What is Analytical: Definition and 278 Discussions

Analytical chemistry studies and uses instruments and methods used to separate, identify, and quantify matter. In practice, separation, identification or quantification may constitute the entire analysis or be combined with another method. Separation isolates analytes. Qualitative analysis identifies analytes, while quantitative analysis determines the numerical amount or concentration.
Analytical chemistry consists of classical, wet chemical methods and modern, instrumental methods. Classical qualitative methods use separations such as precipitation, extraction, and distillation. Identification may be based on differences in color, odor, melting point, boiling point, solubility, radioactivity or reactivity. Classical quantitative analysis uses mass or volume changes to quantify amount. Instrumental methods may be used to separate samples using chromatography, electrophoresis or field flow fractionation. Then qualitative and quantitative analysis can be performed, often with the same instrument and may use light interaction, heat interaction, electric fields or magnetic fields. Often the same instrument can separate, identify and quantify an analyte.
Analytical chemistry is also focused on improvements in experimental design, chemometrics, and the creation of new measurement tools. Analytical chemistry has broad applications to medicine, science and engineering.

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  1. T

    Basic electrostatics problem; analytical solution?

    Homework Statement For the system given, both objects have the same charge and same mass (both given). I'm also given string length, L. I need to solve for θ. Homework Equations Coulomb's Law, W=mg The Attempt at a Solution Using simple equilibrium force analysis (with weight, tension, and...
  2. at94official

    Analytical Geometry (Division of line segments)

    1. Here is the Problem: A line passes through A(2,3) and B(5,7). Find: (a) the coordinates of the point P on AB extended through B to P so that P is twice as far from A as from B; (b) the coordinates if P is on AB extended through A so that P is twice as far from B as from A. Homework...
  3. C

    I Convergence of Taylor series in a point implies analyticity

    Suppose that the Taylor series of a function ##f: (a,b) \subset \mathbb{R} \to \mathbb{R}## (with ##f \in C^{\infty}##), centered in a point ##x_0 \in (a,b)## converges to ##f(x)## ##\forall x \in (x_0-r, x_0+r)## with ##r >0##. That is $$f(x)=\sum_{n \geq 0} \frac{f^{(n)}(x_0)}{n!} (x-x_0)^n...
  4. P

    What is the scope of analytical research in astrophysics?

    Nowadays much of the community of astronomy and astrophysics is focused on simulations and data analysis. Thus people, who do not have access to grids and data, must resort to analytical analysis. What are the challenging areas of astronomy and astrophysics that rely on analytical workout rather...
  5. TheCapacitor

    Classical Best analytical mechanics textbook recommandation

    Hello, I'm a second year physics student. We are going to use "hand and finch analytical mechanics", however the reviews I saw about this book are bad. I've already taken calculus for mathematicians, linear algebra, classical mechanics, special relativity, and electromagnetism. The topics it...
  6. V

    Analytical solution of photon diffusion in finite media

    Homework Statement I'm trying to derive an analytical expression for the photon backscatter flux in finite turbid media using the diffusion equation and the method of images. What I want to write is: for a given volume (x,y,z), where a coherent light source is incident on the x-y plane and z is...
  7. S

    I Analytical solution to b=a*x^-theta - x?

    I wonder if there is an analytical solution to: b=a*x-θ - x with a>0, b>0, x>0, θ>1
  8. D

    A Is there an analytical solution to the following problem?

    Differential equation \begin{align} \frac{{\partial}^2 T (x,t)}{\partial x^2} = \frac{1}{\alpha}\frac{\partial T(x,t)}{\partial t}, \end{align} boundary conditions \begin{equation} \begin{aligned} T(x, 0) = T_\infty \\ -k\frac{\partial T(0,t)}{\partial x}= h(T_{max} - T(0,t)) \\...
  9. Doney Felipe MEjia

    Can someone help me with an analytical dynamics exercise?

