculus questions, on tangent lines, are presented along with detailed solutions. Questions with detailed solutions on the second theorem of calculus are presented.

Questions on Functions with Solutions. Several questions on functions are presented and their detailed solutions discussed. Questions on Composite Functions with Solutions. Questions on composite functions are presented along with their detailed solutions. The graphical derivation in the text is then followed by: "We have discussed this from the point of view of the graphs, which is easy to understand but is not normally considered a rigorous proof" it is too easy to be led astray by pictures that seem reasonable but that miss some hard point.

It is possible to do this derivation without resorting to pictures, and indeed we will see an alternate approach soon. Left and right continuity are not mentioned in the text unusual , and nor are one-sided derivatives usual. Conversely, of course, an instructor using this text may wish not to follow the rigorous epsilon-delta approach to limits. For this reviewer, in first year, I take the limit laws to be all intuitively obvious, and no use at all on all of the "interesting" limits what I call the indeterminate forms! The exercises at the end of each section are well chosen and numerous enough in applications such as optimization and related rates where they need to be.

They range from routine practice to more challenging questions, and most have short answers in the back of the book. Overall, I like this book a lot.

Differential Calculus | Khan Academy

It is very well written and friendly to read, without the usual clutter of sidebars, footnotes and appendices! It moves quickly through all the important definitions and theorems of calculus with many examples and also a certain amount of just-in-time precalculus for example, with the exponential and logarithm functions. There is appropriate rigour throughout, though the book is not at all in the style of Rudin's classic graduate text, "Principles of Mathematical Analysis! Maybe slightly too much so, as sometimes definitions or important formulas appear in the flow of the discourse and are not highlighted for easy visual reference for the student.

Differentiation – Introduction

Most are numbered, but the conversion formulas for switching from polar to rectangular coordinates in The text appears to be remarkably free of errors of any kind, and any question of bias in the sense intended here not applicable. I did notice somewhere a period missing at the end of a sentence. Also, in the remark in parentheses at the end of Example 1. Of course there are natural biases expected in terms of style, rigour, choice of definitions etc. It does go slightly against the grain however, to allow as the book does, the endpoints of an interval [a, b] to be local extrema.

I like the book's treatment in 6. Both texts state the theorem and illustrate its usefulness and interpretation with respect to motion. The text under review fully proves it from Rolle's Theorem, which in turn is proved from the unproved Extreme Value Theorem. By contrast, Stewart does not mention Rolle's Theorem or prove the MVT, but does provide diagrams making it seem plausible. Annoyingly, however, the hypothesis in Stewart's MVT is that f x is differentiable on the closed interval [a, b], making it not applicable, for example, to the square root function on the interval [0, A].

The content in a mainstream calculus text such as this is relatively timeless. The book is regularly being updated by the author, taking into account feedback from users of the text. I will leave it to other reviewers more familiar with manipulating source code to comment on the ease of editing the text. There are no significant interface issues with this text. The internal hyperlinks in the pdf version of the text are a very nice feature, taking you instantly to a referenced diagram, definition, or solution of an exercise.

However, it would be nice if there was a way to return to the exact previous position in the text with a single click, after viewing the reference, rather than having to navigate back using the bookmarked pages or sections of the text. I did find that clicking on the external links labeled AP that are attached to many of the diagrams resulted only in "page not found.

It has been a real pleasure reading this book. The textbook covers all the topics necessary for a Calculus 1 course. A chapter on differential equations is made mention of in the small print on the inside front cover, but does not appear in the contents. Updated versions of the textbook are made available on the website.


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The TeX files used to generate the textbook are freely available as well, thus allowing users to update and edit the text themselves, if required. Some familiarity with LaTeX is required, in this regard, simply downloading the TeX files and using LaTeX to generate a pdf textbook won't work without some tinkering with the various options on offer.

PDF Basic Differentiation (Calculus Revision Book 2)

A conversational writing style makes the text very readable and the presentation of material has a natural flow. Section and subsection labeling are used well. Definitions, Theorems, Examples, and Exercises are helpfully numbered. The textbook has a sensible ordering of chapters and sections that, for the most part, follows the usual structure of other introductory calculus textbooks. Organization of the material that is perhaps slightly unusual includes introducing the derivative before introducing continuity, leaving limits at infinity until later Section 4.

The partition between a Calculus 1 and a Calculus 2 course is often such that some integral applications are required as part of the Calculus 1 syllabus, but that integration by parts and integration using partial fractions is not encountered until Calculus 2. Again, having the tex files allows for rearranging and omitting certain material as required for particular course offerings.

Some figures contain so-called "AP" links to interactive applets, these were broken in the copy under review. This is only relevant for the pdf of the textbook. This could be quickly and easily changed, if desired, by running a Canadian English spell check through the textbooks. By the natural of the textbook in question issues of cultural relevance are limited. However, Math examples involving cultural references are U. Imperial rather than metric measurement units are frequently used e. The text is straightforward in appearance, e. No special attention is made, therefore, on highlighting key material and core ideas.

Review of Basic Differentiation (2 of 2: Considering derivatives visually)

On the other hand, students can have free reign of the highlighter pen and annotate the text to their hearts content without any fear of reducing the resale prize on the second-hand textbook market! The text is also free of the little historical vignettes or anecdotes that are often found in the major Calculus textbooks. The material is too the point and keeps the book to a reasonable length.

There are less figures and diagrams than is standard in the major textbooks.

More graphs and in some cases coloured lines on existing graphs may improve explanations for students. Calculus students may find themselves wanting more worked examples, although presumably these would be provided in class lectures. On a similar note, the question sets are small, instructors may find themselves needing to set problems outside of those provided.

This would also be important to avoid too much repetition with multiple offerings of the course year in, year out. Students themselves may like to try further exercises than the textbook currently supplies.


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  • A supplementary worked examples and problem set may need to be provided in addition to the textbook. Reviewed by James L. It was reviewed in and revised in This document has a list of core topics which all first year two semester Science Calculus courses must include and a list of additional topics, at least four of which must be chosen.


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    • Any text which is adopted for a first year Science Calculus course must be consistent with this report. Core topics: Limits, continuity, intermediate value theorem. Limits are introduced in Section 2. Properties of limits are stated in Theorem 2. One sided limits are defined, together with an example, in Section 2. Continuity is covered in Section 2.

      There is a problem with Figure 2. It is claimed that Figure 2. In fact, the function would be continuous if it were not defined at these values. There is no discussion of removable or jump discontinuities. The Intermediate Value Theorem is found in Section 2. Differentiation First and second derivatives with geometric and physical interpretations. Section 2.