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A First Course in Linear Algebra: Study Guide for the Undergraduate Linear Algebra Course
http://www.merlot.org/merlot/viewMaterial.htm?id=1026760
In this book, there are five chapters: Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic Equation of Matrix, and Matrix Dot Product. It has also exercises at the end of each chapter above to let students practice additional sets of problems other than examples, and they can also check their solutions to some of these exercises by looking at “Answers to OddNumbered Exercises” section at the end of this book. This book is very useful for college students who studied Calculus I, and other students who want to review some linear algebra concepts before studying a second course in linear algebra. This book is available online for free in google books and ResearchGate in PDF format under a Creative Commons license.
Wed, 20 May 2015 02:25:04 0700

A Friendly Introduction to Differential Equations
http://www.merlot.org/merlot/viewMaterial.htm?id=1026757
In this book, there are five chapters: The Laplace Transform, Systems of Homogeneous Linear Differential Equations (HLDE), Methods of First and Higher Orders Differential Equations, Extended Methods of First and Higher Orders Differential Equations, and Applications of Differential Equations. In addition, there are exercises at the end of each chapter above to let students practice additional sets of problems other than examples, and they can also check their solutions to some of these exercises by looking at "Answers to OddNumbered Exercises" section at the end of this book. This book is a very useful for college students who studied Calculus II, and other students who want to review some concepts of differential equations before studying courses such as partial differential equations, applied mathematics, and electric circuits II. This book is available online for free in google books and ResearchGate in PDF format under a Creative Commons license.
Wed, 20 May 2015 02:09:44 0700

Introduction to Vectors  YouTube classes with Dr Chris Tisdell
http://www.merlot.org/merlot/viewMaterial.htm?id=1017024
'״Introduction to Vectors" takes learning to a new level by combining written notes with online video. Each lesson is linked with a YouTube video from awardwinning teacher and bestselling author Dr Chris Tisdell, where he explains the material in an inspiring and engaging way. Vectors provide a fascinating tool to describe motion and forces in physics and engineering. They also provide a simple framework for understanding geometry. Download the book and subscribe to Dr Chris Tisdell's YouTube channel!'
Tue, 21 Apr 2015 14:34:05 0700

A Short Course in Predicate Logic
http://www.merlot.org/merlot/viewMaterial.htm?id=1017022
'In my experience students often struggle to understand Predicate Logic: they drown in the complicated notation; they do not understand the difference between syntax and semantics, proof and truth; they do not appreciate the importance of logic within mathematics and formal methods in general. This book was written specifically to address these issues, at the same time presenting a full and rigorous treatment of the subject requiring only basic mathematics.The presentation is based on a course for final year undergraduate students of mathematics, computer science and philosophy supplemented with additional material for masters students. Numerous problems, together with detailed solutions, are provided to consolidate the students' understanding.'
Tue, 21 Apr 2015 14:27:40 0700

Exercises in Statistical Inference with detailed solutions
http://www.merlot.org/merlot/viewMaterial.htm?id=1016990
'Statistical inference is a process of drawing general conclusions from data in a specific sample. Typical inferential problems are: Does alternative A give higher return than alternative B? Is drug A more effective than drug B? In both cases solutions are based on observations in a single sample.To solve inferential problems one has to deal with the problems: (i) How to find the best estimate of an unknown quantity, (ii) How to find an interval that covers the true unknown value and (iii) How to test hypothesis about the value of an unknown quantity. The treatment of these issues can be found in a large amount of statistical textbooks. The present book differs from the latter since it focuses on problem solving and only a minimum of the theory needed is presented.'
Tue, 21 Apr 2015 14:21:59 0700

Differential Equations with YouTube Examples
http://www.merlot.org/merlot/viewMaterial.htm?id=1017019
'This review book, used in conjunction with free online YouTube videos, is designed to help students prepare for exams, or for selfstudy. The topics covered here are most of the standard topics covered in a first course in differential equations.The chapters and sections of this review book, organized by topics, can be read independently. Each chapter or section consists of three parts: (1) Theory; (2) YouTube Example; and (3) Additional Practice. In Theory, a summary of the topic and associated solution method is given. It is assumed that the student has seen the material before in lecture or in a standard textbook so that the presentation is concise. In YouTube Example, an online YouTube video illustrates how to solve an example problem given in the review book. Students are encouraged to view the video before proceeding to Additional Practice, which provides additional practice exercises similar to the YouTube example. The solutions to all of the practice exercises are given in this review book’s Appendix.For students who selfstudy, or desire additional explanatory materials, a complete set of free lecture notes by the author entitled An Introduction to Differential Equations can be downloaded by clicking HERE. This set of lecture notes also contains links to additional YouTube tutorials. The lecture notes and tutorials have been extensively used by the author over several years when teaching an introductory differential equations course at the Hong Kong University of Science and Technology.'
Tue, 21 Apr 2015 14:17:40 0700

