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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
Traveling is extremely arduous for microscopic sperm -- think of a human trying to swim in a pool made of...other humans. We can compare the journey of a sperm to that of a sperm whale by calculating the Reynolds number, a prediction of how fluid will behave, often fluctuating due to size of the swimmer. Aatish Bhatia explores the great (albeit tiny) sperm's journey.
- Subjects:
- Physics
- Keywords:
- Fluid dynamics Sperm whale Spermatozoa
- Resource Type:
- Video
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Video
You stick cookie dough into an oven, and magically, you get a plate of warm, gooey cookies. Except it's not magic; it's science. Stephanie Warren explains via basic chemistry principles how the dough spreads out, at what temperature we can kill salmonella, and why that intoxicating smell wafting from your oven indicates that the cookies are ready for eating.
- Subjects:
- Chemistry and Food Science
- Keywords:
- Food -- Composition Food -- Analysis
- 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
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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
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Courseware
This course is focused on physical understanding of materials processing, and the scaling laws that govern process speed, volume, and material quality. In particular, this course will cover the transport of heat and matter as these topics apply to materials processing.
- Subjects:
- Mechanical Engineering and Materials Science
- Keywords:
- Mass transfer Heat -- Transmission Transport theory Manufacturing processes Fluid mechanics
- Resource Type:
- Courseware
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Video
Berg begins his lecture with a brief history of observations of bacterial motion. He then uses physics to describe the many hurdles that E. coli must overcome as it tries to swim up or down a chemical gradient. For instance, an entity as tiny as E. coli is constantly buffeted by Brownian motion and can neither stay still nor swim in a straight line. Then there is the question of how E. coli senses a gradient and translates that information into a change in its direction of movement. And finally, how does E. coli use its flagella to generate thrust at all? In Part 2, Berg explains that E. coli travels using a series of runs, when it moves in a straight line, and tumbles, when it changes direction. During a run, all of the flagella are moving counterclockwise in a tight bundle. During a tumble, one or more flagella switch to a clockwise movement and disengage from the bundle causing a change in the swimming direction. The motor that drives the rotation of the flagella is an amazing structure made of about 20 different protein parts. Berg tells us that chemosensory receptors on the cell surface detect a chemical gradient and transfer this information, via protein phosphorylation, to the motor. This chemical modification determines the direction of motor rotation and, hence, the direction the E. coli swims. An amazing system that E. coli has been perfecting for millions of years!
- Subjects:
- Physics and Biology
- Keywords:
- Bacteria -- Motility Physics Escherichia coli
- Resource Type:
- Video
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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
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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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Video
When two people join a dating website they are matched according to shared interests and how they answer a number of personal questions. But how do sites calculate the likelihood of a successful relationship? Christian Rudder one of the founders of popular dating site OKCupid details the algorithm behind 'hitting it off.'
- Subjects:
- Computing and Mathematics and Statistics
- Keywords:
- Dating services Computer algorithms Online dating
- Resource Type:
- Video
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Video
Having trouble remembering the order of operations? Let's raise the stakes a little bit. What if the future of your (theoretical) kingdom depended on it? Garth Sundem creates a world in which PEMDAS is the hero but only heroic when in the proper order.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Games in mathematics education Games -- Mathematics
- Resource Type:
- Video
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e-book
Taking into consideration the outstanding importance of studying and applying the biological means to remove or mitigate the harmful effects of global pollution on the natural environment, as direct consequences of quantitative expansion and qualitative diversification of persistent and hazardous contaminants, the present book provides useful information regarding New Approaches and Prospective Applications in Environmental Biotechnology. This volume contains twelve chapters divided in the following three parts: biotechnology for conversion of organic wastes, biodegradation of hazardous contaminants and, finally, biotechnological procedures for environmental protection. Each chapter provides detailed information regarding scientific experiments that were carried out in different parts of the world to test different procedures and methods designed to remove or mitigate the impact of hazardous pollutants on environment. The book is addressed to researchers and students with specialties in biotechnology, bioengineering, ecotoxicology, environmental engineering and all those readers who are interested to improve their knowledge in order to keep the Earth healthy.
- Subjects:
- Environmental Sciences and Biology
- Keywords:
- Biotechnology -- Environmental aspects Hazardous wastes -- Biodegradation Organic wastes
- Resource Type:
- e-book
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e-book
"Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some preparation in linear algebra. In writing this book I have been guided by the these principles: An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student's place, and have chosen to err on the side of too much detail rather than not enough. An elementary text can't be better than its exercises. This text includes 2041 numbered exercises, many with several parts. They range in difficulty from routine to very challenging. An elementary text should be written in an informal but mathematically accurate way, illustrated by appropriate graphics. I have tried to formulate mathematical concepts succinctly in language that students can understand. I have minimized the number of explicitly stated theorems and defonitions, preferring to deal with concepts in a more conversational way, copiously illustrated by 299 completely worked out examples. Where appropriate, concepts and results are depicted in 188 figures."--BCcampus website.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Differential equations Textbooks
- Resource Type:
- e-book
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e-book
Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student's place, and have chosen to err on the side of too much detail rather than not enough. An elementary text can't be better than its exercises. This text includes 1695 numbered exercises, many with several parts. They range in difficulty from routine to very challenging. An elementary text should be written in an informal but mathematically accurate way, illustrated by appropriate graphics. I have tried to formulate mathematical concepts succinctly in language that students can understand. I have minimized the number of explicitly stated theorems and definitions, preferring to deal with concepts in a more conversational way, copiously illustrated by 250 completely worked out examples. Where appropriate, concepts and results are depicted in 144 figures. Although I believe that the computer is an immensely valuable tool for learning, doing, and writing mathematics, the selection and treatment of topics in this text reflects my pedagogical orientation along traditional lines. However, I have incorporated what I believe to be the best use of modern technology, so you can select the level of technology that you want to include in your course. The text includes 336 exercises – identified by the symbols C and C/G – that call for graphics or computation and graphics. There are also 73 laboratory exercises – identified by L – that require extensive use of technology. In addition, several sections include informal advice on the use of technology. If you prefer not to emphasize technology, simply ignore these exercises and the advice.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Differential equations Partial Boundary value problems
- Resource Type:
- e-book
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e-book
This text is intended for a brief introductory course in plane geometry. It covers the topics from elementary geometry that are most likely to be required for more advanced mathematics courses. The only prerequisite is a semester of algebra. The emphasis is on applying basic geometric principles to the numerical solution of problems. For this purpose the number of theorems and definitions is kept small. Proofs are short and intuitive, mostly in the style of those found in a typical trigonometry or precalculus text. There is little attempt to teach theorem-proving or formal methods of reasoning. However the topics are ordered so that they may be taught deductively. The problems are arranged in pairs so that just the odd-numbered or just the even-numbered can be assigned. For assistance, the student may refer to a large number of completely worked-out examples. Most problems are presented in diagram form so that the difficulty of translating words into pictures is avoided. Many problems require the solution of algebraic equations in a geometric context. These are included to reinforce the student's algebraic and numerical skills, A few of the exercises involve the application of geometry to simple practical problems. These serve primarily to convince the student that what he or she is studying is useful. Historical notes are added where appropriate to give the student a greater appreciation of the subject. This book is suitable for a course of about 45 semester hours. A shorter course may be devised by skipping proofs, avoiding the more complicated problems and omitting less crucial topics.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Geometry
- Resource Type:
- e-book