I assume a basic knowledge of calculus and linear algebra with some commonly used mathematical terminology. The title, the poor mans introduction to tensors, is a reference to gravitation by misner, thorne and wheeler. Ive tried to make these notes as self contained as possible and so all the information needed to read through them is either from an algebra or trig class or contained in other sections of the notes. I might selfstudy calculus iii at some point before taking the class so i have thorough preparaation.
Joyce pepple, acquisitions director, consumer dummies kristin a. Calculus i or needing a refresher in some of the early topics in calculus. There is online information on the following courses. Cliffsnotes study guides are written by real teachers and professors, so no matter what youre studying, cliffsnotes can ease your homework headaches and help you score high on exams. Calculus with parametric equationsexample 2area under a curvearc length.
Calculus made easy free book by murray bourne, 25 apr 2009. I may keep working on this document as the course goes on, so these notes will not be completely. Length of a curve calculus with parametric equations let cbe a parametric curve described by the parametric equations x ft. Calculus for dummies cheat sheet kris bunces digital. The precalculus for dummies pdf free download was released in ebook and paperback years before the kindle revolution, so i found it challenging to market the digital version of the book, which was also the less expensive format. Download it once and read it on your kindle device, pc, phones or tablets. The scalar product is a tensor of rank 1,1, which we will denote i and call the identity tensor. An introduction to tensors for students of physics and engineering joseph c.
An ndimensional vector eld is described by a onetoone correspondence between nnumbers and a point. Calculus requires knowledge of other math disciplines. Limits will be formally defined near the end of the chapter. Mary jane sterling aught algebra, business calculus, geometry, and finite mathematics at bradley university in peoria, illinois for more than 30 years. For example, if you own a motor car you might be interested in how much a change in the amount of. The conventional approach to calculus is founded on limits. Lecture notes weng cho chew1 october 5, 2012 1the author is with u of illinois, urbanachampaign. Mathematics learning centre, university of sydney 1 1 introduction in day to day life we are often interested in the extent to which a change in one quantity a. Preface this book is a revised and expanded version of the lecture notes for basic calculus and other similar courses o ered by the department of mathematics, university of hong kong, from the. Home math calculus an intuitive introduction to limits. I decided to put them in the public domain hoping they may be bene cial to some students in their e ort to learn this subject.
If you think of the duration of time for one hour, you may if you like think of it as cut up into 3600 little bits called seconds. In this course we will cover the calculus of real univariate functions, which was developed during. Limits, the foundations of calculus, seem so artificial and weasely. Lecture notes multivariable calculus mathematics mit. There are videos pencasts for some of the sections. In this book, much emphasis is put on explanations of concepts and solutions to examples. Here are my online notes for my calculus i course that i teach here at lamar university. Within this book, you may note that some web addresses break. These notes are being written for an introductory honors calculus class, math. Calculus for dummies from calculus for dummies by mark ryan calculus requires knowledge of other math disciplines. This book is a revised and expanded version of the lecture notes for basic calculus and other similar courses o ered by the department of mathematics, university of hong kong, from the. Lecture notes in calculus einstein institute of mathematics. In this course we will cover the calculus of real univariate functions, which was developed during more than two centuries.
The mere thought of having to take a required calculus course. Note the computation 3 shows how calculus needs algebra. We will use limits to analyze asymptotic behaviors of functions and their graphs. It was submitted to the free digital textbook initiative in california and will remain unchanged for at least two years. These are general notes on tensor calculus originated from a collection of personal notes which i prepared some time ago for my own use and reference when i was studying the subject. Preface these lecture notes, written for the ma4g6 calculus of variations course at the university of warwick, intend to give a modern introduction to the calculus of variations. Math 221 first semester calculus fall 2009 typeset. Slay the calculus monster with this userfriendly guide calculus for dummies, 2nd edition makes calculus.
Presentation mode open print download current view. Calculus for dummies, 2nd edition calculus mathematics. Cocks, product development director, consumer dummies michael spring, vice president and publisher, travel kelly regan, editorial director, travel publishing for technology dummies andy cummings, vice president and publisher, dummies technologygeneral user composition services. Use features like bookmarks, note taking and highlighting while reading calculus ii for dummies. Kolecki national aeronautics and space administration glenn research center cleveland, ohio 445 tensor analysis is the type of subject that can make even the best of students shudder. Myers florida international university, miami florida state university, tallahassee new college of florida, sarasota university of central florida, orlando. Ok, it looks old and dusty, but calculus made easy pdf is an excellent book and i strongly recommend it to those of you who are struggling with calculus concepts. In this chapter, we will develop the concept of a limit by example. Calculus for dummies makes learning calculus a breeze.
Lecture notes single variable calculus mathematics mit. Whether its to pass that big test, qualify for that big promotion or even master that cooking technique. Dummies has always stood for taking on complex concepts and making them easy to understand. Quotes from calculus for dummies thats calculus in a nutshell. These notes are intended to be a summary of the main ideas in course math 2142. The simplest notation for defining a sequence is a variable with the subscript n surrounded by braces. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work. The following links are pdf files of notes we took inclass for each section. But you can take some of the fear of studying calculus away by understanding its basic principles, such as derivatives and antiderivatives, integration, and solving compound functions. Use study notes and other basic study techniques in conjunction with textbooks such as barrons ap calculus or kaplans ap calculus.
