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4434Analysis
http://www.merlot.org/merlot/viewMaterial.htm?id=437407
This is a free, online textbook that is also part of an online course. According to the author, "Analysis is the study of limits. Anything in mathematics which has limits in it uses ideas of analysis. Some of the examples which will be important in this course are sequences, infinite series, derivatives of functions, and integrals. As you know from calculus, limits are the basis of understanding integration and differentiation, and, as you also know from calculus, these things are the basis of everything in the world you could ever need to know.״A First Course in Complex Analysis
http://www.merlot.org/merlot/viewMaterial.htm?id=518850
According to OER Commons, 'These are the lecture notes of a one-semester undergraduate course which we taught at SUNY Binghamton. For many of our students, Complex Analysis is their first rigorous analysis (if not mathematics) class they take, and these notes reflect this very much. We tried to rely on as few concepts from real analysis as possible. In particular, series and sequences are treated "from scratch." This also has the (maybe disadvantageous) consequence that power series are introduced very late in the course.'Analysis 1
http://www.merlot.org/merlot/viewMaterial.htm?id=906080
'Part 1 consists of three units:Unit 1 - Analysis on the real lineIn this unit we start by decomposing the set of real numbers into its subsets. We then define the so called standard metric on to be able to study its structure which consists of concepts like open and closed intervals, neighbourhoods, interior and limit points leading to examples of open and closed subsets of . Countability of such subsets and numerical sequences are also essential in the structure of as a metric space. We also study functions defined on sets of real numbers with respect to concepts of continuity differentiability and integrability.Unit 2 – Vector AnalysisThis unit deals with mainly vector calculus and its applications. Thus we specifically consider concepts like gradient, divergence and curl. This leads to well known theorems like Green’s stokes divergence theorems and other related results. The curvilinear coordinates system is also given a treat in this unit.Unit 3 – Complex AnalysisThe main objective in the study of this unit is to define a function of a complex variable and then look at its degree of smoothness such as existence of limit, continuity and differentiability along the lines of calculus of functions of a real variable. Also a look at integration and power series involving a function of a complex variable will complete this unit.In addition to downloading the files below, you can also view them directly:Module part 1 (Scribd)Intro to module (YouTube)Overview of module (YouTube)'Basic Analysis: Introduction to Real Analysis
http://www.merlot.org/merlot/viewMaterial.htm?id=800937
'This free online textbook (e-book in webspeak) is a one semester course in basic analysis. This book started its life as my lecture notes for Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in the fall semester of 2009, and was later enhanced to teach Math 521 at University of Wisconsin-Madison (UW-Madison). A prerequisite for the course is a basic proof course. It should be possible to use the book for both a basic course for students who do not necessarily wish to go to graduate school, but also as a first semester of a more advanced course that also covers topics such as metric spaces.'Complex Analysis
http://www.merlot.org/merlot/viewMaterial.htm?id=437630
This is a free, online textbook for an introductory course in complex analysis. General topics include Complex Numbers, Complex Functions, Elementary Functions, Integration, Cauchy's Theorem, More Integration, Harmonic Functions, Series, Taylor and Laurent Series, Poles, Residues, and All That, and Argument Principle. Each chapter from the book can be downloaded as a free pdf file.Complex Functions Examples c-3 - Elementary Analytic Functions and Harmonic Functions
http://www.merlot.org/merlot/viewMaterial.htm?id=513199
This is a free, online textbook offered by Bookboon.com. Topics include: 1. Some necessary theoretical results, 2. Polynomials, 3. Fractional functions, 4. The exponential function and the logarithm function, 5. Trigonometric and hyperbolic functions, and 6. Harmonic functions.Complex Functions Examples c-4 - Power series
http://www.merlot.org/merlot/viewMaterial.htm?id=513201
This is a free, online textbook offered by Bookboon.com. Topics include: 1. Some simple theoretical results concerning power series, 2. Simple Fourier series in the Theory of Complex Functions, 3. Power series, 4. Analytic functions described as power series, 5. Linear differential equations and the power series method, 6. The classical differential equations, 7. Some more difficult differential equations, 8. Zeros of analytic functions, 9. Fourier series, and 10. The maximum principle.Complex Functions Examples c-5 - Laurent Series
http://www.merlot.org/merlot/viewMaterial.htm?id=513203
This is a free, online textbook offered by Bookboon.com. "This is the fifth textbook you can download for free containing examples from the Theory of Complex Functions. In this volume we shall consider the Laurent series and their relationship to the general theory, and finally the technique of solving linear differential equations with polynomial coefficients by means of Laurent series.״Complex Functions Theory c-11
http://www.merlot.org/merlot/viewMaterial.htm?id=837447
This is a free textbook offered by BookBoon.'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 complex functions, calculus of residua and its application to e.g. integration are illustrated.This book requires knowledge of Calculus 1 and Calculus 2.'Elementary Analytic Functions - Complex Functions Theory a-1
http://www.merlot.org/merlot/viewMaterial.htm?id=838706
This is a free textbook offered by BookBoon.'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 complex functions, calculus of residua and its application to e.g. integration are illustrated.This book requires knowledge of Calculus 1 and Calculus 2.'