Calculus Lecture Notes Ppt

, martingale. Study Skills and Note Taking Skills. PowerPoint Lectures for AB and BC Calculus These lectures may be freely copied and distributed to calculus teachers and students. In this chapter, you will learn how to evaluate limits and how they are used in the two basic problems of calculus: the. The notes are designed to be used in conjunction with a set of online homework exercises which help the students read the lecture notes and learn basic linear algebra skills. CONSUMERS AND UTILITY MAXIMIZATION. Free Presentations in PowerPoint format. I highly recommend this product to any Calculus teacher, especially new ones!" -Christine Baccaro "I have just completed my 4th year teaching Calc AB and my 1st year teaching Calc BC…Without Rita's powerpoint notes, I would have spent all of my prep time creating class presentations instead of preparing to teach. Go to: Mr. download 9. Lecture 8 (PPT) June 4, 2008: Lecture 9 (PPT) June 6, 2008: Lecture-review 2(PPT). the methods will be illustrated during the lectures. -Animage is a 2D function, so operators describing edges are expressed using partial derivatives. My students will take a full-length AB test at the conclusion of the review to provide a capstone for the first calculus course and a checkpoint of their progression. Sequences 1. The pioneers were Isaac Newton (1642-1737) and Gottfried Wilelm Leibniz (1646-1716). Advice on applying machine learning: Slides from Andrew's lecture on getting machine learning algorithms to work in practice can be found here. pdf Pre-Calculus - 4. Introduction To Mathematical Analysis John E. Advice | Help. Notes 7: Knowledge Representation, The Propositional Calculus ICS 271 Fall 2008 Outline Representing knowledge using logic Agent that reason logically A knowledge based agent Representing and reasoning with logic Propositional logic Syntax Semantic validity and models Rules of inference for propositional logic Resolution Complexity of. the vector is drawn as an arrow from the initial point pointed toward the terminal point. -----2019/9/30 Exercise Class for Chapter 2: Derivatives and Differentials. – A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow. It is the informality that often allows writers of lecture notes or expository articles to mention some "trivial fact" that every textbook leaves out. Strength of Material 3. The files below are the powerpoint files used for the lectures so far. The pioneers were Isaac Newton (1642-1737) and Gottfried Wilelm Leibniz (1646-1716). Derivatives 8. Instead of using these rectangular coordinates, we can use a coordinate system to circular. Digital Lessons View or print these PowerPoint slides to enhance your understanding of the topics covered in this course. These are the Power Point Lecture slides of the whole book of Cost and Management Accounting. There are a number of important problems here. If you need to download it to your own computer for free, here is the website:. Please complement them with your own notes. It can be used as a textbook or a reference book. Here, we are interested in using scipy. The word Calculus comes from Latin meaning "small stone", Because it is like understanding something by looking at small pieces. Lecture Notes for Introductory Probability Janko Gravner Mathematics Department University of California Davis, CA 95616 [email protected] Gallery of animated and graphical demonstrations of calculus and related topics, from the University of Vienna. optimize for black-box optimization: we do not rely. Before we get your account setup, we need to confirm you are a human. It has been used for our undergraduate complex analysis course here at Georgia Tech and at a few other places that I know of. Optimization 68 4. With few. Calculus 140, section 2. The lecture notes and YouTube videos are already available, and you can have a look at. This post contain KTU Lecture Notes for Engineering Chemistry. 9: Exponential & Logarithmic Functions [APCalcAB] Objective: Given an exponential or logarithmic function, find its derivative function algebraically. Calculus Animations, Graphics and Lecture Notes: A collection of animations and notes by Kelly Liakos. To illustrate, consider the following example. Please try again later. 