    At a certain instant, the velocity and acceleration of a particle ar defined by v= 3i + 4j - 6k m/s and a=-2i + 3k m/s2. Find the radius of curvature and change of speed of the particle at the instant.
  10. Kelly Green

    Bragg's Law (X-Ray Analytical Methods)

    Homework Statement Explain using word, diagrams, and/or calculations.. (1) Why must n always be <= 2d/λ? (2) If λ is significantly greater then d, why will no diffraction occur? Homework Equations Bragg's Law nλ=2dsinθ n has its maximum when sinθ is 1 (at 90°) The Attempt at a Solution I am...
  11. P

    FRM Fission Barrier Analytical Sketch

    I'm trying to work out an analytical approach to plotting fission barriers of heavy atoms as a function of angular momentum. I've visited some articles but I have found no way of calculating it. Has anyone any ideas?
  12. M

    Analytical Expressions for Frequency Response

    Hi, I am struggling to understand the maths in the text shown below. (1) How does: r(t) = Acos(wt)+Bsin(wt) become; sqrt((A^2)+(B^2))cos(wt - arctan(B/A))? (2) He states that we can represent the input as a phasor and in one of three ways but doesn't say which one. (3) He then focus on the...
  13. M

    A Laplace equation on a trapezoid

    Hello everybody! I know how to solve Laplace equation on a square or a rectangle. Is there any easy way to find an analytical solution of Laplace equation on a trapezoid (see picture). Thank you.
  14. H

    Analytical Exp[((-i Phi)/2)*h3]

    the closed analytical solution of exp [((- i phi)/2) * h3] someone could help!
  15. amjad-sh

    Prerequisites needed to grasp analytical mechanics.

    1.What are the mathematical prerequisites needed to grasp analytical mechanics conceptually and technically? 2.To understand the very concept of analytical mechanics, do I need to train my self in Euclidean and Riemannian manifolds, and do I need to have good knowledge in topology and...
  16. Z

    Preparing a Solution using ppm and ppb -

    I would like to prepare 50.0 g of 50 ppb Pb standard solution in 1% HNO3 gravimetrically, in a 50.0mL plastic tube from a stock solution of 50 ppm Pb. From what I understand, this is a dilution...so C1V1 = C2V2 I like working in mg/L more than ppb and ppm so I converted 50 ppb = 0.05 mg/L 50...
  17. Lagraaaange

    General GRE Tomorrow: Skip Analytical Writing sections?

    What's your take on preserving stamina/maximum mental capacity for quant and skipping the essays? I hear physics grad programs don't care at all, some don't even take the scores. Thoughts?
  18. D

    Analytical solution to mx"(t)+b(x'(t))x'(t)+k(p)x(t)=0

    Hello guys! I have following differential equation mx"(t)+b(x'(t))x'(t)+k(p)x(t)=0. As can be seen, "attenuation term" is dependent of velocity x'(t). Also stiffness term k(p) is dependent of term p, which is p=k(p)x(t)/A. In this equation A is constant and k(p) means, of course, same term as...
  19. Gvido_Anselmi

    Analytical methods in theoretical physics

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  20. davidbenari

    Classical Studying Analytical Mechanics this July

    So I'm taking analytical mechanics next semester. The textbook they use is Thornton and Marion's "Classical Dynamics of Particles and Systems". I want to learn it all this month. It is feasible, but extenuating. But there is another option. I could read Robert Fitzpatrick's Newtonian Dynamics...
  21. Frimus

    Classical Analytical Mechanics by Johns

    Is there someone in PF community who knows "Analytical Mechanics for Relativity and Quantum Mechanics" by Johns? What is your opinion on the book?
  22. M

    Analytical continuation by contour rotation

    Hi All, reading a paper by Langer (Theory of the Condensation Point, Annals of Physics 41, 108-157, 1967), I came across an analytical continuation technique which I do not understand (would like to upload the paper PDF but I am not so sure this is allowed). Essentially, he deals with the...
  23. M

    Analytical continuation free energy

    Hi All, reading a paper by Langer (Theory of the Condensation Point, Annals of Physics 41, 108-157, 1967), I came across an analytical continuation technique which I do not understand (would like to upload the paper PDF but I am not so sure this is allowed). Essentially, he deals with the...
  24. davidbenari

    Classical Should I read Thornton's or Lanczos' for Analytical Mech?

