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4434Introduction to Complex Numbers
https://www.merlot.org/merlot/viewMaterial.htm?id=1227009
This is a free book offered by BookBoon.This ebook makes learning "complex" numbers easy through an interactive, fun and personalized approach. Features include: live YouTube video streams and closed captions that translate to 90 languages!Complex numbers "break all the rules" of traditional mathematics by allowing us to take a square root of a negative number. This "radical" approach has fundamentally changed the capabilities of science and engineering to enhance our world through such applications as: signal processing, control theory, electromagnetism, fluid dynamics, quantum mechanics, cartography, and vibration analysis. A particularly beautiful connection between art and complex numbers lies in fractals, such as the Mandelbrot set.Tue, 30 Aug 2016 13:12:01 -0700Concepts in Calculus III
https://www.merlot.org/merlot/viewMaterial.htm?id=1224778
From the University of Florida Department of Mathematics, this is the third volume in a three volume presentation of calculus from a concepts perspective. The emphasis is on learning the concepts behind the theories, not the rote completion of problems.Mon, 22 Aug 2016 15:17:25 -0700Concepts in Calculus II
https://www.merlot.org/merlot/viewMaterial.htm?id=1224775
This is the second volume in a three volume presentation of calculus from a concepts perspective. The emphasis is on learning the concepts behind the theories, not the rote completion of problems.Mon, 22 Aug 2016 15:10:30 -0700MILAGE Learn+
https://www.merlot.org/merlot/viewMaterial.htm?id=1223112
The MILAGE Learning+ is an application for mobile devices that has been developed at the University of Algarve, enabling students to access educational content in and outside the classroom.This app works as a support tool for students which provides them with the opportunity to autonomously solve given exercises compiled in worksheets, while also supporting the teacher in managing classroom time, to the extent that the teacher does not have to provide solutions to exercises in the classroom which are already integrated into the MILAGE Learning+ app.In order to stimulate and support the implementation of the various activities proposed, the MILAGE Learning+ app interface incorporates gamification features, segmenting different levels of exercise difficulty to support students with greater difficulties and also motivate more advanced students in learning mathematics.To include all students, the app provides detailed videos with the resolution of exercises for students with more difficulties. There is also a concise video with the essential steps to guide you through the resolution of the exercise.In addition, the MILAGE Learning+ app also includes a self-assessment scheme and peer review to stimulate the student to work independently. The review of the content and the ability to identify key steps in solving exercises allows for the better storage of knowledge in the long-term memory.Within the project, another application was also created – the MILAGE Learning + Teachers – which is a back office, free for teachers and schools, who wish to join the development of content in mathematics teaching, as well as other subjects that can be included in the MILAGE Learning+ app.The MILAGE Learn+ app is free and is available for Android and Apple iOS.Tue, 16 Aug 2016 23:48:07 -0700Calculus for Life Scientists
https://www.merlot.org/merlot/viewMaterial.htm?id=1221905
This is the MATH 140 (Calculus for Life Scientists) Course materials taugth by Mohammed Kaabar at Washington State University. The material includes lecture notes, handouts, writen assignments, and study guides. Sat, 13 Aug 2016 20:22:52 -0700Parallel Spectral Numerical Methods
https://www.merlot.org/merlot/viewMaterial.htm?id=1221576
Parallel Spectral Numerical Methods starts by taking a quick look at finite precision arithmetic. It then discusses how to solve ordinary differential equations (ODE) and partial differential equations (PDE) using separation of variables. Next, it introduces numerical time-stepping schemes that can be used to solve ODEs and PDEs. This is followed by an introduction to pseudo spectral methods through an overview of the discrete Fourier Transform (DFT) and the Fast Fourier Transform (FFT) algorithm that is used to quickly calculate the DFT. Finally it will combine all of these to solve a couple of different PDEs first in a serial setting and then in a parallel setting.The programs will use Matlab and Fortran. A Python implementation of some of the Matlab programs is also provided.Fri, 12 Aug 2016 15:12:44 -0700SINGLE VARIABLE CALCULUS I: Early Transcendentals
https://www.merlot.org/merlot/viewMaterial.htm?id=1221254
The emphasis in this course is on problems—doing calculations and story problems. To master problem solving one needs a tremendous amount of practice doing problems. The more problems you do the better you will be at doing them, as patterns will start to emerge in both the problems and in successful approaches to them. You will learn quickly and effectively if you devote some time to doing problems every day. Typically the most difficult problems are story problems, since they require some effort before you can begin calculating. Here are some pointers for doing story problems:Carefully read each problem twice before writing anything.Assign letters to quantities that are described only in words; draw a diagram if appropriate.Decide which letters are constants and which are variables. A letter stands for a constant if its value remains the same throughout the problem.Using mathematical notation, write down what you know and then write down what you want to find.Decide what category of problem it is (this might be obvious if the problem comes at the end of a particular chapter, but will not necessarily be so obvious if it comes on an exam covering several chapters).Double check each step as you go along; don’t wait until the end to check your work.Use common sense; if an answer is out of the range of practical possibilities, then check your work to see where you went wrongThu, 11 Aug 2016 19:06:18 -0700Precalculus
