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課程簡介：微分表切線斜率，積分表曲線下圍出的面積，兩截然不同的東西透過微積分基本定理連結在一起。
 Course related:
 AMA1007 Calculus and Linear Algebra
 Subjects:
 Mathematics and Statistics
 Keywords:
 Calculus
 Resource Type:
 Video

ebook
"This book is a polished version of the author's notes for a course entitled Several Complex Variables. It should be suitable for a semesterlong topics course or for selfstudy as an introduction to the subject. The prerequisites are decent knowledge of vector calculus, basic real analysis, and a working knowledge of complex analysis in one variable. It should be accessible to beginning graduate students after a complex analysis course, and perhaps even very advanced undergraduates. This is enough material for a semesterlong course, including quite a few exercises sprinkled throughout the text, all of which the reader should at least be attempting. It is not meant as an exhaustive reference, but simply as a whirlwind tour of several complex variables"BCcampus website.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Textbooks Functions of complex variables
 Resource Type:
 ebook

ebook
"Calculus arose as a tool for solving practical scientific problems through the centuries. However, it is often taught as a technical subject with rules and formulas (and occasionally theorems), devoid of its connection to applications. In this textbook, the applications form an important focal point, with emphasis on life sciences. This places the techniques and concepts into practical context, as well as motivating quantitative approaches to biology taught to undergraduates. While many of the examples have a biological flavour, the level of biology needed to understand those examples is kept at a minimum. The problems are motivated with enough detail to follow the assumptions, but are simplified for the purpose of pedagogy"BC Campus website.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Life sciences Differential calculus Textbooks
 Resource Type:
 ebook

ebook
"In 2013, Lyryx forked the nowpopular Calculus open textbook written by David Guichard. Michael Cavers of the University of Calgary, together with the Lyryx editorial team, further redeveloped the content, examples, diagrams, and overall lookandfeel of the book, making it more accessible to first year college and university students. Additional contributors have helped improve the content, including Mark Blenkinsop of Carleton University. In particular, there was the addition of an introductory chapter reviewing the fundamental topics required in a first semester Calculus course, and the paring down of topics that are typically beyond the scope of math and engineering service courses. Currently, the book covers the standard Calculus I and II courses, with Calculus III under development."Open Textbook Library.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Calculus Textbooks
 Resource Type:
 ebook

Video
Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilondelta definition of limits.
 Course related:
 AMA1110 Basic Mathematics I – Calculus and Probability & Statistics and BRE2031 Environmental Science
 Subjects:
 Mathematics and Statistics
 Keywords:
 Differential calculus
 Resource Type:
 Video

Others
This learning material covers the topic of differentiation by considering first principles (gradients of chords and tangents).
 Course related:
 AMA1110 Basic Mathematics I – Calculus and Probability & Statistics
 Subjects:
 Mathematics and Statistics
 Keywords:
 Differential calculus
 Resource Type:
 Others

ebook
This book covers the standard material for a onesemester course in multivariable calculus. The topics include curves, differentiability and partial derivatives, multiple integrals, vector fields, line and surface integrals, and the theorems of Green, Stokes, and Gauss. Roughly speaking the book is organized into three main parts corresponding to the type of function being studied: vectorvalued functions of one variable, realvalued functions of many variables, and finally the general case of vectorvalued functions of many variables. As is always the case, the most productive way for students to learn is by doing problems, and the book is written to get to the exercises as quickly as possible. The presentation is geared towards students who enjoy learning mathematics for its own sake. As a result, there is a priority placed on understanding why things are true and a recognition that, when details are sketched or omitted, that should be acknowledged. Otherwise the level of rigor is fairly normal. Matrices are introduced and used freely. Prior experience with linear algebra is helpful, but not required.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Vector valued functions Calculus Textbooks
 Resource Type:
 ebook

ebook
Esta comunidad tiene como fin construir un texto base, que pretende ser la puerta de entrada al mundo de las matemáticas superiores y sus aplicaciones en el campo de las Ciencias de la Ingeniería.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Calculus Integral Calculus Differential calculus Textbooks
 Resource Type:
 ebook

ebook
Active Calculus Multivariable is the continuation of Active Calculus to multivariable functions. The Active Calculus texts are different from most existing calculus texts in at least the following ways: the texts are free for download by students and instructors in .pdf format; in the electronic format, graphics are in full color and there are live html links to java applets; the texts are open source, and interested instructors can gain access to the original source files upon request; the style of the texts requires students to be active learners — there are very few worked examples in the texts, with there instead being 34 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; the exercises are few in number and challenging in nature.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Calculus Functional analysis Textbooks
 Resource Type:
 ebook

ebook
I intend this book to be, firstly, a introduction to calculus based on the hyperrealnumber system. In other words, I will use infinitesimal and infinite numbers freely. Just as most beginning calculus books provide no logical justification for the real number system, I will provide none for the hyperreals. The reader interested in questions of foundations should consult books such asAbraham Robinson's Nonstandard Analysis or Robert Goldblatt's Lectures onthe Hyperreals. Secondly, I have aimed the text primarily at readers who already have somefamiliarity with calculus. Although the book does not explicitly assume any prerequisites beyond basic algebra and trigonometry, in practice the pace istoo fast for most of those without some acquaintance with the basic notions of calculus.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Calculus Textbooks
 Resource Type:
 ebook
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