1 (Introduction) (PowerPoint format) Notes for parts of Ch. 2 Generalizations (III) Let continuoussquare-integrable martingale. Limits Done Right 54 Chapter 5. PowerPoint Lecture Notes. lesson 37 precalculus: applications of vectors - youtube. • Class Notes • Many students benefit from printing the notes for a lecture beforehand, reviewing them, and commenting on them in class. MIT OpenCourseWare is a free & open publication of material from thousands of MIT courses, covering the entire MIT curriculum. Here are my online notes for my Calculus II course that I teach here at Lamar University. Video, Lecture 1, Part 3. ALGEBRA / TRIGONOMETRY Or PRE-CALCULUS (includes Plane Geometry) (1 Precalculus Trigonometry - video lectures (UCI Open Courseware) (2 Trigonometry - video tutorials, lecture notes, & example problems (OnlineMathLearning. As you work through these lectures with the aid of the videos, it is recommended that you try the problems in the lecture notes prior to watching the solutions. May 01, 2009 · This is a textbook for an introductory course in complex analysis. Advice on applying machine learning: Slides from Andrew's lecture on getting machine learning algorithms to work in practice can be found here. Lecture Notes. To give you a feeling for the issues, suppose you were interested in the temperature T of water in a river. • We will use limits to analyze asymptotic behaviors of functions and their graphs. Lecture Notes PowerPoint Presentation for Quality Management. The Professor's C++ Course. I use these lecture notes in my course Information Theory, which is a graduate course in the first year. 1 Conics and Calculus In this section, we will study conic sections from a few different perspectives. The first few homework exercises ask you to guess at the values of various limits. Among the most important has to do with efficiently searching. These lecture notes are intended to supplement the lectures and other materials for the first half of Economics b at the University of California, Berkeley. Partial Derivative and Gradient. Neurophysiology Ppt. Lecture Notes: The Finite Element Method AurélienLarcher,NiyaziCemDe˜girmenci This document is a collection of short lecture notes written for the course “The. Lecture notes. The Calculus of Basketball. A good book for lots of examples in. Reza Khadem, San Jacinto College, central. Calculus I or needing a refresher in some of the early topics in calculus. Lecture Notes on Classical Mechanics (A Work in Progress) Daniel Arovas Department of Physics University of California, San Diego 5 Calculus of Variations 61. Vahsen for more details. Holsinger Department of Ecology & Evolutionary Biology, U-3043 University of Connecticut Storrs, CT 06269-3043. CS229Lecturenotes Andrew Ng Supervised learning Let’s start by talking about a few examples of supervised learning problems. Digital Image Processing (CS/ECE 545) Lecture 1: Introduction to Image Processing and ImageJ Prof Emmanuel Agu Computer Science Dept. It also assumes that the reader has a good knowledge of several Calculus II topics including some integration techniques, parametric. A PowerPoint presentation highlighting key learning objectives and the main concepts for each chapter are available for you to use in your classroom. AP Physics 1 Notes AP Physics 1 Practice Exams Free Response Notes Videos Study Guides There are some amazing AP Physics 1 notes available. More KTU Lecture Notes will be added soon. Supercourse Lectures in Power Point/pdf Format. *I f you are enrolled in Flipped and Flexible Math 1151: Please note that doing the lessons listed below will not count towards your grade. COURSE INFORMATION AND MATERIALS: To access the PDF files, you'll need Adobe Acrobat. Lecture notes for Physics 10154: General Physics I Hana Dobrovolny Department of Physics & Astronomy, Texas Christian University, Fort Worth, TX December 3, 2012. Part of the APEX (Affordable Print and Electronic TeXtbook) series. Discrete Mathematics CSC 2110; Lecture Notes in Discrete Mathematics by Marcel B Lecture Notes for CS120 An Introduction to Computi CS125 Introduction to Computer Science Lecture No Computer Science from the Bottom Up ebook; University of Calgary CSPC 231 Introduction to Com. Pre-Calculus I 1. Digital Lessons View or print these PowerPoint slides to enhance your understanding of the topics covered in this course. The second day focuses on integrals and the fundamental theorems of calculus. Lecture 8 (PPT) July 9, 2007: University of Florida Department of Physics. My aim is to help students and faculty to download study materials at one place. Calculus 2 Class Notes. VECTOR MECHANICS FOR ENGINEERS: STATICS Ferdinand P. These notes are intended as an elementary introduction into these ideas and the basic prescription of Lagrangian and Hamiltonian mechanics. Introductory General Physics II Lecture Notes. You will also learn how to evaluate improper integrals. This is a very condensed and simplified version of basic calculus, which is a prerequisite for many courses in Mathematics, Statistics, Engineering, Pharmacy, etc. Taking Notes. Gaussian Elimination. Video short lecture on parsing: HTML. about taking notes anymore in AP Chemistry class because of this packet. learn