Study guides understand basic math and biology, as well as advanced topics like organic chemistry and statistics. There are two basic operations that can be performed on vectors. Math 221 1st semester calculus lecture notes version 2. Pdf understanding basic calculus free tutorial for beginners. The approach is quite di erent from that of standard calculus texts. This is a very condensed and simplified version of basic calculus, which is a prerequisite for many courses in mathematics, statistics, engineering, pharmacy, etc.
In most of the popular books on the market, however, the bulk of the. As a result, just as there are many ways to express the same thing, there are many notations for the derivative. Goals of this note is to have a good understanding of concepts of calculus and applications of calculus in sciences and engineering. The videos, which include reallife examples to illustrate the concepts, are ideal for high school students, college students. They cover the properties of the real numbers, sequences and series of real numbers, limits of functions, continuity, di erentiability, sequences and series of functions, and riemann integration. Introduction to calculus differential and integral calculus. Draft calculus notes 11172011 9 preface these notes are being written for an introductory honors calculus class, math 1551, at lsu in the fall of 2011. Pdf these are some lecture notes for the calculus i course. Accompanying the pdf file of this book is a set of mathematica.
Make sure your calculator is set to radians for the computations. Mit professor gilbert strang has created a series of videos to show ways in which calculus is important in our lives. An introduction to lagrangian and hamiltonian mechanics. In fact if i had to choose a subtitle for these notes, it would be an anti calculus. Calculus showed us that a disc and ring are intimately related. Pre calculus involves graphing, dealing with angles and geometric shapes such as circles and triangles, and finding absolute values. These notes are intended as a brief introduction to some of the main. So, in truth, we cannot say what the value at x1 is. This book is a revised and expanded version of the lecture notes for basic calculus and other. In fact if i had to choose a subtitle for these notes, it would be an anticalculustext book. The only physical principles we require the reader to know are. Here is a set of notes used by paul dawkins to teach his calculus i course at lamar university.
It deals with fundamental limits first and the rules of differentiation for all the. These are some notes on introductory real analysis. Whether youre studying sociology, differential equations or french ii, these free cliffsnotes articles can help you when doing your homework, writing papers, or taking tests. Basic concepts introduction in this chapter we introduce limits and derivatives.
This unit explains how to see whether a given rule describes a valid function, and introduces some of the mathematical terms associated with functions. These video tutorials on integral calculus includes all the corresponding pdf documents for your reference, these video lessons on integral calculus is designed for university students, college students and self learners that would like to gain mastery in the theory and applications of integration. Matrices and determinants the material in this chapter will be covered in your linear algebra class math 254 at mesa. This course is a continuation of the concepts you have studied in previous years, as well as an introduction to new topics. Textbook calculus online textbook mit opencourseware. You discover new ways to record solutions with interval notation, and you plug trig identities into your equations. The new system should be easy to solve if you 4 use backsubstitution to find the values of the unknowns. The best way to understand it is to look first at more examples. Functions y fx is a function of x if and only if, for each x in the domain of fx, that is the values of x for which fx is defined, there is exactly one value of fx. Likewise, many essential ideas of calculus can be very well illustrated without getting embroiled in awful algebra or arithmetic, not to mention trigonometry. However, not every rule describes a valid function. Because senior high school is a transition period for students, the latter must also be prepared for collegelevel academic rigor. Finding absolute extrema here is the first application of derivatives that.
Pdf produced by some word processors for output purposes only. Matrices a matrix is basically an organized box or array of numbers or other expressions. The table can also be used to find definite integrals using the fundamental theorem of calculus. We can improve our understanding of the behavior of gx for x. Exams for the basic calculus course may be designed so that calculators are not necessary. Transistors, microchips, lasers, computers, telecommunications, nuclear power and space travel are among the many applications of physics that are so. The sound theory of calculus as we know it today, and as we are going to learn it in this course was mostly developed through out the 19th century, notably by josephlouis lagrange 173618, augustin. Both concepts are based on the idea of limits and functions. Rational functions and the calculation of derivatives chapter 6. You should not expect that notions and theorems we will study in this course are going to apply to any of your particular projects. And sometimes the little things are easier to work with.
