MARTINDALE’S CALCULATORS ONLINE CENTER PHYSICS CENTER PHYSICS BY SUBJECT: FP (Calculators, Applets, Spreadsheets, 
PHYSICS BY SUBJECT: FP Fourier ~
Heim Mass Theory ~
LRC ~
Neutrons ~
Physics of Cooking ~
Fluid Dynamics ~

FEYNMAN PATH INTEGRAL COURSES, LECTURES, TEXTBOOKS, ETC.
WeylOrdering; ProductOrdering; SpaceTime Transformations; Separation of Variables; The Free Particle; The Harmonic Oscillator; The Radial Path Integral; The General Radial Path Integral; The Radial Harmonic Oscillator; Other Elementary Path Integrals; The Coulomb Potential; etc…” For more information see the
QUANTUM FIELD THEORY COURSES, LECTURES, TEXTBOOKS, ETC.
quantum ﬁeld theory for secondyear graduate students…” Example of “Fields” Textbook Parts & Sections include
Spin; Local; Mixed…” Part Two: Quanta
Quantum Guage Theory; Loops; Guage Loops…” Part Three:Higher Spin
Supergravity; Strings; Mechanics…” For more information see
over “30” “Quantum Field Theory (524)” Course Video Lectures…” For more information see QUANTUM CONDENSED MATTER FIELD THEORY COURSES & LECTURES
Second Quantisation; Representation of Operators; Tightbinding and the Mott Transition; Quantum Magnetism and the Ferromagnetic chain; Quantum Antiferromagnetism; Bogoliubov Theory of Weakly Interacting Bose Gas; Feynman Path Integral; Statistical Mechanics and SemiClassics; Applications of the Feynman Path Integral; Double Well Potential: Tunneling and Instantons; Coherent States; Manybody (coherent state) Path Integral; Applications and Connections; Weakly Interacting Electron Gas: Plasma Theory; Random Phase Approximation; BoseEinstein Condensation; Superfluidity; Cooper Instability; BCS Superconductivity; etc…” For more information see the QUANTUM GROUPS COURSES & LECTURES
For more information see the
KNOWN FORCES – COURSES, LECTURES, TEXTBOOKS, MANUALS, ETC.
and a fifth – a new one – whose existence we infer from the discovery of the Higgs particle…” “…what particle physicists mean in describing forces as being weak or strong. It’s terminology that you’ll often see, but unless it’s been explained to you, there’s no way to guess what’s actually meant…” For more information see WAVE PHENOMENA COURSES, LECTURES, TEXTBOOKS, MANUALS, ETC.
Normal Mode Coordinates Initial Value Problem; Linear Chain – Normal Modes; Traveling Waves, Standing Waves, and the Dispersion Relation; General Solution Using Normal Modes; Introduction to Fourier Series; Vector Spaces – Real Space; The Dirac Delta Function; Introduction to Fourier Transforms; 3D Wave Equation and Plane Waves – 3D Differential Operators; Separation of Variables in Cartesian Coordinates; The Wave Equation in Cylindrical Coordinates; Separation of Variables in Spherical Coordinates; A Propagating Wave Packet – Group Velocity Dispersion; etc…” For more information see
FOURIER ANALYSIS COURSES, LECTURES, TEXTBOOKS, MANUALS, ETC.