Calculus III or needing a refresher in some of the topics from the class. The LATEX and Python les. Here you'll find all the information you need about this course. These Lecture Notes can be used for both review and learning, and. Find many great new & used options and get the best deals for AP Calculus BC Lecture Notes : AP Calculus BC Interactive Lectures Vol. Course Description. I have retained the basic structure of his course, with a blend of theory and practice,. CM111A – Calculus I Compact Lecture Notes ACC Coolen Department of Mathematics, King’s College London Version of Sept 2011. -----2019/11/1. Beginning Calculus - The Derivatives - Shahrizal Shamsuddin Norashiqin Mohd Idrus Department of Mathematics, FSMT - UPSI (LECTURE SLIDES SERIES) VillaRINO DoMath, FSMT-UPSI (D2) The Derivatives 1 / 21. Taking Effective Notes. It also assumes that the reader has a good knowledge of several Calculus II topics including some integration techniques, parametric. Search this site. Would recommend to anyone trying to learn AP Calculus!" -Betty. We explain calculus and give you hundreds of practice problems, all with complete, worked out, step-by-step solutions. Temperature T is a scalar, and will certainly be a function of a position vector x = (x,y,z). The vector space operations are the sum A+ Band the scalar multiple cA. A little closer to 3. Lecture notes and articles are where one generally picks up on historical context, overarching themes (the "birds eye view"), and neat interrelations between subjects. Lecture notes for Physics 10154: General Physics I Hana Dobrovolny Department of Physics & Astronomy, Texas Christian University, Fort Worth, TX December 3, 2012. These notes contains some basic concepts and examples of Integral Calculus, Improper Integrals, Beta and Gamma function for B. This feature is not available right now. Lecture Notes: PDF. 4MB) Download Exhibit PowerPoint Chapter 1. Lecture 1, Act 2 Solution : Lecture 1, Act 2 Solution x a v t t t Going up the ball has positive velocity, while coming down it has negative velocity. Based on his notes from StcohasticCalculus course he was teaching at Victoria University in Wellington. Copies of the classnotes are on the internet in PDF format, as given below. (download made easy gate civil engineering hand written notes for free). The remainder of these notes cover either more advanced aspects of topics from the book, or other topics that appear only in our more advanced algorithms class CS 473. The scalar product is a tensor of rank (1,1), which we will denote I and call the identity tensor:. The additional point of interest is the decomposition of the change in the quantity of X consumed into substitution effects and income effects. CliffsNotes study guides are written by real teachers and professors, so no matter what you're studying, CliffsNotes can ease your homework headaches and help you score high on exams. Special software is required to use some of the files in this course:. Check Out Engineering Mathematics 1st-year pdf Notes Download. Calculus 1 Class Notes, Thomas' Calculus, Early Transcendentals, 12th Edition Copies of the classnotes are on the internet in PDF format as given below. The treatment of the topics presented here is deep. The textbook for this course is Stewart: Calculus, Concepts and Contexts (2th ed. Previous projects: A list of last year's final projects can be found here. the purpose of the pdf proof is a final check of the layout, and of tables and figures. Lecture Notes on Sequent Calculus 15-816: Modal Logic Frank Pfenning Lecture 8 February 9, 2010 1 Introduction In this lecture we present the sequent calculus and its theory. Complete notes for 2017/18 MA212 Michaelmas Term Calculus part written in LaTex based on the powerpoint slides provided by the lecturer. Find an x such that f(x)isinS. This website, developed and maintained by Gyula Klima, a professor of philosophy at Fordham University, makes available the lecture notes he used whilst teaching an introductory p. Use Firefox to download the files if you have problems. I may keep working on this document as the course goes on, so these notes will not be completely finished until the end of the quarter. Most certainly a lecture does not mean simply copying notes to the. Note that this calculation does not use the fact that h varies over the set of complex numbers in any special. Game theory lecture notes by field of study. - (Condensed from H. Tutorials on the scientific Python ecosystem: a quick introduction to central tools and techniques. Doron Avramov ב ומרבא ןורוד 'פ ורפ Derivatives Securities. CONSTRUCTION & PHYSICAL APPLICATION OF THE FRACTIONAL CALCULUS‡ Nicholas Wheeler, Reed College Physics Department February 1997 Introduction. The dates by some of the lectures are the date of the most recent revision. Lecture Notes on Special Relativity prepared by J D Cresser Department of Physics Macquarie University 8thAugust2005. Find PowerPoint Presentations and Slides using the power of XPowerPoint. 