    Next semester I begin studying analytical mechanics. The book they use in class is Thornton and Marion "Classical Dynamics of Particles and Systems". I wanted to read something about this during the summer, and stumbled upon Lanczos' book " The Variational Principles of Mechanics". Lanczos'...
  25. SpanishOmelette

    Analytical Geometry: Definition & Basics | Mahmoud

    Maybe a little bit of a fresh mathematical virgin thing to ask, but what exactly is the definition of analytical geometry? I am asking for the reason I have recently acquired a book on the subject, but I found it by accident, and I would like to comprehend the most basic concepts of it! I am...
  26. J

    Mathematical modelling of Electric-Thermal-Structuralphysics

    Hi i am working on a research paper for which i need very good citation for the analytic analysis coupling Electric - Thermal-Structural physics(via Joule Thomson effect & Thermal stress/strain). Please provide any good source of mathematical relations describing the above complete or in part...
  27. A

    Analytical Problem with Coulomb's Law

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  28. andro

    Analytical formulation of Newton's Laws

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  29. Eclair_de_XII

    How are precalculus and analytical geometry different?

    I'm really stressed out at where I should be in my college career. In high school, I had taken trigonometry and analytical geometry. But when I went to college and took calculus, I was completely dumbfounded on what was being taught. I felt like I should have known the material. Google tells me...
  30. A

    How can I find the analytical solution for the system?

    Homework Statement dx(t)/dt = N0*sin(omega*t) * x(t) - ( N0*x^2 / k ) Omega,N0 and k are positive . Homework EquationsThe Attempt at a Solution I tried to solve it using the Bernoulli equations but I could not get the last result.
  31. matt_crouch

    Solve Integral Analytically: Int[(1+x^2)^-n e^-x^2]dx

    can someone suggest a method to solve an integral of the form analytically? ##\int \left[\frac{1}{(1+x^{2})}\right]^{-n}e^{-x^{2}}dx##
  32. S

    Analytical solution for bending stiffness of tapered tube

    How to derive the formula to find the bending stiffness of an isotropic tapered tube which is cantilevered with a point load applied at the free end?
  33. C

    Can you prove a differential equation has no analytical solution?

    Can you prove a differential equation has no analytical solution? Teach me ,please! Thank you a lot!
  34. M

    Analytical Mechanics and Waves

    Hello everyone. I'm taking two physics courses this semester. Analytical Mechanics and Waves. I was hoping if you guys could help me out a little and recommend some good books for both courses. Also, if you know good lectures that were recorded and I have access too (YouTube for example) I...
  35. M

    GRE Analytical Writing: Score Req. for Science/Math/Eng. Progs?

    What is a reasonable analytical writing GRE score for a science/math/engineering programs? I had something like a 4.5/6.0 which seems kind of mediocre. I talked to some professors about why the general GRE is required, but they said that it was mainly aimed towards testing international...
  36. B

    Analytical solution for bound state energies of infinite well

    Hi there I am trying to find bound state energies assuming infinite potential. I have been told it can be done by analytically solving Right Hand Side and Left Hand Side of an equation such as: E^1/2 tan(2ma^2E/4hbar)^1/2 = (V0-E)^1/2 If solved properly, it should give one curve (RHS), crossed...
  37. W

    Analytical solution of Discrete-time Algebraic Riccati Equation

    Homework Statement Solve for X in the DARE (Discrete-time Algebraic Riccati Equation) analytically. A is diagonal A = [-a\;0; 0 \;a], and B = [b; 0] (in MATLAB notation). Any help is very much appreciated! Homework Equations The DARE is given as A'XA - X - (A'PB+S)(B'XB+R)^{-1}(A'XB+S)' + Q =...
  38. C

    Analytical Approach to Impedance Matching

    Homework Statement I am calculating matching impedances for a source and its load using 2 different L-network topologies. One is: source-parallel-to-C, load-series-to-L and the other is: source-parallel-to-L, load-series-to-C. I go through all the calculations and notice that...
  39. O