Lecture 6
Lecture 12
Lecture 15
Lecture: 22
For more information see
complex analysis. It is a course aimed at students majoring in mathematics and science who are at least at their junior level of mathematical maturity. Students are introduced to Fourier series, Fourier transforms, and a basic complex analysis…” Examples of “An Introduction to Fourier and Complex Analysis with Applications to the Spectral Analysis of Signals” Course Lectures include
Fourier Series; Generalized Fourier Series; Complex Integration; Discrete Transforms; Signal Analysis; etc…” For more information see
The Space S(R^{n}) as Frechet Space; The Fourier Transform; Tempered Distributions; Intermediate Banach Spaces, Regularity; The Poisson Summation Formula; Paley Wiener Theroems; Distributions versus Tempered Distributions; etc…” For more information see
The Calderon Zygmund Decomposition; The Littlewood Paley Square Function; Khintchine’s Inequality; The Space BMO as Function Space; Maximal Truncated Singular Integrals; Paraproducts and a Discrete T1 Theorem; The CotlarStein Lemma; etc…” For more information see
Lebesgue integral with applications to probability, and half to Fourier series and Fourier integrals…” Examples of “Fourier Analysis: Theory and Applications” Course Lectures include
Lp Theory; Hilbert Space and Orthonormal Bases; Fourier Series; Fourier Integrals; Fourier Integrals, Measures, and Central Limit Theorem; etc…” For more information see
Roth’s theorem; Equidistribution of polynomials over finite fields; The inverse conjecture for the Gowers norm I. The finite field case; The inverse conjecture for the Gowers norm II; The integer case Linear equations in primes; etc…” Chapter II: Related Articles
Higher order Hilber spaces; etc…” For more information see
Harmonic Functions on the Disk and Poisson Kernel; L^{1} bounded analytic functions and the F. & M. Riesz theorem; The Conjugate Harmonic Function; CalderonZygmund Theory of Singular Integrals; Almost Orthogonality; Schauder Estimates; L^{P} multipliers, Mikhlin theorem and LittlewoodPaley theory; Restriction of the Fourier transform, SteinTomas theorem, Strichartz estimates; The endpoint for the SteinTomas theorem and Strichartz estimates; Some pointwise questions for Fourier series: the case of L^{1} (T); etc…” For more information see the FOURIER TRANSFORM CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS
FOURIER TRANSFORMS CALCULATORS & APPLETS FFT ALGORITHM CALCULATORS & APPLETS
a step feature which allows the user to see what is going on in the algorithm, and a multimedia section…” For more information see
For more information see
Fourier approximation of degree at most 20…” For more information see
The pointset is generated by the plane space groups (see Project 22). You may transform all points…” For more information see

DISCRETE FOURIER TRANSFORM CALCULATORS & APPLETS
send bits representing a character (coded as the 8bit ASCI code) though a wire that includes a “lowpass” filter, i.e. frequencies above a certain point are filtered out…” Fast Fourier Transform of Arbitrary Function Calculator
For more information see FOURIERLAPLACE CALCULATORS & APPLETS
Laplace transform of a function, and their inverse transforms…” For more information see FOURIER TRANSFORM CALCULATORS & APPLETS – IMAGE PROCESSING
FOURIER SERIES CALCULATORS & APPLETS
a Fourier series by means of scroll bars and to look at the graph of the resulting function…” For more information see
rectangular, triangular or trapezoidal shaped waveform & Plots both the timedomain waveform and the magnitude of the coefficients…” For more information see
sum of cosine terms. In other words, Fourier series can be used to express a function in terms of the frequencies…” For more information see FOURIER SYNTHESIS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS
Fourier series, i. e. as a sum of sinusoidal and cosinusoidal oscillations…” For more information see
Fourierzerlegung mathematisch…” For more information see 
FRICTION COURSES, LECTURES, LESSONS, CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS
FRICTION AT THE ATOMIC SCALE COURSES, PUBLICATIONS, LESSONS, CALCULATORS, ANIMATIONS, ETC.
via arrangement of the ions relative to the substrate. By varying the ion number, we also show that this strong dependence of friction on the structural mismatch, as predicted by manyparticle models, already emerges at the level of two or three atoms. This model system enables a microscopic and systematic investigation of friction, potentially even into the quantum manybody regime…” For more information see
GRAVITATIONAL WAVES COURSES, PUBLICATIONS, TECHNICAL REPORTS, ETC.