1 Vector calculus According to classical physics, "reality" takes place in a product space R3 × R,. The following links are pdf files of notes we took in-class for each section. Broken down in to topics and sections. Precise Definition of Limit 6. Some of the material in Chapter 3 involves time-dependent perturbation theory, which is described in the notes here, but the. Need help with Calculus? Here are Videos & Notes for the whole year of AP Calculus AB. It can be used as a textbook or a reference book. The treatment of the topics presented here is deep. These are notes for a one-semester graduate course on numerical optimisation given by Prof. We turn to that subject. As an alternative notation, given y(x), know how to nd y0(x) and y00(x). Lecture 1, Act 2 Solution : Lecture 1, Act 2 Solution x a v t t t Going up the ball has positive velocity, while coming down it has negative velocity. Russell Johnston, Jr. It is nicely broken down into sections for easy references. Subtraction is the “backwards” of addition: 2+3 = 5 ⇒5−3 = 2. to Computing Algorithms Spring 2003 Algorithms Networks Wireless Networks Fall 2002. The notes has illustrative examples that are able to sharpen the learner. Previous projects: A list of last year's final projects can be found here. Subtitles and transcripts available. Taking Lecture Notes. Lecture Notes: The Finite Element Method AurélienLarcher,NiyaziCemDe˜girmenci This document is a collection of short lecture notes written for the course “The. Professor Shankar introduces the course and answers student questions about the material and the requirements. Initial value problems. Taking Notes. It is not comprehensive, and absolutely not intended to be a substitute for a one-year freshman course in differential and integral calculus. The notes are brief but comprehensive as they cover the entire course outline. If you continue browsing the site, you agree to the use of cookies on this website. Lectures on theoretical physics from Cambridge University. Instead of using these rectangular coordinates, we can use a coordinate system to circular. It is customary to enclose the elements of a matrix in parentheses, brackets, or braces. Lectures 1-3 (I-week) Lecture 1 Why real numbers? Example 1 Gaps in the rational number system. Calculus 2 Class Notes. Broken down in to topics and sections. pdf), Text File (. The first half uses only quantum mechanics and is at a level suitable for undergraduates. Her lectures are rigorous, effective and engaging. ppt Precalculus - 4. Math 214-2 Calculus II Definite integrals and areas, the Fundamental Theorems of Calculus, substitution, integration by parts, other methods of integration, numerical techniques, computation of volumes, arc length, average of a function, applications (to physics, engineering, and probability), separable differential equations, exponential growth, infinite series, and Taylor. Students frequently credit their success on the AP Exam to these thorough, detailed and concise lecture notes. 1 Vector calculus According to classical physics, "reality" takes place in a product space R3 × R,. Notes on Matrices 4-1-2 Definition of a Matrix Element **A matrix can be named using its dimensions. 380 music notes kostenlos vectors. Given a function f and a set S: 1. Don't show me this again. 6-Brief Calculus with Integrated Precalculus by Joseph Collison. GEOS 4430 Lecture Notes: Well Testing Dr. Navigation. The dates by some of the lectures are the date of the most recent revision. flippingphysics. Here you can find lecture notes, ebooks and ppt covering subject-wise full syllabus. It contains slides of all Powerpoint presentations on topics covered by the BC only part of the BC Exam. Mathematical optimization deals with the problem of finding numerically minimums (or maximums or zeros) of a function. Please note that the first recitation will meet on Tuesday, January 16, and the first lecture will take place on Wednesday, January 17. Many of us will take out a mortgage so that we. Why Engineering in K-12 • Real-world engineering applications and examples concretize complex math and science concepts • Students are engaged in experiential learning • Students’ creativity is challenged, developed,. Contains 16 pages of condensed notes of all definitions and theorems required for this course. from one split second to the next. Lecture No-1 Introduction – Calculus is the mathematical tool used to analyze changes in physical quantities. Dec 06, 2018 · Here’s how I take notes using the 2018 iPad Pro 11″/12. Would recommend to anyone trying to learn AP Calculus!" -Betty. 