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4434A ProblemText in Advanced Calculus
http://www.merlot.org/merlot/viewMaterial.htm?id=314603
Advanced Calculus open textbook. Download LaTeX source or PDF. Creative Commons BY-NC-SA.Calculus
http://www.merlot.org/merlot/viewMaterial.htm?id=351066
OCW is pleased to make this textbook available online. Published in 1991 and still in print from Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor's Manual and a student Study Guide.Vector Calculus
http://www.merlot.org/merlot/viewMaterial.htm?id=350952
Book description: This is a text on elementary multivariable calculus, designed for students who have completed courses in single-variable calculus. The traditional topics are covered: basic vector algebra; lines, planes and surfaces; vector-valued functions; functions of 2 or 3 variables; partial derivatives; optimization; multiple integrals; line and surface integrals.Elementary Calculus: An Approach Using Infinitesimals
http://www.merlot.org/merlot/viewMaterial.htm?id=302292
'This first-year calculus book is centered around the use of infinitesimals, an approach largely neglected until recently for reasons of mathematical rigor. It exposes students to the intuition that originally led to the calculus, simplifying their grasp of the central concepts of derivatives and integrals. The author also teaches the traditional approach, giving students the benefits of both methods.Chapters 1 through 4 employ infinitesimals to quickly develop the basic concepts of derivatives, continuity, and integrals. Chapter 5 introduces the traditional limit concept, using approximation problems as the motivation. Later chapters develop transcendental functions, series, vectors, partial derivatives, and multiple integrals. The theory differs from traditional courses, but the notation and methods for solving practical problems are the same. The text suggests a variety of applications to both natural and social sciences.'Single Variable Calculus
http://www.merlot.org/merlot/viewMaterial.htm?id=650886
'From the MAA review of this book: "The discussions and explanations are succinct and to the point, in a way that pleases mathematicians who don't like calculus books to go on and on.״There are eleven chapters beginning with analytic geometry and ending with sequences and series. The book covers the standard material in a one variable calculus course for science and engineering except for numerical integration. The size of the book is such that an instructor does not have to skip sections in order to fit the material into the typical course schedule.There are sufficiently many exercises at the end of each sections, but not as many as the much bigger commercial texts. Some students and instructors may want to use something like a Schaum's outline for additional problems.'Brief Calculus
http://www.merlot.org/merlot/viewMaterial.htm?id=298012
'This short text is designed more for self-study or review than for classroom use; full solutions are given for nearly all the end-of-chapter problems.''The focus is mainly on integration and differentiation of functions of a single variable, although iterated integrals are discussed. Infinitesimals are used when appropriate, and are treated more rigorously than in old books like Thompson's Calculus Made Easy, but in less detail than in Keisler's Elementary Calculus: An Approach Using Infinitesimals.Numerical examples are given using the open-source computer algebra system Yacas, and Yacas is also used sometimes to cut down on the drudgery of symbolic techniques such as partial fractions. Proofs are given for all important results, but are often relegated to the back of the book, and the emphasis is on teaching the techniques of calculus rather than on abstract results.'A Problem Text in Advanced Calculus
http://www.merlot.org/merlot/viewMaterial.htm?id=906145
'In American universities two distinct types of courses are often called “Advanced Calculus”: one, largely for engineers, emphasizes advanced computational techniques in calculus; the other, a more “theoretical” course, usually taken by majors in mathematics and physical sciences (and often called elementary analysis or intermediate analysis), concentrates on conceptual development and proofs. This ProblemText is a book of the latter type. It is not a place to look for post-calculus material on Fourier series, Laplace transforms, and the like. It is intended for students of mathematics and others who have completed (or nearly completed) a standard introductory calculus sequence and who wish to understand where all those rules and formulas come from. Many advanced calculus texts contain more topics than this ProblemText. When students are encouraged to develop much of the subject matter for themselves, it is not possible to “cover” material at the same breathtaking pace that can be achieved by a truly determined lecturer. But, while no attempt has been made to make the book encyclopedic, I do think it nevertheless provides an integrated overview of Calculus and, for those who continue, a solid foundation for a first year graduate course in Real Analysis. As the title of the present document, ProblemText in Advanced Calculus, is intended to suggest, it is as much an extended problem set as a textbook. The proofs of most of the major results are either exercises or problems. The distinction here is that solutions to exercises are written out in a separate chapter in the ProblemText while solutions to problems are not given. I hope that this arrangement will provide flexibility for instructors who wish to use it as a text. For those who prefer a (modified) Moore-style development, where students work out and present most of the material, there is a quite large collection of problems for them to hone their skills on. For instructors who prefer a lecture format, it should be easy to base a coherent series of lectures on the presentation of solutions to thoughtfully chosen problems.'A ProblemText in Advanced Calculus
http://www.merlot.org/merlot/viewMaterial.htm?id=516784
This is a free, online textbook that, according to the author, "is intended to suggest, it is as much an extended problem set as a textbook. The proofs of most of the major results are either exercise or problems. For instructors who prefer a lecture format, it shjould be easy to base a coherent series of lectures on the presentation of solutions to thoughtfully chosen problems.״A Summary of Calculus
http://www.merlot.org/merlot/viewMaterial.htm?id=556424
This is a free, online textbook in which the author attempts to "summarize calculus.״ A youtube Calculus Workbook (Part I)
http://www.merlot.org/merlot/viewMaterial.htm?id=803561
This is a free textbook offered by BookBoon.'This book is a guide through a playlist of Calculus instructional videos. The format, level of details and rigor, and progression of topics are consistent with a semester long college level first Calculus course, or equivalently an AP Calculus AB course. The book further provides simple summary of videos, written definitions and statements, worked out examples--even though fully step-by-step solutions are to be found in the videos-- and an index. The playlist and the book are divided into 15 thematic learning modules. At the end of each learning module, one or more quiz with full solutions is provided. Every 3 or 4 modules, a mock test on the previous material, with full solutions, is also provided. This will help you test your knowledge as you go along. The book can be used for self study, or as a textbook for a Calculus course following the “flipped classroom” model.'