Years to Search: Click “Past Year”; Title: Gravitational Waves; Do Search…” For more information see
Gravitational Waves; History of Relativity; Mathematical Relativity; Numerical Relativity; Physical Cosmology; Quantum General Relativity; Relativity in Astrophysics; String Theory and Gravitation
Sounds of Extreme Spacetimes in Gravitational Waves (Black Holes, Neutron Stars, etc.); Movies of Extreme Spacetimes (Gravitational Waves From a Pair of Black Holes, etc.); Lectures (Relativity, Gravitational Waves Astronomy & Numerical Relativity); etc…” QUANTUM GRAVITY COURSES, LECTURES, TEXTBOOKS, ETC.
For more information see the
from the canonical quantization of general relativity. A covariant (path integral) formulation of the theory is expected to be in the form of a spin foam model…” For more information see GRAVITY CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS
theory of universal gravitation and Einstein’s general relativity…” For more information see
HEIM MASS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS
Messon pi (zero); Messon k (charge); Messon eta; Messon k (zero); Baryon proton; Baryon neutron; Baryon lambda; etc…” Heim Mass Calculator INPUT Values include
For more information see INTEGRALS CALCULATORS & APPLETS
Wolfram Mathematica Online Integrator
syntax. It can also parse many expressions when they are not in exactly the right form, so people who are unfamiliar with Mathematica syntax details will not usually encounter problems…” For more information see 
LRC CIRCUIT CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS
a capacitor and an inductor react with one another in a system…” For more information see
MAGNETISM & MAGNETIC MATERIALS COURSES, LECTURES, ETC.
Diamagnetic and paramagnetic materials; Ferromagnetic materials; Ferrimagnetic materials; Relative permeability; Permeability of a vacuum; Mass susceptibility; Magnetic moment; Intensity of magnetization; etc…” For more information see MAGNETIC EXCITATIONS IN FERROMAGNETS CALCULATORS & APPLETS
Processing Magetization Applet Processing Magetization Applet
a twodimensional lattice. The applet shows a 6by6 array of precessing spins. Each of these precessing moments obey the same equations of motion…” ISING MODEL CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS
very simple system. In Ising model interacting spins (magnet vectors) occupy lattice sites. Every spin…” For more information see
estimates of system energy and magnetization…” For more information see PHASE TRANSITIONS CALCULATORS & APPLETS
Percolation; Path Integrals in Quantum Mechanics…” In English & Russian.

MANY BODY PHYSICS RELATED CENTERS FOR RELATED MANY BODY PHYSICS COURSES, TEXTBOOKS, ETC. SEE MANY BODY PHYSICS COURSES, TEXTBOOKS, LECTURES, ETC.
Dynamical Mean Field and Dynamical Cluster Approximation; Hirsh Fye and Continuous time Quantum Monte Carlo Methods; etc…” For more information see NEUTRONS RELATED CENTERS FOR NEUTRON DATABASES SEE NEUTRON COURSES, MANUALS, LECTURES, ETC.