1 About these notes This is a working set of lecture notes for the Part A Electromagnetism course, which is part of the mathematics syllabus at the University of Oxford. DIFFERENTIAL CALCULUS Download: ENGINEERING MATHEMATICS Civil Engineering Lecture Notes for All Universities & Lab Manuals for All Semester. Calculus Lecture Notes from the University of Toronto at Scarsborough. It also assumes that the reader has a good knowledge of several Calculus II topics including some integration techniques, parametric. Some of the Lecture Notes may be incomplete or unavailable. Practice makes perfect! Anywhere, Anytime! You can access all of Educator. • You may want to take personalized "sketch notes" in class. 1 Introduction Calculus is the mathematical tool used to analyze changes in physical quantities. pdf format (Ken Kuniyuki, San Diego Mesa College). 2 NUMERICAL METHODS FOR DIFFERENTIAL EQUATIONS Introduction Differential equations can describe nearly all systems undergoing change. MATH 685/ CSI 700/ OR 682 Lecture Notes Lecture 10. Faucette University of West Georgia Adapted from Calculus on Manifolds by Michael Spivak – A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow. From experience we know, that each lecture is different. For example, rivers, lakes, rain, snow, atmospheric moisture, soil water, groundwater, etc. Nedjla Ougouag, PhD: Mathematics Department, Harold Washington College : Office: HWC - 30 E. It contains slides of all Powerpoint presentations on topics covered by the BC only part of the BC Exam. The following links are pdf files of notes we took in-class for each section. Single Variable Calculus Mika Seppälä of Florida State University and the University of Helsinki presents classroom type notes on calculus, in pdf and powerpoint format. PowerPoint files based on OpenStax Calculus II (View Complete Item Description) I have used OpenStax textbooks for years. Lecture Notes on the Lambda Calculus Peter Selinger Department of Mathematics and Statistics Dalhousie University,Halifax, Canada Abstract This is a set of lecture notes that developed out of courses on the lambda calculus that I taught at the University of Ottawa in 2001 and at Dalhousie University in 2007 and 2013. Welcome! This is one of over 2,200 courses on OCW. If you miss anything, the complete notes will be posted after class. Given a function f and a set S: 1. Free Biochemistry Coaching for CSIR UGC JRF NET Life Science Examination. 380 music notes kostenlos vectors. My hand written class lecture notes are being scanned and uploaded for you to view. A little closer to 3. The limiting stochastic process xt (with = 1) is known. Notes on Optimization was published in 1971 as part of the Van Nostrand Reinhold Notes on Sys-tem Sciences, edited by George L. Loy 1995/6/7 Department of Mathematics School of Mathematical Sciences. Abikoye's ppt are now filled in & written with LIGHT RED fonts. Calculus I and II). Nov 03, 2014 · Benginning Calculus Lecture notes 3 - derivatives 1. pdf), Text File (. Vector Calculus lecture notes Thomas Baird course we will mainly be concerned with doing calculus in R3, but many of the ideas extend transparently to all n. Calculus for business and social sciences, I:. Note Taking. Doron Avramov ב ומרבא ןורוד 'פ ורפ Derivatives Securities. View and Download PowerPoint Presentations on Precalculus PPT. Abikoye's ppt are now filled in & written with LIGHT RED fonts. These notes are intended to guide the student through problem solving using Laplace and z-transform techniques and is intended to be part of MATH 206 course. Engineering Notes and BPUT previous year questions for B. With few. This book complies with 2017 AP College Board requirements. These notes are based on the 12th edition of Thomas' Calculus. Download Exhibit PowerPoint Appendix A (application/zip) (3. finden sie über eine million kostenlose vektoren, clipart graphics, vektorgrafiken und design vorlagen die von designern auf der ganzen welt erstellt wurden. For example, rivers, lakes, rain, snow, atmospheric moisture, soil water, groundwater, etc. Analytic Solutions of Partial Di erential Equations MATH3414 School of Mathematics, University of Leeds 15 credits Taught Semester 1, Year running 2003/04. In particular, check for changes to duedates and guest lectures. Lecture notes. You may click on either the VIDEO link or the YouTube link, whichever works better for you. He is a professor at Northwestern University. I highly recommend this product to any Calculus teacher, especially new ones!" -Christine Baccaro "I have just completed my 4th year teaching Calc AB and my 1st year teaching Calc BC…Without Rita's powerpoint