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Mehrdimensionale Integration

Track :

Science

Lessons no : 15

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What will you learn in this course?
  • Understand and set up multiple integrals for functions of two or more variables in various coordinate systems including Cartesian, cylindrical, and spherical coordinates
  • Apply Fubini’s theorem to evaluate double and triple integrals efficiently in real-world problems involving volume, mass, and probability
  • Compute volume, surface area, and mass of complex 3D objects using multiple integration techniques in physics, engineering, and computer graphics
  • Analyze and interpret the results of multiple integrals to solve practical problems in fields like fluid dynamics, electromagnetism, and statistical mechanics
  • Utilize symmetry and substitution methods to simplify complex multi-variable integrals for easier computation
  • Implement numerical methods for approximating multiple integrals when analytical solutions are difficult or impossible
  • Develop skills to visualize multi-dimensional regions and integrals for better understanding and problem-solving in higher-dimensional calculus
  • Apply multiple integration concepts to optimize real-world applications such as center of mass, moments of inertia, and probability distributions

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Lessons | 15


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Kavitha.M

Very good 2023-03-14

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Ein Mehrfachintegral ist eine Art bestimmtes Integral, das erweitert wurde, um Funktionen einzuschließen, die in mehr als einer Variablen definiert sind, wie z. B. {\displaystyle f\, } oder {\displaystyle f\, }. Die Integrale einer Funktion von zwei Variablen über dem Bereich R³ heißen binäre Integrale, und die Integrale einer Funktion von drei Variablen über dem Bereich R³ heißen Tripel