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Operations Research (OR) is a multidisciplinary field that uses mathematical models, statistical analysis, and optimization techniques to solve complex decision-making problems in various industries such as manufacturing, transportation, healthcare, finance, and logistics.
Algorithm design and analysis form the backbone of computer science and computational theory. Algorithms are step-by-step procedures or formulas for solving problems, and their efficiency determines how well software performs in terms of speed, memory usage, and scalability.
Neural networks are the backbone of modern artificial intelligence (AI), powering applications like image recognition, natural language processing, and autonomous vehicles,
Classical mechanics, developed primarily through the work of Sir Isaac Newton and subsequent physicists such as Euler, Lagrange, and Hamilton, provides the foundation for understanding the motion of physical systems under the influence of forces.
In this section, we will derive and provide examples for various reduction formulas used in calculus. Each formula allows us to reduce the complexity of integrals involving different types of functions, such as exponential, trigonometric, inverse trigonometric, hyperbolic, logarithmic, and algebraic functions.
In real analysis, series play an important role in understanding the convergence properties of sequences and functions. A series is essentially the sum of the terms of a sequence, and the study of series provides the foundation for advanced concepts such as Taylor series, Fourier series, and more.
In the study of mathematics and physics, concepts like vectors, kernel, Green’s theorem, bulk modulus, and Gauss’s theorem play vital roles in a variety of fields, ranging from fluid dynamics to material science.
Ordinary Differential Equations (ODEs) are equations involving functions and their derivatives. First-order ODEs involve the first derivative of the unknown function and are crucial in modeling phenomena such as population dynamics, heat conduction, motion under forces, and electrical circuits.
In the realm of linear algebra and differential equations, Wronskian, eigenvalues, and eigenvectors play a crucial role in solving systems of linear equations, studying the behavior of differential equations, and analyzing the stability of systems. In this blog, we will dive deep into each of these concepts, provide formal definitions, and illustrate them with practical…
In the study of partial differential equations (PDEs), one of the key characteristics used to classify and understand them is the **order** of the equation. The order of a PDE refers to the highest derivative of the unknown function in the equation. Understanding the order is crucial for identifying the complexity of the equation and…
