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#Fourierseries Reel by @itutorial.jabalpur - A Fourier series is a way of expressing a periodic function as a sum of simple sine and cosine waves. The key idea is that even very complicated repea
208
IT
@itutorial.jabalpur
A Fourier series is a way of expressing a periodic function as a sum of simple sine and cosine waves. The key idea is that even very complicated repeating patterns can be built from smooth oscillations with different frequencies, amplitudes, and phases. Each sine or cosine term captures a specific frequency component, and when you add enough of them together, the sum can closely approximate the original function. This decomposition reveals how much of each frequency is present, which is why Fourier series are so powerful in understanding signals, sound waves, heat flow, and vibrations. One of the most remarkable aspects of Fourier series is that they can represent functions that are not smooth. Even functions with sharp corners or jump discontinuities can be approximated by adding more and more terms, though near jumps you observe small oscillations known as the Gibbs phenomenon. As the number of terms increases, the approximation improves almost everywhere. This ability to translate complex behavior into a structured sum of simple waves makes Fourier series a foundational tool in mathematics, physics, and engineering, and it serves as the basis for many modern techniques in signal processing and data analysis. Like this video and follow @itutorial.jabalpur for more! #math #fourier #physics #foryou #wave less
#Fourierseries Reel by @frameswithak_ (verified account) - Bernoulli's equation is a fundamental principle in fluid mechanics that describes the conservation of energy for a flowing fluid. It states that for a
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FR
@frameswithak_
Bernoulli’s equation is a fundamental principle in fluid mechanics that describes the conservation of energy for a flowing fluid. It states that for an incompressible, non-viscous fluid in steady flow, the sum of pressure energy, kinetic energy per unit volume, and potential energy per unit volume remains constant along a streamline.  The Equation The standard form relates the properties of a fluid at two different points (1 and 2):\(P_{1}+\frac{1}{2}\rho v_{1}^{2}+\rho gh_{1}=P_{2}+\frac{1}{2}\rho v_{2}^{2}+\rho gh_{2}\)Variables: \(P\): Static pressure of the fluid.\(\rho \) (rho): Density of the fluid.\(v\): Flow velocity.\(g\): Acceleration due to gravity.\(h\): Elevation (height) of the point.  Core Concepts Bernoulli Effect: As the speed of a moving fluid increases, the pressure within that fluid decreases. This is why air moving faster over the top of an airplane wing creates lower pressure, resulting in lift.Assumptions: To use this simplified equation, the fluid must be incompressible (constant density), non-viscous (no friction), and the flow must be steady (not changing over time) and streamline. Real-World Applications Aviation: Explains how wings generate lift by creating pressure differences.Venturi Meters: Used to measure fluid flow rates in pipes by observing pressure drops at narrow sections.Pitot Tubes: Speedometers on aircraft that measure “stagnation pressure” to determine airspeed.Medicine: Used in echocardiography to estimate pressure gradients in blood flow near blockages.Daily Phenomena: Explains why a shower curtain pulls inward or how a curveball “breaks” in baseball.  - #instagram #posting #explore #relatable #memes
#Fourierseries Reel by @emet.labs - The origins of Dirichlet forms lie in the 19th-century contributions of Peter Gustav Lejeune Dirichlet to potential theory. In the 1840s, Dirichlet fo
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EM
@emet.labs
The origins of Dirichlet forms lie in the 19th-century contributions of Peter Gustav Lejeune Dirichlet to potential theory. In the 1840s, Dirichlet formulated the Dirichlet principle, which asserts that the solution to the boundary value problem for Laplace's equation—seeking harmonic functions with prescribed boundary values—can be found by minimizing the associated energy integral over admissible functions. This variational approach, motivated by analogies to electrostatic equilibrium and minimum potential energy, marked a pivotal advancement in solving partial differential equations through calculus of variations. The modern theory of Dirichlet forms emerged in the mid-20th century through the work of Arne Beurling and Jacques Deny, who generalized Dirichlet's ideas beyond classical harmonic functions to abstract settings involving Markov processes. In their seminal 1958 paper, Beurling and Deny defined Dirichlet spaces as Hilbert spaces equipped with a semi-inner product satisfying specific axioms related to contraction properties and density of continuous functions, providing a framework for potential theory without relying on explicit kernels. They further elaborated on these concepts in a 1959 expository article, emphasizing applications to capacity, balayage, and the representation of elements as potentials. A key milestone in the 1960s was the development of the Beurling-Deny formula by Jacques Deny, which decomposes symmetric Dirichlet forms into strongly local, jump, and killing parts, establishing a direct link between these forms and the generators of associated contraction semigroups on function spaces. This formula unified variational and probabilistic perspectives, facilitating the study of diffusion processes. The theory gained further momentum in the 1970s and 1980s from the Japanese school of probabilists, led by Masatoshi Fukushima, who integrated Dirichlet forms with stochastic analysis and symmetric Markov processes.