https://www.merlot.org/merlot/viewMaterial.htm?id=1221252
These are notes for a course in precalculus, as it is taught at New York CityCollege of Technology - CUNY (where it is offered under the course numberMAT 1375). Our approach is calculator based. For this, we will use thecurrently standard TI-84 calculator, and in particular, many of the exampleswill be explained and solved with it. However, we want to point out thatthere are also many other calculators that are suitable for the purpose ofthis course and many of these alternatives have similar functionalities as thecalculator that we have chosen to use. An introduction to the TI-84 calculatortogether with the most common applications needed for this course is providedin appendix A. In the future we may expand on this by providing introductionsto other calculators or computer algebra systems.This course in precalculus has the overarching theme of “functions.” Thismeans that many of the often more algebraic topics studied in the previouscourses are revisited under this new function theoretic point of view. However,in order to keep this text as self contained as possible we always recall allresults that are necessary to follow the core of the course even if we assumethat the student has familiarity with the formula or topic at hand. After a firstintroduction to the abstract notion of a function, we study polynomials, rationalfunctions, exponential functions, logarithmic functions, and trigonometricfunctions with the function viewpoint. Throughout, we will always place particularimportance to the corresponding graph of the discussed function whichwill be analyzed with the help of the TI-84 calculator as mentioned above.These are in fact the topics of the first four (of the five) parts of this precalculuscourse.In the fifth and last part of the book, we deviate from the above themeand collect more algebraically oriented topics that will be needed in calculusor other advanced mathematics courses or even other science courses. Thispart includes a discussion of the algebra of complex numbers (in particularcomplex numbers in polar form), the 2-dimensional real vector space R2 sequences and series with focus on the arithmetic and geometric series (whichare again examples of functions, though this is not emphasized), and finallythe generalized binomial theorem.Thu, 11 Aug 2016 19:01:14 -0700Precalculus
https://www.merlot.org/merlot/viewMaterial.htm?id=1221249
Table of Contents Chapter 1: Relations and FunctionsChapter 2: Linear and Quadratic FunctionsChapter 3: Polynomial FunctionsChapter 4: Rational FunctionsChapter 5: Furthur Topics in FunctionsChapter 6: Exponential and Logarithmic FunctionsChapter 7: Hooked on ConicsChapter 8: Systems of Equations and MatricesChapter 9: Sequences and the Binomial TheoremChapter 10: Foundations of TrigonometryChapter 11: Applications of TrigonometryThu, 11 Aug 2016 18:54:18 -0700Introductory Statistics
https://www.merlot.org/merlot/viewMaterial.htm?id=1221239
In many introductory level courses today, teachers are challenged with the task of fitting in all of the core concepts of the course in a limited period of time. The Introductory Statistics teacher is no stranger to this challenge. To add to the difficulty, many textbooks contain an overabundance of material, which not only results in the need for further streamlining, but also in intimidated students. Shafer and Zhang wrote Introductory Statistics by using their vast teaching experience to present a complete look at introductory statistics topics while keeping in mind a realistic expectation with respect to course duration and students’ maturity level.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. Shafer and Zhang believe that the students in this course are best served by a focus on that core material and not by an exposure to a plethora of peripheral topics. Therefore in writing Introduction to Statistics they have sought to present only the core concepts and use a wide-ranging set of exercises for each concept to drive comprehension. As a result Introduction to Statistics is a smaller and less intimidating textbook that trades some extended and unnecessary topics for a better-focused presentation of the central material.You will not only appreciate the depth and breadth of exercises in Introduction to Statistics, but you will also like the close attention to detail that Shafer and Zhang have paid to the student and instructor solutions manuals. This is one of few books on the market where the textbook authors have written the solutions manuals to maintain the integrity of the material.In addition, in order to facilitate the use of technology with the book the authors included “large data set exercises,” where appropriate, that refer to large data sets that are available on the web, and for which use of statistical software is necessary.Thu, 11 Aug 2016 18:39:29 -0700