Neutron spectroscopy; Reflectometry; Small angle scattering; etc…” For more information see NEUTRON CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS
Scattering Length Density Calculator for Thermal Neutron Cross Sections Scattering Length Density Calculator
in g/cm^{3} this applet can calculate the real and imaginary portions of the scattering length density of the material for neutrons and xrays…”
You can also smear the SANS data using a set of instrument parameters…”
media and calculate neutron reflectivities…” NMR PERIODICAL TABLES NMR CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS
a static magnetic field and exposed to a second oscillating magnetic field. Some nuclei experience this phenomenon, and others do not, dependent upon whether they possess a property called spin…” Examples of “The Basic of NMR” Course Chapters include
The Mathematics of NMR; Spin Physics; NMR Spectroscopy; Fourier Transforms; Pulse Sequences, NMR Hardware; Practical Considerations; Carbon13 NMR; 2D Techniques; Advanced Spectroscopic Techniques; etc…” For more information see the
images of the inside of the human body. MRI is based on the principles of nuclear magnetic resonance (NMR), a spectroscopic technique used by scientists to obtain microscopic chemical and physical information about molecules. The technique was called magnetic resonance imaging rather than nuclear magnetic resonance imaging (NMRI) because of the negative connotations associated with the word…” Examples of “The Basics of MRI” Course Chapters include
The Mathematics of NMR; Spin Physics; NMR Spectroscopy; Fourier Transforms; Imaging Techniques; Fourier Transform Imaging Principles; Basic Imaging Techniques; Imaging Hardware; Advanced Imaging Techniques; etc…” For more information see the
NMR CALCULATORS & APPLETS
Group for PointandClick; MHz (60, 90, 200, 300, 400, 600); 2nd Order, Text Lines, etc…” For more information see
the processing of 2dimensional and 3dimensional NMR data sets. Data can be processed with normal FT methods or by maximum entropy reconstruction methods…”
to be used for the collection of nonuniform NMR data sets. Reasonable values for the parameters which define the sample schedule are determined after…”
processing of 2dimensional and 3dimensional NMR data sets…”
The calculator includes options to deal with shaped pulses and amplifier compression…”
Alpha Substituents; Beta Substituents; Gamma Substituents…”
Coupling Constants…” PHOTOELECTRIC EFFECT CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS
Planck constant and the work function: A single spectral line is filtered out from the light of a mercury lamp…” For more information see PHYSICS OF COOKING COURSES, LECTURES, ETC.
both everyday cooking and haute cuisine. Each lecture features a worldclass chef who visited and presented their remarkable culinary designs…” “…The lectures then use these culinary creations as inspiration to delve into understanding how and why cooking techniques and recipes work, focusing on the physical transformations of foods and material properties…” For more information see
PHYSICS OF MUSIC COURSES, LECTURES, ANIMATIONS, SIMULATIONS, ETC.
Flute Acoustics; Clarinet Acoustics; Saxophone Acoustics; Brass Acoustics; Didjeridu Acoustics; Violin Acoustics; Guitar Acoustics; Voice Acoustics; etc…” For more information see
response of your own ears. The flash script allows you to play sound files with a range of frequencies and sound levels with the click of a mouse…” “…Results using this test cannot be regarded as clinical data. Although the sound files have been carefully prepared, the actual sound level and spectral purity depend on the frequency response of your sound card and headphones. They may, however, be helpful for comparison, such as left vs right ear, or for changes in hearing over time, assuming that you use the same hardware…”
of the amount of vibration at each individual frequency. It is usually presented as a…”
(technically, a control oscillator). The reed, in cooperation with the resonances in the air in the instrument, produces an oscillating component of both flow and pressure. Once the air in the saxophone is vibrating, some of the energy is radiated as sound out of the bell and any open holes…”
air in the instrument, produces an oscillating component of the flow. Once the air in the flute is vibrating, some of the energy is radiated as sound out of the end and any open holes…”
Sound Waves and Radiation from Sources; Complicated Wave Phenomena; Room Acoustics; Vibration of 1DOF Simple Oscillators; Vibration of MultiDOF Systems; etc…” For more information see
to study the vibration of an electric guitar in order to determine its natural frequencies and mode shapes…”
maybe 1/2 a mile across or so. During the day you can see campers on the other side of the lake, but you cannot hear them. At night, however, you can not only see the campers on the other side of the lake but you can also hear their conversations as they sit around their camp fire. This phenomena is due to the refraction of sound waves…”
Radiation from a dipole source; Radiation from a lateral quadrupole source…”
has become my primary area of research. I have been able to correlate the vibrational frequencies of bat barrels to measured performance, and have signicantly contributed to an understanding of the trampoline effect in a hollow bat. In addition, my vibrational analysis of the bending modes of a bat has added to the understanding of perception and feel, including why some bats sting more or less than others…” 
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