    Problem in understanding analytical solution of LCR circuit

    Hi all, I in my text they first did a phasor-diagram solution to a series LCR circuit and brought Z= under root of (R^2 +(Xc^2-XL^2)). After this they use a differential equation for series LCR circuit and actually did not solve such hard two degree differential equation, rather they...
  40. N

    Analytical Mechanics: Proving Equilibrium at Bottom of Bowl

    Homework Statement A point particle of mass m is confined to the frictionless surface of a spherical bowl. There are 2 degrees of freedom. 1. Prove that the equilibrium point is the bottom of the bowl. , 2.Does the bowl need to be exactly spherical for this to be true ? 3. Near the...
  41. M

    Integral -- analytical way to prove this integral is non-negative?

    Is there any analytical way to prove that the integral \int_{2.04}^\infty \frac{\sin x}{x^2}dx is nonegative? I tryed to use geometrical approach, i.e. the graph of the integrand look like: The magnitude became smaller and smaller, since \sin x is multiplied by the decreasing function...
  42. P

    Analytical approach to rectangular membrane vibration

    Homework Statement I'm following a procedure in a particular paper as part of my Masters project. The paper is called 'Theoretical investigation of the sound attenuation of membrane-type acoustic metamaterials - Y Zhang, J Wen, Y Xiao, X Wen and J Wang (2012)' and can be seen...
  43. hideelo

    Resources for analytical mehanics

    As the spring semester is over and the summer is now beginning I was thinking that I would like to get a start on analytical mechanics on my own as a summer project. I was wondering if anyone knows an online lecture series on analytical mechanics, preferably with an assigned textbook and...
  44. M

    Solving a PDE: Analytical Solution for $$\alpha \frac{\partial f}{\partial r}$$

    hey pf! i was wondering if you could help me out with a pde, namely $$\alpha ( \frac{z}{r} \frac{\partial f}{\partial r} + \frac{\partial f}{\partial z} ) = \frac{2}{r} \frac{\partial f}{\partial r} + \frac{\partial^2 f}{\partial r^2} + \frac{\partial^2 f}{\partial z^2} + 2 \frac{z}{r}...
  45. marellasunny

    A system of differential equations not having a analytical solution

    I am going to quote an article below and there is a part I would like clarification.I do not understand why chaotic differential systems do not have an analytical solutions. In the simplest form,an equation such as this one [sin(x) + x - 0.5 = 0] does not have an analytical solution i.e it can...
  46. P

    MHB Solving Coupled ODEs: Analytical Solutions?

    Hello everyone, I have the following coupled ODEs (r\geq 0) g^2v^2f(r)h^2(r)+\frac{6}{r}f'(r)-3f''(r)=0, r^2h''(r)-4f^2(r)h(r)=0, with boundary conditions f(\infty)=1, h(\infty)=1. The other 2 boundary conditions are arbitrary. Also v and g are constants, that could be set to a fixed value...
  47. P

    Analytical kinematics of a 6-bar mechanism

    Homework Statement This is a mechanism I'm working with for my undergrad project (its Modelled in Msc ADAMS) https://www.flickr.com/photos/35430110@N04/13902494524/ https://www.flickr.com/photos/35430110@N04/13902494524/ And to give you an idea of how it operates; position 1...
  48. 0

    Vector algebr and analytical geometry textbook

    Vector algebra and analytical geometry textbook I have a very comprehensive textbook written in portuguese about vector algebra and analytical geometry, but the author didn't include a bibliography at the book's end. What textbooks, in english, contains these syllabus (I'm pasting the list of...
  49. P

    Analytical mechanics question.

    Hi, Homework Statement I was given the setup in the attachment and was asked to find the angular frequency of small oscillations around the equilibrium. m1=m; m2=√3m Homework Equations The Attempt at a Solution I have found L = 1/2*(3+√3)*mR2\dot{θ}2 + mgRcosθ+√3mgRsinθ and the...
  50. B

    Analytical chemistry solutions

    If a polynomial equation is solved for multiple roots in a system of equilibria (e.g. calculating extent of a reaction, or solving for [H+] in a complicated acid-base system, to give two basic examples) how do we know which, among the roots, is the correct solution (e.g. the correct extent or...
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