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 8.5, Problem 18P

Recall from Chapter 3, equation (8.5), that a set of functions is linearly independent if their Wronskian is not identically zero. Calculate the Wronskian of each of the following sets to show that in each case they are linearly independent. For each set, write the differential equation of which they are solutions. Also note that each set of functions is a set of basis functions for a linear vector space (see Chapter 3, Section 14, Example 2 ) and that the general solution of the differential equation gives all vectors of the vector space.

e a x , x e a x , x 2 e a x

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Chapter 8.5, Problem 17P

Chapter 8.5, Problem 19P

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Chapter 8 Solutions

Mathematical Methods in the Physical Sciences

Ch. 8.1 - Verify the statement of Example 2. Also verify...Ch. 8.1 - Solve Example 4 using the general solution...Ch. 8.1 - Verify that y=sinx,y=cosx,y=eix, and y=eix are all...Ch. 8.1 - Find the distance which an object moves in time t...Ch. 8.1 - Find the position x of a particle at time t if its...Ch. 8.1 - A substance evaporates at a rate proportional to...Ch. 8.1 - The momentum p of an electron at speed v near the...Ch. 8.2 - For each of the following differential equations,...Ch. 8.2 - For each of the following differential equations,...Ch. 8.2 - For each of the following differential equations,...

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