100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Solutions for A Short Introduction to Mathematical Concepts in Physics, 1st Edition Napolitano (All Chapters included) $29.49   Add to cart

Exam (elaborations)

Solutions for A Short Introduction to Mathematical Concepts in Physics, 1st Edition Napolitano (All Chapters included)

 20 views  1 purchase
  • Course
  • Math
  • Institution
  • Math

Complete Solutions Manual for A Short Introduction to Mathematical Concepts in Physics, 1st Edition by Jim Napolitano ; ISBN13: 9781032404301. (Full Chapters included Chapter 1 to 9).... 1. Basic Concepts 2. Infinite Series 3. Ordinary Differential Equations 4. Vector Calculus and Partial Diffe...

[Show more]

Preview 3 out of 77  pages

  • February 24, 2024
  • 77
  • 2023/2024
  • Exam (elaborations)
  • Questions & answers
  • Math
  • Math
avatar-seller
mizhouubcca
Solutions to Exercises in
A Short Introduction to
Mathematical Concepts in Physics


Jim Napolitano

November 1, 2023



Complete Chapter Solutions Manual
are included (Ch 1 to 9)




** Immediate Download
** Swift Response
** All Chapters included

,Contents

1 Solutions 5

2 Solutions 13

3 Solutions 19

4 Solutions 37

5 Solutions 47

6 Solutions 53

7 Solutions 67

8 Solutions 73

9 Solutions 79

, Chapter 1

Solutions

(1) The answers are all straightforward:
z12 = (1 + i)2 = 1 + 2i − 1 = 2i
z1∗ = 1 − i
z1 z2∗ = (1 + i)(3 + 4i) = 3 + 3i + 4i − 4 = −1 + 7i
√ √ √
|z1 | = 1 + 1 = 2 and |z2 | = 9 + 16 = 5
√ √
|z1 z2 | = |(1 + i)(3 − 4i)| = |3 + 3i − 4i + 4| = |7 − i| = 49 + 1 = 5 2
= |z1 ||z2 |

(2) [P V ] = [Force]L−2 L3 = M LT −2 ]L−2 L3 = M L2 T −2 = [Energy]. From the ideal gas law,
since N is dimensionless, kT must have the dimensions of energy. The SI unit of energy is
Joule, so the units of k are Joule/K.
(3) First find [k] = [Force]/[Distance] = M LT −2 L−1 = M T −2 . (a) Write ϵ = mx k y Az ,
so
M L2 T −2 = M x M y T −2y Lz = M x+y T −2y Lz
and y = 1, z = 2, and x = 0. That is, the energy scale is ϵ = kA2 . You’ll recall that
the potential energy of a harmonic oscillator with amplitude A is kA2 /2 so the scale is the
correct energy to within a factor of two. (b) Write ϵ = mx k y ℏz , so
M L2 T −2 = M x M y T −2y L2z M z T −z = M x+y+z T −2y−z L2z
and z = 1, 2y + z = 2y + 1 = 2 so y = 1/2, and x + y + z = x + 3/2 = 1 so x = −1/2.
Therefore ϵ = ℏ(k/m)1/2 . In quantum mechanics you will learn that the energy spacing in
the harmonic oscillator is indeed ℏω where ω = (k/m)1/2 .
(4) The calculation is straightforward:
τ = mx ℓy g z

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller mizhouubcca. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $29.49. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

78998 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
$29.49  1x  sold
  • (0)
  Add to cart