Boas Definition and 38 Threads

I can use the convolution integrals and get the idea of this concept for t<a. But, I can't get the answer for t>a. MY idea is substitute ##f(t) = 0## to the ODE, then I have second order linear differential equations with right hand is zero. So, the solution is $$y=Ae^{i\omega t} + Be^{-i\omega...

With the new variable, I got: $$p^2 (p'_y)^{2}=k^2(1+p^2)$$ where ##p'_y## is ##\frac{dp}{dy}##. I modified the equation so the variable p and dp can be separated from dy. Here what I got: $$\frac{p}{\sqrt{p^2+1}} dp=k dy$$ I substitute ##p^2+1=u## so I got $$\sqrt{u}=ky+c_1$$ Back substitution...

$$p=\gamma m v$$ $$F = \frac {md (\gamma v}{dt}$$ $$\int{F dt} = \int{md (\gamma v}$$ $$F t= \gamma mv$$ At this step, I don't know how to make v as explicit function of t, since gamma is a function of v too. Thankss

First, I tempted to use this kind of chain rule: $$(\frac {\partial u}{\partial x})_z = (\frac {\partial u}{\partial x})_y (\frac {\partial x}{\partial x})_z + (\frac {\partial u}{\partial y})_x (\frac {\partial y}{\partial x})_zz$$ Then, I think that ##(\frac {\partial x}{\partial x})_z = 1## i...

First I assume that $$(1+n^2)^\frac{1}{\ln n}=\exp {\ln (1+n^2)^\frac{1}{\ln n}} $$But, $${\ln (1+n^2)^\frac{1}{\ln n}}={\frac{\ln (1+n^2)}{\ln n}}$$ By L'Hopital Rule, I got $$\lim_{n\to\infty} {\frac{\ln (1+n^2)}{\ln n}}=\frac{\lim_{n\to\infty} (\frac{2n}{1+n^2})}{\lim_{n\to\infty} 1/n}$$...

So using $$L=\frac{mv^2}{2} - \frac{1}{2} m lnx$$ and throwing it into the Euler-L equation I agree with kcrick & OlderDan that we can manipulate this to either $$\frac{d}{dt} m\dot{x} = -\frac{m}{2x}$$ or $$2vdv = -\frac{dx}{x}$$ but I'm not having any epiphanies on how to turn the above into...

Homework Statement The question is : "In a water purification process, one-nth of the impurity is removed in the first stage. In each succeeding stage, the amount of impurity removed is one-nth of that removed in the preceding stage. Show that if n = 2, the water can be made as pure as you...

Homework Statement Show that u(x, y) = y/π ∫-∞∞ f(t) dt / ((x - t)2+y2) satisfies uxx + uyy = 0. Homework Equations Leibniz' Rule The Attempt at a Solution I'm not even sure Leibniz' Rule can be applied here since there seems to be a discontinuity in the integrand when x=t and y=0. When I...

Homework Statement Test the series for convergence or divergence ##1/2^2-1/3^2+1/2^3-1/3^3+1/2^4-1/3^4+...## Homework Equations rn=abs(an+1/an) The Attempt at a Solution With some effort I was able to figure out the 'n' th tern of the series an = \begin{cases} 2^{-(0.5n+1.5)} & \text{if } n...

Homework Statement Homework EquationsThe Attempt at a Solution [/B] The % of course passing students who fail the prelim test is 38%. So, the required probability is 38 %. Isn't the probability of a student failing the prelim when he his passing the course is known already = probability...

Homework Statement If ## z=x^2+2y^2 ##, find the following partial derivative: \Big(\frac{∂z}{∂\theta}\Big)_x Homework Equations ## x=r cos(\theta), ~y=r sin(\theta),~r^2=x^2+y^2,~\theta=tan^{-1}\frac{y}{x} ## The Attempt at a Solution I've been using Boas for self-study and been working on...

In Mary L. Boas' Mathematical Methods in the Physical Science, 3rd ed, on page 17 it goes over absolute convergence, and defines the test for alternating series as follows: An alternating series converges if the absolute value of the terms decreases steadily to zero, that is, if |an+1| ≤ |an|...

From Mary Boas' "Mathematical Methods in the Physical Sciences" Third Edition. I'm not taking this class but I was going through the textbook and ran into an issue. The problem states: If you invest a dollar at "6% interest compounded monthly," it amounts to (1.005)n dollars after n months. If...

Is there any alternative books that teach you how to just do the problems rather than emphasizing why, and is there any books that emphasize why in an easier format? Something like a "mathematical methods for dummies" book? This is the book I'm referring to (...

I am home studying the basics of quantum physics, starting with Mary Boas' "Mathematical Methods in the Physical Sciences". When I take a look at some of the topics of this forum, there might be better books to start with. Now I am not so sure anymore if this book of Boas is a good book to start...

I started with Mary Boas' book "Mathematical Methods in the Physical Sciences". Now it is stressed in the introduction to make homework and do the problems. However, I would very much like to know if I got the answers right, and I even prefer if the problems are worked-out. So I guess my...

