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kind of formula for S(x) in terms of what is called a power series, the most important topic in Calculus II. Before talking about power series, let’s return to familiar territory. Some of the simplest functions that you are familiar with are polynomials. For example, f(x) = x x3=6 is a polynomial function. Amazingly,
This booklet contains the note templates for courses Math 150/151 - Calculus I at Simon Fraser University. Students are expected to use this booklet during each lecture by following along with the instructor, filling in the details in the blanks provided. Definitions and theorems appear in highlighted boxes.
These notes are intended to be a summary of the main ideas in course MATH 214-2: Integral Calculus. 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. The textbook for this course is Stewart: Calculus, Concepts and Contexts (2th ed.), Brooks/Cole. With few ...
learn Calculus II or needing a refresher in some of the topics from the class. These notes do assume that the reader has a good working knowledge of Calculus I topics including limits, derivatives and basic integration and integration by substitution.
gration, we are measuring accumulation or the limit of a summation of smaller parts2. In Calculus II, we will build upon this idea that we can use integrals to calculate and model complex situations by accumulating the sums of simpler parts. We will also learn techniques used in calculating and
Fundamental Formula of Calculus (FFC) Z b f(x) dx = F (b) F (a) b. also written F (x) for any antiderivative F of f on [a; b], meaning F 0 = f on [a; b].y Since any two such antideriva-tives di er by a constant (a consequence of the Mean Value Theorem (MVT)) it follows that any antiderivative can be used; the constants will cancel!
MATH 124 – Calculus II Page 8 of 37 Aside on sigma notation and useful formulas Pn i=1 Ai is a shorthand for A1 + A2 + ··· + An. In general, anything of the form Pn i=1(···) means “plug all values of i from 1 to n in the formula (···), and sum all n terms that result.” In doing area calculations, there are some useful formulas to ...
