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所在平台: Udemy |
课程主页: https://www.udemy.com/course/triple-and-double-integrals-college-mathematics/
课程评论：没有评论
**课程名称：** Multivariable Calculus useful for Machine Learning **课程概述：** 本课程由数学教育家 Suman Mathews 教授，旨在帮助学习者掌握多变量微积分中重要的积分技巧，并强调其在机器学习领域的应用。课程内容涵盖： * **多重积分的计算：** 学习如何计算二重积分和三重积分，包括基本评估技巧。 * **区域积分：** 掌握在指定区域上进行双重积分的方法，并学习如何确定积分区域（例如，椭圆的第一象限、由直线定义的三角形）。重点强调在计算涉及曲线交点的积分时，找到交点的重要性。 * **积分次序的变换：** 学习如何改变积分的次序（例如，从 dx dy 变为 dy dx），包括如何调整积分限，以及如何处理无界区域的积分次序变换。课程将通过具体例子（如抛物线与直线围成的区域、半圆形区域）进行讲解。 * **应用与技巧：** 涵盖了在区间 [-a, a] 上对奇函数进行积分，以及在特定区域（如 x 轴、直线 x=2a 和抛物线 $x^2=4ay$ 围成的区域）上的积分计算。 * **极坐标系：** 介绍极坐标系及其在积分中的应用，重点讲解如何变换积分限并进行计算，强调极坐标系在数学中的重要性。 * **向量场与线积分：** 学习向量场和线积分的概念，掌握如何计算曲线上的线积分，包括参数化函数的线积分。 * **重要定理：** 讲解格林公式（Greens Theorem）及其问题解决，并介绍高斯散度定理（Gauss Divergence Theorem）在问题解决中的基础应用。 * **其他概念：** 包含弧长、微分位移和保守场等概念。 **学习目标：** 通过本课程，学习者将能够： * 熟练掌握多重积分的计算方法。 * 理解并运用积分区域的设定与分析。 * 灵活地进行积分次序的变换。 * 了解并应用极坐标系进行积分。 * 理解向量场、线积分及其相关定理。 * 为进一步学习机器学习中的相关数学概念打下坚实基础。 **先修要求：** * 需要掌握基本的曲线知识，如圆、抛物线、椭圆和直线。 **建议：** 本课程适合希望深入理解多变量微积分积分技巧的学习者，特别是对机器学习感兴趣的初学者。即使不完整参与课程，预览部分也能带来收益。
Hi, I am Suman Mathews, math educator. I can help you learn how to integrate over a region by simple curve sketching, how to change the order of integration and more in this course. I can help you overcome your doubts over this topic.If you want to learn more about integration in Multivariable Calculus, then join this course. If not, then you can benefit from the preview. My students have always found my teaching interesting.Here, you will learn how to integrate double and triple integrals, Basic techniques of evaluating definite double and triple integrals are taught. You need to remember basic curves such as circle, parabola, ellipse, straight lines.You will then proceed to evaluating double integrals over a specified region. Some of the regions explained include the first quadrant of an ellipse, a triangle bounded by the lines y = 0, y = x, y+x=2. Given two curves, you need to note that is important to first find the point of intersection of the two curves.Next , you will learn how to change the order of integration. How to change the limits when dx dy changes to dy dx and vice versa. How to change the limits for unbounded regions is also shown. One of the examples include changing the order of integration when the region is enclosed between a parabola and a straight line. Another example is changing the order of integration of a semicircle.The session concludes with an assignment. You will learn how to evaluate the integral of an odd function within the limits -a to a. Integrating over a region bounded by the x axis, the ordinate x = 2a and the parabola x^2=4ay is also shown.Bonus:You are introduced to polar coordinates and how to integrate using these. It is exciting to note how the limits change and how to calculate them. Note that polar coordinates are extremely important in Mathematics.Learn about Vector fields and Line Integrals and how to evaluate line integrals over a curve. Also learn how to evaluate line integrals of parametric functions. Tackle Green's Theorem-Problems and Solutions. Learn Fundamentals of Gauss Divergence Theorem in Problem Solving.You'll learn about arc length, differential displacement and conservative fields. Don't be afraid to take the first step to start learning!