I'm on final of the chapter 7 yet, but i want to know when i finish this book, which book i should get to continue to learn the math necessary to more advance topics(GR, Condensed Matter, EM Theory(Jackson level), Analytic Mechanics and others..)? and if exists a book like Boas i would be so...

It's awful, the reading of this first chapter is extremely boring, he appears only to cover divergence and convergence of series, should i skip this chapter?

Hello! I'm looking to study Mary Boas' Book on mathematical methods and i'd like to know if the prerequisites can be covered in ocw mit courses or any other open courses. Please do suggest if any. Also are there any parallels that can be drawn with the ocw mit courses for the various topics...

I study in high school, but I know a fair amount of math (differential, integral, and vector calc., differential equations, linear algebra, etc.) Would you recommend this book if I want to pursue higher levels of math such as PDE's and Tensors and so on? Does this book explain things clearly...

On page 671 Mary Boas has her Theorem III for that chapter. Roughly it tells us that if f(z) -a complex function- is analytic in a region, inside that region f(z) has derivatives of all orders. We can also expand this function in a taylor series. I get the part about a Taylor series, that's...

I am looking to replace the book I am using in a mathematical methods in physics course I am teaching. We currently use a more mathematical book in Swedish and it is missing some content which we would like to include. I had my eyes on the mathematical methods book by Mary Boas but it is kind of...

I'm currently a rising sophomore (undergrad), and I'm trying to fill in some gaps in my applied math background this summer. So far, I've taken linear algebra and multi/intro analysis, but they were both theory-only and had very few applications (ex: I finished LA without knowing the various...

Mclaurin Series with Division by Zero? Boas: Mathematical Methods for Phys Sci Pr.1.13.25 Homework Statement Using the methods of this section: (a) Find the first few terms of the Maclaurin series for each of the following functions. (b) Find the general term and write the series in...

Homework Statement Using the methods of this section: (a) Find the first few terms of the Maclaurin series for each of the following functions. (b) Find the general term and write the series in summation form. (c) Check your results in (a) by computer. (d) Use a computer to plot the...

Homework Statement 4. Write the Maclaurin series for 1/√(1 + x) in ∑ form using the binomial coefficient notation. Then find a formula for the binomial coefficients in terms of n as we did in Example 2 above.Homework Equations { \left( 1+x \right) }^{ P }=\sum _{ n=0 }^{ \infty }{ \left(...

Which textbook explain concepts with more intuition and in comprehensive manner for engineering students? Advance engineering mathematics by Erwin kreysizg Or Mathematical methods in physical science by Mary l. Boas.

Author: Mary L. Boas Title: Mathematical Methods in the Physical Sciences Amazon Link: https://www.amazon.com/dp/0471198269/?tag=pfamazon01-20 Prerequisities: Calculus Table of Contents: Infinite Series, Power Series The Geometric Series Definitions and notation Applications of...

Hello PF, I'm going to be heading to my 3rd year as a Physics major and I want to make this last month of summer a tad productive. So my plan was to review/self study math using the mathematical methods book by Boas (and maybe some online resources to get more depth on some particular...

I'm an electrical engineer student, with a big passion for physics. I've started working on Mary L Boas' Mathematical Methods in the Physical Sciences, and I'll have finished the book by the end of the summer (I'm in a coop program so I have a lot of free time in the summer to work on personal...

Sorry if this is the wrong section, it wouldn't let me post in the Science Learning Material area. Basically I started self-studying Mary L Boas book Mathematical Methods in the Physical Sciences. I've seen a lot of great things about the book and I know it's very popular in Mathematical...

In Boas' book I can read that the definition of center of mass of a body has coordinates x_{CM}= \int x_{CM}dM= \int x dM. Shouldn't it be this same integral but divided by M?! Also, I didn't find the definition of center of mass for particles or any non continuous bodies. I'd be grateful if...

I am having trouble evaluating the Legendre Polynomials (LPs). I can do it by Rodrigues' formula but I am trying to understand how they come about. Basically I have been reading Mary L. Boas' Mathematical Methods in the Physical Sciences, 3E. Ch.12 §2 Legendre Polynomials pg566. In the...

I find that Chapter 3(Linear Algebra) in Boas is not very clear in certain areas. Could someone please recommend a book which does so more clearly?

I'm going to pick up a math methods book to beef up my more physicsy math, as it were, since the math program at my school is less geared to physics and engineering and more towards education, business, and computer science (and the physics program itself is falling apart). All the rage seems...

will the solutions manual for the second edition to Boas Mathematical Methods for the Physical Sciences suffice if I'm using the third edition? If not, where can I get the solutions to the problems?

Preface to the First Paperback Edition of The Culture of Critique: An Evolutionary Analysis of Jewish Involvement in Twentieth-Century Intellectual and Political Movements Originally published in 1998 by Praeger Publishers, Westport, CT © 2001 Kevin MacDonald Department of...