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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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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
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e-book
This free undergraduate textbook provides an introduction to proofs, logic, sets, functions, and other fundamental topics of abstract mathematics. It is designed to be the textbook for a bridge course that introduces undergraduates to abstract mathematics, but it is also suitable for independent study by undergraduates (or mathematically mature high-school students), or for use as a very inexpensive supplement to undergraduate courses in any field of abstract mathematics.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics Textbooks
- Resource Type:
- e-book
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e-book
You are probably asking yourself the question, "When and where will I use statistics?". If you read any newspaper or watch television, or use the Internet, you will see statistical information. There are statistics about crime, sports, education, politics, and real estate. Typically, when you read a newspaper article or watch a news program on television, you are given sample information. With this information, you may make a decision about the correctness of a statement, claim, or "fact." Statistical methods can help you make the "best educated guess."
- Subjects:
- Management and Mathematics and Statistics
- Keywords:
- Industrial management -- Statistical methods Commercial statistics Textbooks
- Resource Type:
- e-book
-
e-book
A casual glance through the Table of Contents of most of the major publishers' College Algebra books reveals nearly isomorphic content in both order and depth. Our Table of Contents shows a different approach, one that might be labeled “Functions First.” To truly use The Rule of Four, that is, in order to discuss each new concept algebraically, graphically, numerically and verbally, it seems completely obvious to us that one would need to introduce functions first. (Take a moment and compare our ordering to the classic “equations first, then the Cartesian Plane and THEN functions” approach seen in most of the major players.) We then introduce a class of functions and discuss the equations, inequalities (with a heavy emphasis on sign diagrams) and applications which involve functions in that class. The material is presented at a level that definitely prepares a student for Calculus while giving them relevant Mathematics which can be used in other classes as well. Graphing calculators are used sparingly and only as a tool to enhance the Mathematics, not to replace it. The answers to nearly all of the computational homework exercises are given in thetext and we have gone to great lengths to write some very thought provoking discussion questions whose answers are not given. One will notice that our exercise sets are much shorter than the traditional sets of nearly 100 “drill and kill” questions which build skill devoid of understanding. Our experience has been that students can do about 15-20 homework exercises a night so we very carefully chose smaller sets of questions which cover all of the necessary skills and get the students thinking more deeply about the Mathematics involved.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Precalculus Trigonometry Algebra Textbooks
- Resource Type:
- e-book
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e-book
"Precalculus (was College Algebra) is an introductory text. The material is presented at a level intended to prepare students for Calculus while also giving them relevant mathematical skills that can be used in other classes. The authors describe their approach as "Functions First," believing introducing functions first will help students understand new concepts more completely. Each section includes homework exercises, and the answers to most computational questions are included in the text (discussion questions are open-ended). Graphing calculators are used sparingly and only as a tool to enhance the Mathematics, not to replace it. Note: this book was updated on the BC Open textbook Project site on February, 17, 2015 to include the version of the textbook with chapters on Trigonometry."--BCcampus website.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Precalculus Textbooks
- Resource Type:
- e-book
-
Courseware
This course offers a rigorous treatment of linear algebra, including vector spaces, systems of linear equations, bases, linear independence, matrices, determinants, eigenvalues, inner products, quadratic forms, and canonical forms of matrices.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Algebras Linear
- Resource Type:
- Courseware
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e-book
"This book is meant to be a textbook for a standard one-semester introductory statistics course for general education students.Over time the core content of this course has developed into a well-defined body of material that is substantial for a one-semester course. The authors believe that the students in this course are best served by a focus on the core material and not by an exposure to a plethora of peripheral topics. Therefore in writing this book we have sought to present material that comprises fully a central body of knowledge that is defined according to convention, realistic expectation with respect to course duration and students' maturity level, and our professional judgment and experience."--BCcampus website.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Statistics Textbooks
- Resource Type:
- e-book
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e-book
Introductory Statistics follows the scope and sequence of a one-semester, introduction to statistics course and is geared toward students majoring in fields other than math or engineering. This text assumes students have been exposed to intermediate algebra, and it focuses on the applications of statistical knowledge rather than the theory behind it. The foundation of this textbook is Collaborative Statistics, by Barbara Illowsky and Susan Dean, which has been widely adopted. Introductory Statistics includes innovations in art, terminology, and practical applications, all with a goal of increasing relevance and accessibility for students. We strove to make the discipline meaningful and memorable, so that students can draw a working knowledge from it that will enrich their future studies and help them make sense of the world around them. The text also includes Collaborative Exercises, integration with TI-83,83+,84+ Calculators, technology integration problems, and statistics labs. OpenStax College has compiled many resources for faculty and students, from faculty-only content to interactive homework and study guides.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Statistics Textbooks
- Resource Type:
- e-book
-
e-book
This is a text for a two-term course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathematical maturity that can be gained from an introductory real analysis course. The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calculus sequence is the only specific prerequisite for Chapters 1–5, which deal with real-valued functions. (However, other analysis oriented courses, such as elementary differential equation, also provide useful preparatory experience.) Chapters 6 and 7 require a working knowledge of determinants, matrices and linear transformations, typically available from a first course in linear algebra. Chapter 8 is accessible after completion of Chapters 1–5.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical analysis Textbooks
- Resource Type:
- e-book
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