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Video
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
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e-book
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 Non-standard 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:
- e-book
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e-book
An introductory level single variable calculus book, covering standard topics in differential and integral calculus, and infinite series. Late transcendentals and multivariable versions are also available. This textbook has been used in classes at:Boise State University,Claremont McKenna College,University of Minnesota, University of Puget Sound, Western Connecticut State University, Whitman College.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- Resource Type:
- e-book
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e-book
"This book is a polished version of the author's notes for a course entitled Several Complex Variables. It should be suitable for a semester-long topics course or for self-study 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 semester-long 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:
- e-book
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Video
Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta 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
-
e-book
This book covers the standard material for a one-semester 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: vector-valued functions of one variable, real-valued functions of many variables, and finally the general case of vector-valued 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:
- e-book
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Courseware
Math 2B is the second quarter of Single-Variable Calculus and covers the following topics: Definite integrals; the fundamental theorem of calculus. Applications of integration including finding areas and volumes. Techniques of integration. Infinite sequences and series. Parametric and polar equations.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus
- Resource Type:
- Courseware
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Courseware
UCI Math 2A is the first quarter in Single-Variable Calculus and covers the following topics: Introduction to derivatives, calculation of derivatives of algebraic and trigonometric functions; applications including curve sketching, related rates, and optimization. Exponential and logarithm functions.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus
- Resource Type:
- Courseware
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Courseware
This Pre-Calculus course is designed to prepare students for a calculus course. This course is taught so that students will acquire a solid foundation in algebra and trigonometry. The course concentrates on the various functions that are important to the study of the calculus.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Precalculus Trigonometry Algebra
- Resource Type:
- Courseware
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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
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