Analysis Definition and 999 Threads

What book do MHB members regard as the best for a rigorous but clear and (moderately) easily understood introduction to complex analysis? (Note - would be good if the book had hints to solutions of exercise.) Peter

https://www.engr.colostate.edu/~allan/thermo/page8/page8.html The link above takes you to a site I have found to be very helpful in my studies of the Otto cycle, but on this particular page, it depicts an equation for the rate of change of cylinder Pressure vs. crank angle, and in this...

In our study, we measured the seasonal abundance of selected genes from two sites. We want to make a comparison between the seasonal trends between the genes (i.e. which genes had similar trends and which didn't). What would be the best statistical analysis for this purpose? Thanks!

I found an interesting thing when trying to derive the spherical harmonics of QM by doing what I describe below. I would like to know whether this can be considered a valid derivation or it was just a coincidence getting the correct result at the end. Starting making a Fundamental Assumption...

What can spectra tell us? They can tell us the speed of the object, its temperature, size and some more, but how can we do this at home with a glass prism? Do you know?

Hi, May someone helps me regarding this!? i have a controller which will control AC motor as attached. in this controller, a stage comes where I need to use a Derivative Block before point 'B' as shown in the attached picture " controller block diagram" [...

Hi, all. I would like to read books about the topics - Geometry, Real Analysis and Electricity and Magnetism. And I find the followings. Are they decent and rigorous? Geometry The Real Numbers and Real Analysis Introduction to Electrodynamics Classical Electricity and Magnetism Electricity...

Nearly every analysis reference I come across defines the derivative for functions on an open interval ##f:(a, b) \rightarrow \mathbb{R}##. I understand that, in constructing the definition of ##f## being differentiable on a point ##c##, we of course want it to first be a point it's domain, so...

Hello, I have got results for a modal analysis (mesh of 150 shell elements) in ascii format. I have also got (from another process) forces to apply at each element; how do it compute the deflection? I get that it's a form of summation of all the modes, but I am stuck. Thanks! BB

Hello everyone.. Here is the thing I am working on a project where I am manufacturing Furfural from bagasse. The reaction is thermodynamically possible. I took some amount of bagasse and added it to a reactor at atmospheric pressure. I then added diluted Sulphuric acid which acts as catalyst...

It seems that most recently published analysis textbooks are written from a more abstract perspective, e.g., dealing with functions on general metric spaces or with spaces of functions. However, often solving a problem requires some "get your hands dirty" classical or "hard" analysis -- for...

Hi All, I am doing some FA on SPSS. I entered 9 columns from an Excel file into SPSS. I am just not sure of how the order of the initial columns corresponds to the order of the components that have been extracted; specifically, in the "total Variance Explained" section of the outputs. Would...

Hi, I'm trying to figure out the forces Fx in the drawing I have uploaded. If I have a vertical force Fy acting on the bracket I have drawn. I know from experience that this force is going to pull my bracket horizontally but I can't figure out how I work out a horizontal force from a vertical...

This is the problem I'm currently working on: The pi groups I identified were h1, h2, d, D, g, t, and velocity, but when I looked at the solution, it selected Δh, D, t, ρ, d, ϒ, h1, with no explanation why those variables are needed. If I was solving with the Bernoulli equation, I wouldn't...

1. The problem statement: Let ##f:[a, b] \rightarrow \mathbb{R}##. Prove that if ##f## is continuous, then ##f## is bounded. 2. Relevant Information This is the previous exercise. I have already proved this result, and the book states to use it to prove the next exercise. It also hints to use...

Hi All, I am trying to wrap my brain around Latent Class Analysis (LCA). In the mean time, does anyone know how to test for goodness of fit and whether a given number of classes is somehow optimal? AFAIK, Log-Likelihood should decrease as a measure of improved fit when adding latent classes...

Hi. Can someone point me to a good (and really basic) PDF file or text regarding Finite Element analysis? I would prefer it having an example where it would solve the 1D heat equation or the Laplace equation so I can extend what I know from finite difference methods to it. Sorry if this seems...

I'm looking for a good Complex book, but the options seem slim. I was thinking about Rudin's Real and Complex. My only reservation is that it is not structured like any other book I've seen. I've had advanced analysis and measure and integration theory, so rigour is not a concern. I saw Alfohr's...

Hi, In next semester, I am going to take vector calculus. Here is the course description: Vector fields, line and surface integrals, Green's Theorem, Stokes' Theorem, Divergence Theorem and advanced topics such as differential forms or applications to mechanics, fluid mechanics, or...

Assume student has taken around 8 upper division math courses including abstract algebra 1 and abstract algebra 2.

Hi All, I need to do some work on Factor Analysis on Non-Continuous variables. I have searched the web, but found nothing of much substance. I would appreciate references on helpful sources on it. Thanks.

Hello, I've a following question: Is necessary know well func. analysis, and all its theorems to handle well quantum physics...?

I am studying the modal analysis of a mechanism and I am only interested in the transverse modes, I wonder if there is a way to formulate my problem so that the results show only the transverse modes without the torsional and longitudinal ones, this would help in the post-processing a lot.

I am stuck on the questions, 5.3.10 and 5.3.11 which are part of a chapter on dimensional analysis in fluid mechanics by Streeter. Question 5.3.10 (see also the attachment): It asks me for the given fluid dynamic problems, where is the inertial force not important. It lists several fluid...

Hello all. I'm a mathematics undergrad student who finished his first university year succesfully. I got courses of calculus, but these weren't very rigorous. I did learn about stuff like epsilon and delta proofs but we never made exercises on those things. The theory I saw contained proofs but...

