Mathematical Methods in the Physical Sciences

3rd Edition

ISBN: 9780471198260

Author: Mary L. Boas

Publisher: Wiley, John & Sons, Incorporated

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Textbook Question

Chapter 11.13, Problem 14MP

Identify each of the following integrals or expressions as one of the functions of this chapter. Check your work by evaluating both your answer and the original problem by computer. Be sure you understand your computer program’s notation.

∫ 1 ∞ e − x 2 / 2 d x

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Chapter 11.13, Problem 13MP

Chapter 11.13, Problem 15MP

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Question 1 i Let G be the graph given by the following drawing. g a d b (a) Draw the induced subgraph of G on vertex set {a, d, e, f, g, h}. [4] (b) Draw a subgraph of G that is isomorphic to the graph H with V (H) = {r, s, t, u, v, w, x, y, z} and E(H) = {rs, rt, ru, st, sv, tw, ux, vy, wz}. (c) Draw a spanning tree of G whose set of leaves is {a, b, g, j}, or explain why such a spanning tree does not exist. [4] [4] Call a cycle of a graph H a Hamiltonian cycle of H if it contains every vertex of H. (d) Give a Hamiltonian cycle of G, or explain why such a cycle does not exist. Let G be an arbitrary simple graph, n = = |V(G)|, and m = |E(G)|. [4] (e) Assume that the complement of G is connected. Show that m ≤ ½n² − ³n +1. [8]

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Chapter 11 Solutions

Mathematical Methods in the Physical Sciences

Ch. 11.3 - The integral in ( 3.1) is improper because of the...Ch. 11.3 - Use the recursion relation (3.4), and if needed,...Ch. 11.3 - Use the recursion relation (3.4), and if needed,...Ch. 11.3 - Use the recursion relation (3.4), and if needed,...Ch. 11.3 - Use the recursion relation (3.4), and if needed,...Ch. 11.3 - Use the recursion relation (3.4), and if needed,...Ch. 11.3 - Use the recursion relation (3.4), and if needed,...Ch. 11.3 - Express each of the following integrals as a ...Ch. 11.3 - Express each of the following integrals as a T...Ch. 11.3 - Express each of the following integrals as a ...

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