#Fourierseries Reel by @vv__math - sol. 25 #calculus #math #mathematics #integral #equation
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@vv__math
sol. 25 #calculus #math #mathematics #integral #equation
#Fourierseries Reel by @emet.labs - The origins of Dirichlet forms lie in the 19th-century contributions of Peter Gustav Lejeune Dirichlet to potential theory. In the 1840s, Dirichlet fo
789.8K
EM
@emet.labs
The origins of Dirichlet forms lie in the 19th-century contributions of Peter Gustav Lejeune Dirichlet to potential theory. In the 1840s, Dirichlet formulated the Dirichlet principle, which asserts that the solution to the boundary value problem for Laplace's equation—seeking harmonic functions with prescribed boundary values—can be found by minimizing the associated energy integral over admissible functions. This variational approach, motivated by analogies to electrostatic equilibrium and minimum potential energy, marked a pivotal advancement in solving partial differential equations through calculus of variations. The modern theory of Dirichlet forms emerged in the mid-20th century through the work of Arne Beurling and Jacques Deny, who generalized Dirichlet's ideas beyond classical harmonic functions to abstract settings involving Markov processes. In their seminal 1958 paper, Beurling and Deny defined Dirichlet spaces as Hilbert spaces equipped with a semi-inner product satisfying specific axioms related to contraction properties and density of continuous functions, providing a framework for potential theory without relying on explicit kernels. They further elaborated on these concepts in a 1959 expository article, emphasizing applications to capacity, balayage, and the representation of elements as potentials. A key milestone in the 1960s was the development of the Beurling-Deny formula by Jacques Deny, which decomposes symmetric Dirichlet forms into strongly local, jump, and killing parts, establishing a direct link between these forms and the generators of associated contraction semigroups on function spaces. This formula unified variational and probabilistic perspectives, facilitating the study of diffusion processes. The theory gained further momentum in the 1970s and 1980s from the Japanese school of probabilists, led by Masatoshi Fukushima, who integrated Dirichlet forms with stochastic analysis and symmetric Markov processes.
