By Louis Lyons

ISBN-10: 0521434661

ISBN-13: 9780521434669

This is often an exceptional device package for fixing the mathematical difficulties encountered by way of undergraduates in physics and engineering. This moment e-book in a quantity paintings introduces critical and differential calculus, waves, matrices, and eigenvectors. All arithmetic wanted for an introductory path within the actual sciences is integrated. The emphasis is on studying via figuring out genuine examples, exhibiting arithmetic as a device for realizing actual structures and their habit, in order that the coed feels at domestic with genuine mathematical difficulties. Dr. Lyons brings a wealth of educating event to this clean textbook at the basics of arithmetic for physics and engineering.

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**Extra info for All You Wanted to Know about Mathematics but Were Afraid to Ask - Mathematics Applied to Science**

**Example text**

Prove that ∞ (a) If a series ∞ un converges, so also does n=1 ∞ kun , where k is any constant. n=1 ∞ un diverges, so also does (b) If a series n=1 ∞ kun , where k is any constant. n=1 ∞ un converges, so also does (c) If a series n=n0 un , where n1 > n0 . 2. Prove the following limit tests for a series of terms un : (a) If, for some p > 1, lim np un < ∞, then n→∞ ∞ un converges. n ∞ (b) If lim nun > 0, then n→∞ un diverges. 3. (a) Show that the series 1 n (ln n)2 n=2 converges. (b) Write a symbolic computation program that will evaluate 1000 n=2 1 , n (ln n)2 and, using Eq.

Determine whether each of these series is convergent, and if so, whether it is absolutely convergent: (a) ln 2 ln 3 ln 4 ln 5 ln 6 − + − + − ··· , 2 3 4 5 6 (b) 1 1 1 1 1 1 1 1 + − − + + − − + ··· , 1 2 3 4 5 6 7 8 (c) 1 − 1 1 1 1 1 1 1 1 1 1 1 1 1 − + + + − − − − + ···+ − ···− +··· . 2. Catalan’s constant, sometimes designated β(2), is deﬁned by the series ∞ β(2) = (−1)k (2k + 1)−2 = k=0 1 1 1 − 2 + 2 − ··· . 12 3 5 Using symbolic computations, calculate β(2) to six-digit accuracy. Hint. The rate of convergence is enhanced by pairing the terms: (4k − 1)−2 − (4k + 1)−2 = 16k .

Note also CHAPTER 1. COMPUTERS, SCIENCE, AND ENGINEERING 30 that once a procedure has been deﬁned, it remains available for use until the end of the maple or mathematica session unless its name has been undeﬁned or deﬁned to be something else. In maple, our procedure is ⎡ > squaresum := proc(n) local j,S; squaresum must start with a letter, ⎢> S= 0; ⎢ may continue with letters or numbers. ⎢> for j from 1 to n do ⎢ j and S are deﬁned as local to avoid ⎢> S= S + j^2 end do; ⎢ collisions with other programming.

### All You Wanted to Know about Mathematics but Were Afraid to Ask - Mathematics Applied to Science by Louis Lyons

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