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所在平台: Udemy |
课程主页: https://www.udemy.com/course/math-2-w/
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课程名称：数学2 课程概述： 《数学2》是一门全面的课程，旨在帮助工程和计算机科学的学生深入理解高级数学概念，这些概念对高层次学习和实际应用至关重要。课程涵盖广泛的主题，连接微积分与线性代数，特别强调实用问题解决能力。 课程首先介绍涉及一、二、三个变量的函数的定义域和范围，这是多变量微积分的基础知识。随后，我们将进入圆锥曲线的优雅世界，包括抛物线、椭圆和双曲线，并探索三维的二次曲面。课程的重要部分集中于偏微分及其在优化和逼近中的应用。学习者将掌握笛卡尔坐标、极坐标、圆柱坐标和球坐标下的双重和三重积分，特别强调计算面积、体积及解决工程问题。 课程的第二部分转向线性代数。从行列式和矩阵开始，学习如何找到逆矩阵，解决线性系统，并进行LU分解。学生还将探讨线性组合、生成空间、线性无关等关键概念，并最后深入研究特征值和特征向量，这是数据科学、机器学习及工程仿真的核心主题。 每节课内容清晰简洁，并辅以逐步解释，确保学生能够深入理解，而不仅仅是记忆。无论是为考试做准备，还是巩固数学基础技能，这门课程将为您提供成功所需的工具。
This comprehensive Math 2 course is designed for engineering and computer science students who are looking to deepen their understanding of advanced mathematical concepts essential for higher-level studies and real-world applications. The course covers a wide range of topics that bridge Calculus and Linear Algebra, with a strong focus on practical problem-solving.We begin with Domain and Range of functions involving one, two, and three variables-foundational knowledge for multivariable calculus. Then we move into the elegant world of Conic Sections, including Parabolas, Ellipses, and Hyperbolas, and explore Quadratic Surfaces in three dimensions.A significant portion of the course focuses on Partial Differentiation and its applications in optimization and approximation. You'll then master Double and Triple Integrals in Cartesian, Polar, Cylindrical, and Spherical coordinates, with a special emphasis on calculating areas, volumes, and solving engineering problems.The second part of the course transitions into Linear Algebra. Starting from Determinants and Matrices, you'll learn how to find Inverse Matrices, Solve Linear Systems, and perform LU Factorization. You'll also explore critical concepts like Linear Combinations, Spans, Linear Independence, and conclude with a deep dive into Eigenvalues and Eigenvectors-a core topic in data science, machine learning, and engineering simulations.Each lecture is clear, concise, and supported with step-by-step explanations to ensure deep understanding, not just memorization.Whether you're preparing for exams or strengthening your core math skills, this course will give you the tools you need to succeed
