'Harmonic series' presentation slideshows

INFINITE SEQUENCES AND SERIES

12. INFINITE SEQUENCES AND SERIES. INFINITE SEQUENCES AND SERIES. 12.2 Series. In this section, we will learn about: Various types of series. SERIES. Series 1. If we try to add the terms of an infinite sequence we get an expression of the form

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INFINITE SEQUENCES AND SERIES

11. INFINITE SEQUENCES AND SERIES. INFINITE SEQUENCES AND SERIES. 11.2 Series. In this section, we will learn about: Various types of series. SERIES. Series 1. If we try to add the terms of an infinite sequence we get an expression of the form

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Stable Marriage Problem Introductory talk

Stable Marriage Problem Introductory talk. Yosuke KIKUCHI Dept Comp. and Info. Eng. Tsuyama College of Tech OKAYAMA, JAPAN. Contents. Original stable marriage problem Experimental study Scored stable marriage . My lab. member. Stable marriage problem.

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Calculus II (MAT 146) Dr. Day Wednesday April 16, 2014

Calculus II (MAT 146) Dr. Day Wednesday April 16, 2014. Tests for Series Convergence Integral Test (11.3) Comparison Tests (11.4). Polynomial Approximators. Our goal is to generate polynomial functions that can be used to approximate other functions near particular values of x .

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Calculus II (MAT 146) Dr. Day Monday April 14, 2014

Calculus II (MAT 146) Dr. Day Monday April 14, 2014. Infinite Series: Converging or Diverging? (11.2) Tests for Series Convergence Integral Test (11.3) Comparison Tests (11.4). Polynomial Approximators.

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L 15 Brass Instruments

L 15 Brass Instruments. A trumpet can play a) all harmonics b) all harmonics except the fundamental c) all even harmanonics d) all odd harmonics except the fundamental e) none of the above.

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Quicksort

Quicksort. 6.1 Quicksort Quicksort ( A [ p .. r ]) Divide: ? A [ p .. r ] ?? A [ p .. q -1] ? A [ q +1.. r ] A A Conquer: ??? A [ p .. q -1] ? A [ q +1.. r ] ?? Combine: ???????. p. r. x. pivot. A [ p .. q -1]. q. A [ q +1.. r ]. x. Quicksort(A, p, r)

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Analysis of Algorithms CS 477/677

Analysis of Algorithms CS 477/677. Instructor: Monica Nicolescu Lecture 2. Algorithm Analysis. The amount of resources used by the algorithm Space Computational time Running time: The number of primitive operations (steps) executed before termination Order of growth

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9.4

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Sequences and Series

Sequences and Series. Andrew Taylor Alec Seco. Basic Sequences. Sequence : a function whose domain is a set of positive integers Ex. {1,1/2,1/4,1/8,1/16} or ( a n = ( 1/2 ) n-1 ) Either converges or diverges converge : sequence approaches some number L

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Chapter 12

Chapter 12. Section 3: Harmonics. Objectives. Differentiate between the harmonic series of open and closed pipes. Calculate the harmonics of a vibrating string and of open and closed pipes. Relate harmonics and timbre.

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Calculus II (MAT 146) Dr. Day Monday Nov 4, 2013

Calculus II (MAT 146) Dr. Day Monday Nov 4, 2013. Convergent and Divergent Series (11.2) Series Worth Remembering Geometric Series Harmonic Series Telescoping Sums Our First Convergence Test The n th -Term Test aka The Divergence Test Assignments and Announcements.

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11.3

The Integral Test. 11.3. The Comparison Tests. 11.4. 11.5. Alternating Series. 11.6. Ratio and Root Tests. Definition of Convergence for an infinite series:. Let be an infinite series of positive terms. The series converges if and only if the sequence of partial sums,

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Calculus II (MAT 146) Dr. Day Wednesday April 2, 2014

Calculus II (MAT 146) Dr. Day Wednesday April 2, 2014. Sequences and Series: Searching for Patterns (11.1/11.2). Why Study Sequences and Series in Calc II?. Taylor Polynomials applet Re-Expression! Infinite Process Yet Finite Outcome . . . How Can That Be? Transition to Proof.

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Nicole Oresme (1323-1382)

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A Curious Convergent Series

A Curious Convergent Series . Harmonic Series. We Know that the Series . Diverges Proof : If Possible suppose it converges to H , i.e. H = . Then, H. H. This Contradiction Concludes the Proof. Kempner Series: A modification of harmonic Series.

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Recurrence Relations

Recurrence Relations. Useful Facts. Arithmetic series More generally, if a n = a n-1 +c, where c is a constant, then. Useful Facts. Geometric series More generally, if a n = ca n-1 ,where c?1 is a constant, then If 0< c< 1, then the sum of the infinite geometric series is. Useful Facts.

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Summation

Summation. Summation notation. Gauss summation trick. Geometric series. Harmonic series. ( r < 1). Summation notation. a k. k 0 + 1. k 0 - 1. k 0. k f - 1. k f. k f + 1. k. Summation notation. a k. k 0 + 1. k 0 - 1. k 0. k f - 1. k f. k f + 1. k. Summation notation.

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Harmonics

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