This is a self contained set of lecture notes for Math 221. The notes were written by Sigurd Angenent, starting from an extensive collection of notes and problems compiled by Joel Robbin. The LATEX and Python les which were used to produce these notes are available at the following web site http://www.math.wisc.edu/~angenent/Free-Lecture-Notes
1.1.3. Birth of modern science and of calculus Stage III, around 1680: how to speak the language of mathematics! (i) state a hypothesis, (ii) devise an experiment to test it, (iii) carry out the experiment, (iv) accept or reject the hypothesis The problem in making it work in practice: To test hypotheses on forces and movements of objects, one ...
In Calculus II, we built upon this idea that we can use integrals to calculate and model complex situations by accumulating the sums of simpler parts. We also learned techniques used in calculat-
All references to “Thomas” or “the textbook” in these notes refer to Thomas’ CALCULUS 11th edition published by Pearson Addison Wesley in 2005. These notes may be downloaded from http://www.math.wisc.edu/~robbin/221dir/lecs-221.pdf. Some portions of these notes are adapted from http://www.math.wisc.edu/~angenent/Free-Lecture-Notes/.
Two main problems of calculus are 1.Derivative. Find the rate of change of f. 2.Integral. Find the area under a given curve. Both are based on the concept of limit. We say limx!a f (x) ˘L to mean that f (x) is “close enough” to L for any x “close enough” to a. Example 1.1.1. Which value is x close to when x is close to 2? lim x!2 x ˘2 ...
VIDEO LECTURES This book is supplemented by a series of 17 video lectures on "Highlights of Calculus". These are on MIT's OpenCourseWare site ocw.mit.edu and they are freely available to all viewers. My hope is to help students and teachers everywhere. https://ocw.mit.edu/resources/res-18-005-highlights-of-calculus-spring-2010/
Lecture Notes | Single Variable Calculus - MIT OpenCourseWare
This section provides the lecture notes from the course.
LECTURE NOTES Math 2450, Calculus III with Applications Alvaro P´ampano Llarena´ 1 Vectors in Plane and Space (Chapter 9) Definition 1.1The plane can be described as the set, R2 = {(x,y) |x,y∈R}, while the space is the set, R3 = {(x,y,z) |x,y,z∈R}. Both, R2 and R3 are examples of vector and affine spaces.
MATH 114 – Calculus I Page 5 of 26 Calculus I Lecture Notes for MATH 114 Course Syllabus Section numbers refer to the assigned text: James Stewart, Single Variable Calculus: Concepts and Contexts, 3rd edition, Thomson, 2006. 1. Functions domain and range ..... 1.1
Calculus is a mathematical framework for working with and extracting useful information from functions. Thus, in order to understand and appreciate the meat of calculus, we first