Avoid using this symbol outside the context of limits. As a result, just as there are many ways to express the same thing, there are many notations for the derivative. Lecture notes single variable calculus mathematics. Pdf these are some lecture notes for the calculus i course. For now, only the first part of the book, covering calculus i i. What many people do not realize is that calculus is taught because it is used in. This is a self contained set of lecture notes for math 221. These notes are intended to be a summary of the main ideas in course math 2142. Its importance in the world of mathematics is in filling the void of solving complex problems when more simple math cannot provide the answer. Note that some sections will have more problems than others and some will have more or less of a variety of problems. 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 by hand. Here is a set of notes used by paul dawkins to teach his calculus i course at lamar university.
Exponential functions, substitution and the chain rule. I may keep working on this document as the course goes on, so these notes will not be completely. An introduction to basic statistics and probability. There is online information on the following courses.
This page is intended for students who are currently in calculus but have not yet reached the relevant. If you miss anything, the complete notes will be posted after class. These are course notes for mathematics 111 at reed college. I am still working on the second part of the book calculus ii, which i. Calculus i practice problems pauls online math notes. In particular, if p 1, then the graph is concave up, such as the parabola y x2. We will use this idea persistently in developing the basic notions of both integral calculus and di erential calculus. This is the homepage for the free book elementary calculus, by michael corral schoolcraft college. Calculus 3 class notes, thomas calculus, early transcendentals, 12th edition copies of the classnotes are on the internet in pdf format as given below.
They are written for serious liberal arts students who want to understand calculus beyond memorizing formulas and procedures. In this course we will cover the calculus of real univariate functions, which was developed during more than two centuries. In this course we will cover the calculus of real univariate functions. A general element a ijis located in row iand column jsee equation4for a further example. It turns out that if you know a few basic derivatives such as dxndx nxn. Calculus, rather like english or any other language, was developed by several people. Introduction calculus is a branch of mathematics that was invented in the 17th century by i. There are videos pencasts for some of the sections. Print out the skeleton notes before class and bring them to class so that you dont have to write down everything said in class. 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.
The pre calculus course bridges basic mathematics and 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. Calculus has been around since ancient times and, in its simplest form, is used for counting. Probability mass function fx probability mass function for a discrete random. This property is crucial for calculus, but arguments using it are too di cult for an introductory course on the subject. I w ould like to thank the man y studen ts who ha ve tak en calculus using these notes and who ha ve made helpful commen ts and suggestions. Calculus i revision revision notes calculus i 1 proof by. Be sure to get the pdf files if you want to print them. Because senior high school is a transition period for students, the latter must also be prepared for collegelevel academic rigor. F eedbac k ab out the notes is very imp ortan t to me.
This lecture note explains differential and integral calculus of functions of one. We also avoid several stranger aspects of the universe of calculus texts, such as counterintuitive. Cm111a calculus i compact lecture notes faculty of natural. Here are a set of practice problems for the calculus i notes. Qin r3 or rn, let pq denote the arrow pointing from pto q. Selection file type icon file name description size revision time. Calculus lecture notes download book free book centre. Though designed for college students, it could also be used in high schools. It was developed in the 17th century to study four major classes of scienti. If you are looking for the vector calculus homepage, go here. The precalculus course bridges basic mathematics and calculus.
It is highly recommended that students taking ap c also take a calculus course, or have previously taken a calculus course. In fact the idea of prin ted notes ev olv ed from requests from studen ts to mak e the hand written slides available. Calculus this is the free digital calculus text by david r. Exams for the basic calculus course may be designed so that calculators are not necessary. The traditional topics are covered, but the old idea of infinitesimals is resurrected, owing to its usefulness especially in the. It was submitted to the free digital textbook initiative in california and will remain unchanged for at least two years. Click on the solution link for each problem to go to the page containing the solution. Rational functions and the calculation of derivatives chapter 6. Here are my online notes for my calculus i course that i teach here at lamar. We use natural, but occasionally unusual, definitions for basic concepts such as limits. The preceding examples are special cases of power functions, which have the general form y x p, for any real value of p, for x 0. This is the first part calculus i of a text on elementary calculus, designed for students who have completed courses in highschool algebra, geometry, and trigonometry. Math 2210 calculus 3 lecture videos university of utah.
Lecture notes in calculus einstein institute of mathematics. Functions and their graphs, trigonometric functions, exponential functions, limits and continuity, differentiation, differentiation rules, implicit differentiation, inverse trigonometric functions, derivatives of inverse functions and logarithms, applications of derivatives, extreme values of functions, the mean value theorem. The prerequisite is three years of high school mathematics, including algebra, euclidean geometry, analytic geometry, and ideally trigonometry. All of you will have done some basic bits of settheory in school. Calculus 1 class notes, thomas calculus, early transcendentals, 12th edition copies of the classnotes are on the internet in pdf format as given below. Basic calculus teaching guide for senior high school. Chapters 2 and 3 cover what might be called multivariable precalculus, introducing the requisite algebra, geometry, analysis, and topology of euclidean space, and the requisite linear algebra, for the calculus to follow. An introduction to basic statistics and probability p. 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. Understanding basic calculus graduate school of mathematics. Some topics in calculus require much more rigor and precision than topics encountered in previous. Random variable a random variable is a variable whose value is a numerical outcome of a random phenomenon usually denoted by x, y or z. Please note that knowledge of calculus is not required for ap b or aice students.
This is a very condensed and simplified version of basic calculus, which is a prerequisite for many courses in mathematics, statistics, engineering, pharmacy, etc. A list of the basic properties of limits of sequences or functions which can be. This paper is derived from practical situations hence it is open to updating and can be adapted by other calculus teachers in different setups. 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. Math 221 1st semester calculus lecture notes version 2. The notes were written by sigurd angenent, starting from an extensive collection of notes and problems compiled by joel robbin. 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. Math 1210 calculus 1 lecture videos these lecture videos are organized in an order that corresponds with the current book we are using for our math1210, calculus 1, courses calculus, with differential equations, by varberg, purcell and rigdon, 9th edition published by pearson. This course completes the foundational knowledge on algebra, geometry, and trigonometry of students who are planning to take courses in the stem track. Math 221 first semester calculus fall 2009 typeset. 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. This book is a revised and expanded version of the lecture notes for basic. If p 0, then the graph starts at the origin and continues to rise to infinity. 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.
The book is in use at whitman college and is occasionally updated to correct errors and add new material. Likewise, many essential ideas of calculus can be very well illustrated without getting embroiled in awful algebra or arithmetic, not to mention trigonometry. Teaching guide for senior high school basic calculus. Math 2210 calculus 3 lecture videos these lecture videos are organized in an order that corresponds with the current book we are using for our math2210, calculus 3, courses calculus, with differential equations, by varberg, purcell and rigdon, 9th edition published by pearson. Download calculus lecture notes download free online book chm pdf. Lecture notes single variable calculus mathematics mit. Although calculus is usually not used to bake a cake, it does have both rules and formulas that can help you figure out the areas underneath complex functions on a graph. Some of their followers who will be mentioned along this course are jakob bernoulli 16541705. The pioneers were isaac newton 16421737 and gottfried wilelm leibniz 16461716. Use this site to find out what you missed, whats for homework and dates of exams.
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