notes, I would have spent all of my prep time creating class presentations instead of preparing to teach. MIT OpenCourseWare is a free & open publication of material from thousands of MIT courses, covering the entire MIT curriculum. Easy to add chapters. Formorelearningmaterials,pleasevisit:. This schedule is subject to change so check it frequently. Ordinary differential equations. Abikoye's ppt are now filled in & written with LIGHT RED fonts. Some lectures take one class session to cover, some others take two. Pre-Calculus I 1. Study Intermediate Microeconomics: A Modern Approach (Eighth Edition) discussion and chapter questions and find Intermediate Microeconomics: A Modern Approach (Eighth Edition) study guide questions and answers. schoolwires. A random variable is a function from. CALCULUS II LECTURE NOTES 3 1. Some of the Lecture Notes may be incomplete or unavailable. Java Arrays and Collections (Powerpoint) Lecture on Exceptions in Java (Powerpoint) Lecture on Assertions in Java (Powerpoint) Lecture on JDK 1. " - a Chinese proverb. WeBWork, a free online homework system. Exam Fees For B. Calculus I - Lecture 18 - Curve Sketching Gerald Hoehn (based on notes by T. This is a revised edition of my “Notes on Lie Algebras" of 1969. Rita Korsunsky, a High School Mathematics Teacher with many years of experience teaching AP Calculus BC. My aim is to help students and faculty to download study materials at one place. We introduce three field operators which reveal interesting collective field properties, viz. This will ensure that the C++ code is portable between computers. 2 (Syntax and Semantics) (PowerPoint format) Notes for parts of Ch. This is just a sampling of the TONS of stuff that's out there on the web related to Calculus. We strive to challenge every student to think critically, communicate effectively, and work collaboratively to foster social justice. 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). Broken down in to topics and sections. -Points which lie on an edge can be detected by: (1) detecting local maxima or minima of the first deri vative. Remarks on the Early History of the Calculus 45 2. 1 Basic Integration Rules. Iterative Methods for Linear Systems. These lecture notes grew out of an M. Lecture Notes on GRAPH THEORY Tero Harju Department of Mathematics University of Turku FIN-20014 Turku, Finland e-mail: [email protected] Derivatives as. 221A Lecture Notes Variational Method 1 Introduction Most of the problems in physics cannot be solved exactly, and hence need to be dealt with approximately. That is, we can substitute in different values of to get different results. doc _ch_02_lecture_presentation. Analytic Solutions of Partial Di erential Equations MATH3414 School of Mathematics, University of Leeds 15 credits Taught Semester 1, Year running 2003/04. It is used by the pure mathematician and by the mathematically trained scien-tists of all disciplines. The prerequisites are the standard courses in single-variable calculus (a. x The Central Limit Theorem notes by Tim Pilachowski If you haven’t done it yet, go to the Math 111 page and download the handout: Central Limit Theorem supplement. Taking Notes. MIT OpenCourseWare (OCW) is a web-based publication of virtually all MIT course content. A random variable is a function from. These notes are available as textbooks to download in PDF format. 8 Events are subsets of the sample space (A,B,C,). It is nicely broken down into sections for easy references. Hutchinson 1994 Revised by Richard J. Engineering Graphics - Slides/Presentations/PPT Fo Engineering Chemistry Lecture notes; Engineering Physics - SHM ppt By Abhiram Das; Engineering Chemistry Lecture Notes for First year An E Book For Introduction to Civil Engineering By Engineering Physics Slides for KTU; Calculus Lecture Notes for KTU. com: AP Calculus BC Lecture Notes: AP Calculus BC Interactive Lectures Vol. The different chapters each correspond to a 1 to 2 hours course with increasing level of expertise, from beginner to expert. Video Lecture 1, Part 1. Here you can find lecture notes, ebooks and ppt covering subject-wise full syllabus. The following links are pdf files of notes we took in-class for each section. , (II)Let now dsa. Math 155, Lecture Notes- Bonds Name_____ Section 10. Many expressions in calculus are simpler in base e than in other bases like base 2 or base 10 I e = 2:71828182845904509080 I e is a number between 2 and 3. There are also topical questions that can help Price: KES : 100. Selection File type icon File name. The proofs in the lecture notes sometimes di⁄er from those given in [F]:Here is a brief description of the di⁄erences to simplify for the reader. However, some notes are copyrighted and may be used for private use only.