#Fourierseries Reel by @codematrixvishal - 🚀 Visualising wave extrapolation of circle, hexagon and infinity ♾️ wave extrapolation | Fourier Series #codematrixvishal #mathematics #maths #fyp
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CO
@codematrixvishal
🚀 Visualising wave extrapolation of circle, hexagon and infinity ♾️ wave extrapolation | Fourier Series #codematrixvishal #mathematics #maths #fyp
#Fourierseries Reel by @vv__math - sol. 13 #calculus #math #mathematics #integral #limits
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@vv__math
sol. 13 #calculus #math #mathematics #integral #limits
#Fourierseries Reel by @emet.labs - The origins of Dirichlet forms lie in the 19th-century contributions of Peter Gustav Lejeune Dirichlet to potential theory. In the 1840s, Dirichlet fo
431
EM
@emet.labs
The origins of Dirichlet forms lie in the 19th-century contributions of Peter Gustav Lejeune Dirichlet to potential theory. In the 1840s, Dirichlet formulated the Dirichlet principle, which asserts that the solution to the boundary value problem for Laplace's equation—seeking harmonic functions with prescribed boundary values—can be found by minimizing the associated energy integral over admissible functions. This variational approach, motivated by analogies to electrostatic equilibrium and minimum potential energy, marked a pivotal advancement in solving partial differential equations through calculus of variations. The modern theory of Dirichlet forms emerged in the mid-20th century through the work of Arne Beurling and Jacques Deny, who generalized Dirichlet's ideas beyond classical harmonic functions to abstract settings involving Markov processes. In their seminal 1958 paper, Beurling and Deny defined Dirichlet spaces as Hilbert spaces equipped with a semi-inner product satisfying specific axioms related to contraction properties and density of continuous functions, providing a framework for potential theory without relying on explicit kernels. They further elaborated on these concepts in a 1959 expository article, emphasizing applications to capacity, balayage, and the representation of elements as potentials. A key milestone in the 1960s was the development of the Beurling-Deny formula by Jacques Deny, which decomposes symmetric Dirichlet forms into strongly local, jump, and killing parts, establishing a direct link between these forms and the generators of associated contraction semigroups on function spaces. This formula unified variational and probabilistic perspectives, facilitating the study of diffusion processes. The theory gained further momentum in the 1970s and 1980s from the Japanese school of probabilists, led by Masatoshi Fukushima, who integrated Dirichlet forms with stochastic analysis and symmetric Markov processes.
#Fourierseries Reel by @vv__math - sol. 31 #calculus #math #mathematics #integral #integrals
1.3K
VV
@vv__math
sol. 31 #calculus #math #mathematics #integral #integrals
#Fourierseries Reel by @emet.labs - The origins of Dirichlet forms lie in the 19th-century contributions of Peter Gustav Lejeune Dirichlet to potential theory. In the 1840s, Dirichlet fo
2.0K
EM
@emet.labs
The origins of Dirichlet forms lie in the 19th-century contributions of Peter Gustav Lejeune Dirichlet to potential theory. In the 1840s, Dirichlet formulated the Dirichlet principle, which asserts that the solution to the boundary value problem for Laplace's equation—seeking harmonic functions with prescribed boundary values—can be found by minimizing the associated energy integral over admissible functions. This variational approach, motivated by analogies to electrostatic equilibrium and minimum potential energy, marked a pivotal advancement in solving partial differential equations through calculus of variations. The modern theory of Dirichlet forms emerged in the mid-20th century through the work of Arne Beurling and Jacques Deny, who generalized Dirichlet's ideas beyond classical harmonic functions to abstract settings involving Markov processes. In their seminal 1958 paper, Beurling and Deny defined Dirichlet spaces as Hilbert spaces equipped with a semi-inner product satisfying specific axioms related to contraction properties and density of continuous functions, providing a framework for potential theory without relying on explicit kernels. They further elaborated on these concepts in a 1959 expository article, emphasizing applications to capacity, balayage, and the representation of elements as potentials. A key milestone in the 1960s was the development of the Beurling-Deny formula by Jacques Deny, which decomposes symmetric Dirichlet forms into strongly local, jump, and killing parts, establishing a direct link between these forms and the generators of associated contraction semigroups on function spaces. This formula unified variational and probabilistic perspectives, facilitating the study of diffusion processes. The theory gained further momentum in the 1970s and 1980s from the Japanese school of probabilists, led by Masatoshi Fukushima, who integrated Dirichlet forms with stochastic analysis and symmetric Markov processes.
#Fourierseries Reel by @abdoukrs - Fibonacci بالـ Recursion… #Algorithmique #InformatiqueL1 #اعلام_الي #تعلم_البرمجة
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AB
@abdoukrs
Fibonacci بالـ Recursion… #Algorithmique #InformatiqueL1 #اعلام_الي #تعلم_البرمجة

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