Elementary Algebra Textbook (Second Edition: 20122013)
http://www.merlot.org/merlot/viewMaterial.htm?id=1013320
Elementary Algebra (Algebra 1) textbook designed for a onesemester course for college students. Precollege level mathematics (developmental mathematics).Available online and in print ($20 lulu.com). Online, entire textbook can be downloaded (pdf) or each chapter separately. Answers included for oddnumbered problems. Student Solutions Manual available as a separate file. Online version includes "You Try It" feature. Printed version is blackandwhite only.All parts of this Elementary Algebra Textbook (Second Edition: 20122013) are copyrighted in the name Department of Mathematics, College of the Redwoods. They are not in the public domain. However, they are being made available free for use in educational institutions. This offer does not extend to any application that is made for profit. Users who have such applications in mind should contact David Arnold or Bruce Wagner at DavidArnold@redwoods.edu or BruceWagner@redwoods.edu.This work (including all text, photographs, Portable Document Format files, and any other original works), except where otherwise noted, is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 Unported License, and is copyrighted © 2011, Department of Mathematics, College of the Redwoods. Online practice exercises to accompany the textbook are available at http://mathrev.redwoods.edu/cgibin/online/s15/OTcreatepracticequiz.cgi?course=math380
Sat, 11 Apr 2015 18:51:33 0700

Introduction to mathematical analysis
http://www.merlot.org/merlot/viewMaterial.htm?id=1010277
Our goal in this set of lecture notes is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs. The lecture notes contain topics of real analysis usually covered in a 10week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many wellselected exercises of various levels. Although these topics are written in a more abstract way compared with those available in some textbooks, teachers can choose to simplify them depending on the background of the students. For instance, rather than introducing the topology of the real line to students, related topological concepts can be replaced by more familiar concepts such as open and closed intervals. Some other topics such as lower and upper semicontinuity, differentiation of convex functions, and generalized differentiation of nondifferentiable convex functions can be used as optional mathematical projects. In this way, the lecture notes are suitable for teaching students of different backgrounds.
Wed, 1 Apr 2015 09:54:52 0700

Introduction to Probability  Probability Examples c1
http://www.merlot.org/merlot/viewMaterial.htm?id=992042
'In this book you find the basic mathematics that is needed by engineers and university students . The author will help you to understand the meaning and function of mathematical concepts. The best way to learn it, is by doing it, the exercises in this book will help you do just that.Topics as Elementary probability calculus, density functions and stochastic processes are illustrated.This book requires knowledge of Calculus 1 and Calculus 2.'
Tue, 24 Feb 2015 12:30:20 0800

Quantitative Analysis  Algebra with a Business Perspective
http://www.merlot.org/merlot/viewMaterial.htm?id=989756
This is a free textbook from Bookboon.'This tutorial textbook has been organized into 4 chapters (units) with several individual tutorial lessons within each chapter. As presented in the table of contents, each of the tutorials has been listed separately with its objective and its starting page. For coding purposes: “Tutorial N.M” means that the tutorial is the Mth lesson in chapter N.I attempted to present each of the tutorials as if a person (teacher, tutor) was sitting next to the reader talking each of the concepts through. My goal was to make sure that each of the lessons was fully explained but still fully understandable. Hopefully this goal was met. description of whom I believe might be interested in using these tutorials…The purpose of this tutorial textbook is to present mathematical skills (algebraic concepts) and their various applications that may be important to students of management (business) science. The applications included should allow readers to view math in a practical setting relevant to their intended careers.'Topics include:Equations, Inequalities & Linear ProgrammingMatrices & Array OperationsQuadratic & Other Special FunctionsMathematics of FinanceAbout the Author
Thu, 19 Feb 2015 15:34:24 0800