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所在平台: Udemy |
课程主页: https://www.udemy.com/course/precalculus-4/
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课程名称：预备微积分4：指数与对数
课程概述：本课程旨在为学生提供关于指数函数和对数函数的全面介绍，包括它们的外观、描述以及相关的数学概念。课程将探讨这些函数的简单性以及一些复杂性，帮助学生在未来的微积分课程中打下基础。
1. **课程介绍**：您将学习指数与对数函数的基本知识，并了解它们在数学中扮演的重要角色，这些知识是未来更复杂函数学习的基石。
2. **神奇的数字 e、二项式定理和帕斯卡三角形**：您将直观和正式地了解数字 e，以及需要使用的二项式定理，包括阶乘和二项式系数的概念，以及帕斯卡三角形的应用。
3. **不同类型指数的幂**：学习自然数、整数和有理数指数的幂的计算规则，包括乘法法则、除法法则和指数法则，同时探索数的 n 次根的存在性。
4. **幂函数、特性与图形**：了解幂函数的特性（如单调性）以及图形之间的关系，认识到幂函数与指数函数之间的有趣互动，并初步接触导数的概念。
5. **指数函数、特性与图形**：深入学习指数函数 f(x)=a^x 的性质，特别是当 a>1 和 0课程评论(0条)
Precalculus 4: Exponentials and logarithmsMathematics from high school to universityS1. Introduction to the courseYou will learn: you will get a very general introduction to exponential and logarithmic functions: how they look and what they describe; you will learn about their simplicity in some aspects, and about some extraordinary complications you don't necessarily have to think about (but you should have a general idea about them); exponential and logarithmic functions are (next to polynomials, rational functions, power functions, trigonometric and inverse trigonometric functions you have learned about in the previous courses in the Precalculus series) examples of elementary functions: these functions are the building blocks for all the functions we will work with in the upcoming Calculus series.S2.71828.The noble number e, the Binomial Theorem, and Pascal's TriangleYou will learn: about number e, both in an intuitive way (by images) and in a more formal way. In order to be able to perform some formal proofs, you will need the Binomial Theorem: theorem telling you how to raise a sum of two terms to any positive natural power; you will learn about factorial, about binomial coefficients, and Pascal's Triangle (all this will come back in the course in Discrete Mathematics, and then you will get much more practice and combinatorial problems to solve; now we just need the Binomial Theorem as a tool for dealing with e).S3. Powers with various types of exponentsYou will learn: about powers with natural, integer, and rational exponents and the computation rules holding for them (the product rules, the quotient rules, the power rule); you will also get an explanation of a more serious stuff: how we can be sure about existence of nth roots of numbers. We will gradually get more and more understanding about the topic of plotting exponential functions. You will also get plenty of exercise to get comfortable with the topic of powers with various types of exponents, and power-related computations.S4. Power functions, their properties and graphsYou will learn: about power functions and their properties: monotonicity for positive arguments, monotonicity for negative arguments, and how the curves y=x^⍺ and y=x^β are situated in relation to each other for various pairs of ⍺ and β (with some cool interactions between power functions and exponential functions); you will also get a glimpse into the world of derivatives, to illustrate the problem of monotonicity of y=x^⍺ for any real non-zero ⍺ and positive arguments x, and to explain the cusps and rounding in some graphs. S5. Exponential functions, their properties and graphsYou will learn: about exponential functions f(x)=a^x with a>1, and f(x)=a^x with 0
