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Calculus
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Calculus is a branch of mathematics that focuses on the study of change and motion, utilizing two main components: differentiation and integration. Differentiation deals with the calculation of rates of change, while integration focuses on summing quantities to determine areas under curves and accumulated values. Originating in the 17th century, Isaac Newton and Gottfried Wilhelm Leibniz independently developed the foundational principles of calculus, revolutionizing mathematics and science by providing a robust framework to model physical systems and continuous phenomena.
https://en.wikipedia.org/wiki/Calculus
In modern applications, calculus plays a critical role in machine learning, physics, engineering, and economics. For example, gradient calculations in machine learning rely heavily on differentiation to minimize loss functions and optimize model parameters. Integration, on the other hand, is vital in fields such as signal processing and probability, where cumulative quantities or probabilities need to be calculated. The computational power of calculus has also been enhanced by software tools like Mathematica and MATLAB, first introduced in the 1980s, enabling precise and efficient problem-solving.
https://en.wikipedia.org/wiki/Gradient_descent
Beyond its scientific and engineering applications, calculus is foundational to the understanding of advanced mathematical topics such as differential equations, vector calculus, and complex analysis. Its principles underpin the workings of modern technology, from AI systems to robotics and beyond. The education of calculus has also evolved with interactive platforms like Wolfram Alpha and Khan Academy, which make the concepts accessible to students and professionals alike. As computation advances, the integration of calculus into emerging technologies continues to grow.
https://en.wikipedia.org/wiki/Isaac_Newton
https://en.wikipedia.org/wiki/Gottfried_Wilhelm_Leibniz
- Snippet from Wikipedia: Calculus
Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations.
Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus. The former concerns instantaneous rates of change, and the slopes of curves, while the latter concerns accumulation of quantities, and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus. They make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. It is the "mathematical backbone" for dealing with problems where variables change with time or another reference variable.
Infinitesimal calculus was formulated separately in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. Later work, including codifying the idea of limits, put these developments on a more solid conceptual footing. Today, calculus is widely used in science, engineering, biology, and even has applications in social science and other branches of math.
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