In this book, much emphasis is put on explanations of concepts and solutions to examples. This subject constitutes a major part of mathematics, and underpins many of the equations that. Loy 199567 department of mathematics school of mathematical sciences. This text is designed to teach the concepts and techniques of basic linear algebra as a rigorous mathematical subject. Understand the basic concepts of triangles, squares, and circles and how to calculate things like area and perimeter. There are at least two different ways of finding f 1. So it is a special way of saying, ignoring what happens when we get there, but as we get closer and closer the answer gets closer and closer to 2 as a graph it looks like this. Included are detailed discussions of limits properties, computing, onesided, limits at infinity, continuity, derivatives basic formulas, productquotientchain rules lhospitals rule, increasingdecreasingconcave upconcave down, related rates, optimization and basic integrals basic formulas. Calculus i or needing a refresher in some of the early topics in calculus. It is not comprehensive, and absolutely not intended to be a substitute for a oneyear freshman course in differential and integral calculus. For each of the given points determine the value of f. At the same time, study of calculus makes clear how important it is to be able to do the necessary algebra and arithmetic, whether by calculator or.
Teaching guide for senior high school basic calculus. Basic calculus is the study of differentiation and integration. 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. Integral calculus video tutorials, calculus 2 pdf notes. This is shown by the success of dozens of books that have been written since stephen hawking s a brief history of time 1988 became a best seller. There are at least two different ways of finding f1. Calculus produces functions in pairs, and the best thing a book can do early is to show you more of them. Use the information from a to estimate the value of lim. Introduction these notes were written for a broad audiencei wrote these notes to be accessible to anyone with a basic knowledge of linear algebra and vector calculus. These notes are intended to be a summary of the main ideas in course math 2142.
Note that the circle in figure 18c does not define a single valued function. Avoid using this symbol outside the context of limits. Basic properties and formulas if fx and g x are differentiable functions the derivative exists, c and n are any real numbers, 1. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. Some topics in calculus require much more rigor and precision than topics encountered in previous. 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.
Introduction to functions mctyintrofns20091 a function is a rule which operates on one number to give another number. These few pages are no substitute for the manual that comes with a calculator. A gentle introduction to learning calculus betterexplained. A strictly logical organization, complete and exceedingly.
Calculus, rather like english or any other language, was developed by several people. These notes are intended as an elementary introduction into these ideas and the basic prescription of lagrangian and hamiltonian mechanics. Some concepts like continuity, exponents are the foundation of the advanced calculus. Hyperbolic trigonometric functions, the fundamental theorem of calculus, the area problem or the definite integral, the antiderivative, optimization, lhopitals rule, curve sketching, first and second derivative tests, the mean value theorem, extreme values of a function, linearization and differentials, inverse. But it is easiest to start with finding the area under the curve of a function like this. Introduction to calculus for business and economics. Basic calculus explains about the two different types of calculus called differential calculus and integral calculus. Our study of calculus begins with an understanding of the expression lim x a fx, where a is a real number in short, a and f is a function. We encourage teachers and other education stakeholders to email their feedback, comments, and recommendations to the commission on. This is a very condensed and simplified version of basic calculus, which is a prerequisite for many courses. Exponential functions, substitution and the chain rule. More comprehensive tables can usually be found in a calculus textbook, but the ones listed here are good ones to know without having to look up a reference.
Thus, physics is the basic science from which all others have derived. Integration can be used to find areas, volumes, central points and many useful things. Jun 28, 2012 i preface this book is a revised and expanded version of the lecture notes for basic calculus and other similar courseso. Here are my online notes for my calculus i course that i teach here at lamar. Math 221 first semester calculus fall 2009 typeset. It builds upon the pre calculus topics you were introduced to in grade 12 pre calculus mathematics. I may keep working on this document as the course goes on, so these notes will not be completely.
There is online information on the following courses. Introduction to calculus for business and economics i. This is a self contained set of lecture notes for math 221. Chung this book is a revised and expanded version of the lecture notes for basic calculus and other similar courses offered by the department of mathematics, university of hong kong, from the first semester of the academic year 19981999 through the second semester of 20062007.
The basic course of calculus is not in any way a specialized knowledge. Vector calculus lecture notes thomas baird december, 2010 contents. This system will be equivalent to the given system, meaning that they share the same solution set. The notes were written by sigurd angenent, starting from an extensive collection of notes and problems compiled by joel robbin. The complete textbook is also available as a single file.
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