Homework Statement Question: For ##\Lambda^3+\Lambda^2+A=0## , show that for ##A<0## there is some real positive ##\Lambda## which solves this Homework EquationsThe Attempt at a Solution [/B] Attempt: Write ##-A=\hat{A} ##, then ##\hat{A} \in (0,\infty)## and...

Homework Statement The internal and external diameter of a hollow cylinder are measured with the help of a vernier calipers. Their values are (3.87 ± 0.01) cm and (4.23 ± 0.01) cm respectively. The thickness of the wall of the cylinder is ?Homework Equations Thickness of cylinder wall= 1/2...

I am doing FE analysis for symmetric shape in boundary conditions and geometry, I would like to know if I can use symmetry in my analysis or not. I have tried to run trials, the results are very similar but I am not sure if this just a coincident

Hey everyone! (new to the forum) I am currently trying to self study more advanced mathematics. I have taken up to multivariable calculus and have taken a class for an introduction to mathematical proofs/logic (sets, relations, functions, cardinality). I want to get a head start on the...

https://www.amazon.com/dp/1305253663/?tag=pfamazon01-20 Are all these called root finding algorithms? All of it ? <Moderator note: Link changed because of undetermined copyright situation. fresh_42>

Homework Statement Homework EquationsThe Attempt at a Solution For ##0 \ge \theta \ge \pi/2## Forces on the ring, ##Mg + 2N\cos \theta = F\qquad 1## Forces on the beads ##mv^2/R = - N + mg \cos \theta## By conservation of energy when the bead has fallen through some angle ##\theta##...

hey So Fourrier transform is ##f(t) = \frac{1}{2 \pi} \int_{-\infty}^{\infty} F(\omega) e^{i \omega t} d\omega## with ##F(\omega) = \int_{-\infty}^{\infty} f(t) e^{-i \omega t} dt## Question 1 - The Fourier mode for the continuous case is ## \frac{1}{2 \pi} F(\omega) e^{i \omega t}##, is...

I am considering taking it down the line.

I don't understand the motion of an accelerating wedge and a block. I'd really appreciate if you make me understand the motion in both an inertial and a non inertial reference frame. Here's a figure I have made, a0 is the acceleration on the wedge with respect to an inertial frame, towards right.

Dear guys can somebody explain, what is actually the following terms, used in fatigue analysis: 1. Mean stress correction factor 2. Plate thickness correction factor 3. Redundancy factor Thanks guys. you are the best...

A refrigerator operates on a Carnot cycle. In this cycles, it absorbs 120 J of energy at a temperature Tc while 300 J of work is done on the gas undergoing the cycle. How much energy is exhausted as heat during this process? The answer is 420 J. I am unsure of where to start for this...

Hello! Can someone explain to me, in real analysis, what is the difference in expanding a function as a Taylor series around 2 different point. So we have ##f(x)=\sum c_k (z-z_1)^k = \sum d_k (z-z_2)^k## and as ##k \to \infty## the series equals f in both cases, but why would one choose a point...

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown > Hi, I couldn't figure out from the equation that relate the current source IS to IA and IB. If both IA and IB is coming from the same direction and the positive terminal has been predicted...

This is more of a concept question; if I choose different repeating parameters to someone else, say my lecturer, and got different pi groups to him/her, however my groups are still dimensionless (i.e. the units for each pi group cancel to 1), is my answer still correct?

A cool video on ad hominim attacks: https://www.wired.com/video/2017/06/how-to-battle-trolling-ad-hominem-attacks-online/

I know that mie theory is used to analyze the absorption/scattering/extinction of a homogeneous sphere within a homogeneous dielectric medium. However, if I wanted to perform the same analysis on a sphere enclosed by two different media, is there an analytic solution to this?

Hi, I want a book about power system analysis that I can have laying around and read from time to time. I have taken a course in power system analysis some time ago, where I was taught simple fault analysis including unbalanced faults, frequency and voltage control. So to maintain this...

I have to do a teaching assistant job on a multivariable calculus class, I have to survey books that can be useful as resources. Has anyone used this book by Bourne and Kendall? I noticed that the treatment of vector analysis seems good and the chapter on Cartesian tensors seem to be a good...

I analyzed uncertainty analysis of 2 port measurement. I referenced 2 book "Transmission Reflection and Short Circuit Line Methods for Measuring Permittivity and Permeability" at pages 31 equation(2.83) "Transmission and Reflection and SCL Permittivity Measurements" at pages 44 equation(2.67)...

Hello! I see that all theorems in complex analysis are talking about a function in a region of the complex plane. A region is defined as an open, connected set. If I am not wrong, the real line, based on this definition, is a region. I am a bit confused why there are so many properties of the...

Hello! I have this Proposition: "A harmonic function is infinitely differentiable". The book gives a proof that uses this theorem: "Suppose u is harmonic on a simply-connected region G. Then there exists a harmonic function v in G such that ##f = u + iv## is holomorphic in G. ". In the proof...

Can anyone help in the solution of this problem? how can i determine the zero x*??

Homework Statement There is a paper in 1973: T. Kushida, "Energy Transfer and Cooperative Optical Transitions in Rare-Earth Doped Inorganic Materials I. Transition Probability Calculation", J. Phys. Soc. Jpn. 1973, 34, 1318-1326. DOI: http://dx.doi.org/10.1143/JPSJ.34.1318 that explains the...

Homework Statement Suppose f is entire and there exist constants a and b such that ##|f(z)| \le a|z|+b## for all ##z \in C##. Prove that f is a polynomial of degree at most 1. Homework EquationsThe Attempt at a Solution We have that for any ##z \neq 0##, ##\frac{|f(z)|}{a|z|} \le b##. So if we...

I'm reading a book on vortex methods and I came across the above mentioned terms, however, I don't understand what they mean in mathematical terms. The book seems to be quite valuable with its content and therefore I would like to understand what the author is trying to say using the above...