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Calculus II For Dummies®
By: Mark ZegarellieBook Publisher: John Wiley & Sons
Imprint: For Dummies
Format: Adobe Encrypted (DRM)
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An easy-to-understand primer on advanced calculus topics
Calculus II is a prerequisite for many popular college majors, including pre-med, engineering, and physics. Calculus II For Dummies offers expert instruction, advice, and tips to help second semester calculus students get a handle on the subject and ace their exams. It covers intermediate calculus topics in plain English, featuring in-depth coverage of integration, including substitution, integration techniques and when to use them, approximate integration, and improper integrals. This hands-on guide also covers sequences and series, with introductions to multivariable calculus, differential equations, and numerical analysis. Best of all, it includes practical exercises designed to simplify and enhance understanding of this complex subject.
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| Title of eBook: Calculus II For Dummies® | |
| Release Date: 09-02-2008 | |
| Publisher: For Dummies |
This eBook download is available in the following formats:
| Parent title | Calculus II For Dummies® |
|---|---|
| Encrypted (DRM) | Yes |
| SKU | 9780470388587 |
| File size | 5213 |
| Security | n/a |
| Printing | Not allowed |
| Copying | Not allowed |
| Read aloud | No Sys requirements Download reader |
| Devices | Samsung Tablet, Apple Ipad & Iphone, Barnes & Noble Nook, Kobo eReader, Aluratek Libre, Iliad, Nokia, Blackberry, Hanlin |
| Note | Excellent navigation features are available via Adobe such as bookmarks and a quick access table of contents. Text search is easily accessible. An Adobe DRM-protected file is different than a pdf file in that it uses Adobe DRM (Digital Rights Management) technology, which authors and publishers use to protect their content from illegal online distribution and to set certain privileges such as restrictions on copying and printing. |
Calculus II For Dummies®
Chapter One
An Aerial View Of the Area Problem
In This Chapter]
* Measuring the area of shapes by using classical and analytic geometry
* Understanding integration as a solution to the area problem
* Building a formula for calculating definite integrals using Riemann sums
* Applying integration to the real world
* Considering sequences and series
* Looking ahead at some advanced math
Humans have been measuring the area of shapes for thousands of years. One practical use for this skill is measuring the area of a parcel of land. Measuring the area of a square or a rectangle is simple, so land tends to get divided into these shapes.
Discovering the area of a triangle, circle, or polygon is also easy, but as shapes get more unusual, measuring them gets harder. Although the Greeks were familiar with the conic sections - parabolas, ellipses, and hyperbolas - they couldn't reliably measure shapes with edges based on these figures.
Descartes's invention of analytic geometry - studying lines and curves as equations plotted on a graph - brought great insight into the relationships among the conic sections. But even analytic geometry didn't answer the question of how to measure the area inside a shape that includes a curve.
In this chapter, I show you how integral calculus (integration for short) developed from attempts to answer this basic question, called the area problem. With this introduction to the definite integral, you're ready to look at the practicalities of measuring area. The key to approximating an area that you don't know
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