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所在平台: Udemy |
课程主页: https://www.udemy.com/course/math-175-precalculus-aum/
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课程名称：MATH 175：预备微积分（AUM） 课程概述： 本课程内容涵盖了理解函数、微积分及其应用所必需的一系列主题。第1章的内容包括多项重要概念： - CH 1.1：函数、定义域和函数的组合。 - CH 1.2：抛物线图形，这是一个重要的二次函数。 - CH 1.3：线性方程及其图形。 - CH 1.4：将数学概念应用于经济学，重点讨论需求-供给函数、市场均衡及盈亏平衡分析。 课程接下来进入极限的概念： - CH 1.5：引入极限的基本概念。 - CH 1.6：探讨单侧极限和连续性。 在第2章中，主要介绍导数： - CH 2.1：导数的概念，为更高级的主题铺平道路。 - CH 2.2：切线的概念。 - CH 2.3和CH 2.4：学习求导数的各种技术。 - CH 2.5：将所学知识应用于边际分析。 第3章专注于导数的应用： - CH 3.1：探讨导数在现实世界中的应用。 - CH 3.3：涵盖有理函数的渐近线及图形绘制。 课程最后，第4章的内容包括： - CH 4.1、4.2和4.3：研究指数和对数函数及其导数，这些在许多应用场合（如生长和衰减模型）中至关重要。 总体来说，本课程为学生提供了理解和应用数学基本概念的坚实基础。
Course contentCH 1.1 Functions, domain, composition of functionsCH 1.2 Graph of a ParabolaCH 1.3 LinesCH 1.4. Demand-Supply Functions & Market Equilibrium & Break Even AnalysisCH 1.5. LimitsCH 1.6 One-sided limits continuityCH 2.1 DerivativesCH 2.2 Tangent LinesCH 2.2,2.3,2.4. Derivatives and Techniques to find the DerivativesCH2.5 Marginal AnalysisCH 3.1 An application of derivativesCH 3.3 Aysmptotes of Rational FunctionsCH 3.3 Sketching Graphs of Rational FunctionsCH 4.1 4.2 & 4.3 Exponential and Logarithmic Functions and Their DerivativesThe course content covers a range of topics essential for understanding functions, calculus, and their applications. In CH 1.1, students will explore the concept of functions, their domains, and how to compose multiple functions. CH 1.2 introduces the graph of a parabola, an important quadratic function, while CH 1.3 delves into linear equations and their graphs. CH 1.4 applies mathematical concepts to economics, focusing on demand-supply functions, market equilibrium, and break-even analysis.The course then transitions into limits, beginning with CH 1.5 where the fundamental concept of limits is introduced, followed by CH 1.6, which covers one-sided limits and continuity.In CH 2.1, derivatives are introduced, laying the foundation for more advanced topics like tangent lines (CH 2.2). Students will also learn techniques to find derivatives in CH 2.3 and CH 2.4, followed by the application of these concepts in CH 2.5 with marginal analysis.Chapter 3 focuses on applying derivatives, beginning with CH 3.1, where students explore real-world applications. CH 3.3 covers asymptotes and graphing rational functions. The course concludes with CH 4.1, 4.2, and 4.3, exploring exponential and logarithmic functions, and their derivatives, which are key in many applications like growth and decay models in real-life scenarios.