Calculus this is the free digital calculus text by david r. You discover new ways to record solutions with interval notation, and you plug trig identities into your equations. Calculus for dummies, 2nd edition makes calculus manageable. Math study guide study guides math formula sheet calculus notes algebra cheat sheet algebra formulas college math math quotes chemistry notes precalculus semester 2 cheat sheet free download as pdf file. An introduction to tensors for students of physics and. Ap calculus help, notes, equations and answers coursenotes. Pdf produced by some word processors for output purposes only. Be sure to get the pdf files if you want to print them. Calculus is, in my opinion, ultimately is the study of change. Loy 199567 department of mathematics school of mathematical sciences. Lecture notes single variable calculus mathematics.
Draft calculus notes 11172011 11 this idea, of pinning down a value by realizing it as being squeezed in between overestimates and underestimates is an enormously powerful idea, running all through the foundations of calculus. I havent written up notes on all the topics in my calculus courses, and some of these notes are incomplete they may contain just a few examples, with little exposition and few proofs. These lecture notes, written for the ma4g6 calculus of variations course at the university of warwick, intend to give a modern introduction to the calculus of variations. Precalculus a prelude to calculus with exercises luciano battaia, giacomo bormetti, giulia livieri version 1. I tried to be as clear as possible and to highlight the key issues of the subject at an introductory level in a concise form. Our notation will not distinguish a 2,0 tensor t from a 2,1 tensor t, although a notational distinction could be made by placing marrows and ntildes over the symbol, or by appropriate use of dummy indices wald 1984. The pioneers were isaac newton 16421737 and gottfried wilelm leibniz 16461716. Its also great for teachers, to give you ideas on how to explain calculus so it doesnt confuse the hell out of. At studypug were mindful that some of you need a calculus tutor to navigate this new venture many begin by hitting a brick wall right from the get go and think calculus is hard, but such is the nature of new challenges and higher education.
While this version features a new dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product. Understanding sequences is an important first step toward understanding series. Although things should be set up nicely in most of the problems, note that. Calculus ii for dummies cheat sheet by its nature, calculus can be intimidating. This is a self contained set of lecture notes for math 221. Note that if a set is upper bounded, then the upper bound is not unique, for if m is an upper. This book provides instruction parallel to the 1,001 calculus. Calculus 1 tutor, help and practice online studypug. Calculus ii for dummies kindle edition by zegarelli, mark. Introduction to tensor calculus a scalar eld describes a onetoone correspondence between a single scalar number and a point. An intuitive introduction to limits betterexplained. Nevertheless, more readers ask about the ebook availability of my books instead of print nowadays, selling ebooks. Let x approach 0, but not get there, yet well act like its there ugh.
Accompanying the pdf file of this book is a set of mathematica notebook files with extension. Creative writing for dummies by maggie hamand, blogging for dummies by brad hill, drawing for dummies by brenda hoddinott, a. Also discover a few basic rules applied to calculus like cramers rule. We will use this idea persistently in developing the basic notions of both integral calculus and di erential calculus. The book is in use at whitman college and is occasionally updated to correct errors and add new material. The whole of the 3600 little bits added up together make one hour. If the function f and g are di erentiable and y is also a di erentiable function of x, the three derivatives dy dx, dy dt and dx dt are.
In particular, calculus gives us the tools to be able to understand how changing one or more linked variables re ects change in other variables 1. Introduction to tensor calculus for general relativity. Some of their followers who will be mentioned along this course are jakob bernoulli 16541705. In other words, calculus is the study and modeling of dynamical systems2. Find materials for this course in the pages linked along the left. Calculus for dummies, 2nd edition 9781119293491 was previously published as calculus for dummies, 2nd edition 9781118791295. The notes were written by sigurd angenent, starting from an extensive collection of notes and problems compiled by joel robbin. Lecture notes on precalculus eleftherios gkioulekas. Differential calculus for beginners by joseph edwards. Dummies helps everyone be more knowledgeable and confident in applying what they know.
Students interested in enrolling in an ap calculus course should remember that that taking college level courses requires a commitment of their time and energy. This is a very condensed and simplified version of basic calculus, which is a prerequisite for many courses in mathematics, statistics, engineering, pharmacy, etc. Math 221 1st semester calculus lecture notes version 2. To make studying and working out problems in calculus easier, make sure you know basic formulas for geometry, trigonometry, integral calculus, and differential calculus. Precalculus for dummies cheat sheet precalculus, math. Brown physics textbooks introductory physics i and ii a lecture note style textbook series intended to support the teaching of introductory physics, with calculus, at. It takes a problem that cant be done with regular math because things are constantly changing the changing quantities show up on a graph as curves it zooms in on the curve till it becomes straight, and then it finishes off the problem with regular math. The following references were consulted during the preparation of these lecture notes. Properties of limits will be established along the way. These notes, in my view, can be used as a short reference for an introductory course on tensor algebra and calculus.