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Notes on Calculus II Integral Calculus. Miguel A. Lerma. November 22, 2002. Contents. Introduction. 5. Chapter 1. Integrals 6. 1.1. Areas and Distances. The Definite Integral 6. 1.2. The Evaluation Theorem 11. 1.3. The Fundamental Theorem of Calculus 14. 1.4. The Substitution Rule 16. 1.5.
However, Calculus II, or integral calculus of a single variable, is really only about two topics: integrals and series, and the need for the latter can be motivated by the former. The purpose of this rst lecture is
CHAPTER 1 Numbers and Functions The subject of this course is \functions of one real variable" so we begin by wondering what a real number \really" is, and then, in the next section, what a function is. 1. What is a number? 1.1. Di erent kinds of numbers. The simplest numbers are the positive integers 1;2;3;4; the number zero 0; and the ...
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11 Ιουλ 2023 · Calculus II. Here are my online notes for my Calculus II course that I teach here at Lamar University. Despite the fact that these are my “class notes”, they should be accessible to anyone wanting to learn Calculus II or needing a refresher in some of the topics from the class.
Calculus: The study of real functions f, and their derivatives f0 and integrals R f. Let f : [a; b] ! R be continuous. De nition The de nite integral of f from a to b is. where. x. Z b Z b n X f = f(x) dx := lim f(xi) x. a n!1 i=1. = (b a)=n. and. xi = a + i x. Note: x is a \dummy" variable, replaced in many. b b. physical applications by time.