Application of Calculus in Computer Science PDF

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Computer science is the study of processes that interact with data and that can be represented as data in the form of programs. It is the theory experimentation, and engineering that enables the use of algorithms to manipulate, store, and communicate digital information. A computer scientist studies the theory of computation and the practice of designing software systems. Scientific computing. Computer algebra systems that either compute integrals and derivatives directly, symbolically or numerically, are the most blatant examples here, but in addition, any software that simulates a physical system that is based on continuous differential equations necessarily involves computing derivatives and integrals. Design and analysis of algorithms. The behavior of a combinatorial algorithm on very large instances is often most easily analyzed using calculus. This is especially true for randomized algorithms; modern probability theory is heavily analytic. Asymptotic enumeration. Sometimes the only way to get a handle on an enumeration problem is to form a generating function and use analytic methods to estimate its asymptotic behavior. Calculus in computer science Discrete mathematics, clearly necessary to CS, often draws on calculus concepts and techniques. Specific calculus topics are also useful in CS. Numerical analysis, computer graphics, computer vision; machine learning, data mining, and bioinformatics are riddled with calculus techniques and linear algebra. How/when is Calculus used in computer science.

Computer Graphics/Image Processing, and here you will need Analytic Geometry and Linear Algebra. Optimization, non-linear mostly, where multivariate Calculus is the fundamental language used to develop everything. Probability/Statistics. These cannot be seriously studied without multivariate Calculus. Ex. Machine Learning, which makes heavy use of Statistics. Data Mining and related subjects, which use many Statistics. Robotics, where you will need to model physical movements of a robot, so you will need to know partial derivatives and gradients. Uses of calculus in computer science Graphs and visuals – They use calculus in creating visual or graphs. Application to solve problems – They use calculus for general problem solving applications, simulations, and physics engines. Code – In application for solving problems, the basic formula is generally used as well. Binary – It is a number system comprised of only ones and zeros that the computer uses to follow instructions and save data. Information processing – Computer programmers use this in creating statistic solvers, probability, and simulation.

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