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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/precalculus-relations-functions
课程评论：没有评论
课程名称：预备微积分：关系与函数 课程概述：本课程旨在建立数学基础，使学生能够将数学作为工具来建模、理解和解释周围的世界。通过研究函数及其特性，以及在数据分析中的应用，学生将掌握预备微积分的概念，为未来的科学学习和微积分课程做好准备。本课程适合所有学生，尤其是那些对自然科学、计算机科学、心理学、社会学或相关领域感兴趣的学生，会从中获益匪浅。课程内容结合真实数据、练习和定期评估，旨在激发学生的学习兴趣并巩固所学知识。 课程大纲： 模块1：基础及常见函数 描述：函数用于研究两个或多个变量之间的关系，是可视化、分析和解释这些关系的基本定量工具。本模块将介绍函数的概念，并复习课程后期用到的重要代数运算，同时研究图形的关键特征，如定义域、值域和末尾行为。 模块2：直线方程、二次方程及更多函数 描述：本模块将研究两种常见类型的函数：线性函数和二次函数。我们将学习如何识别其图形的共同特征，以及如何将其应用于现实情境建模，特别是在收入和成本方面。此外，还将进一步探讨函数的复合及如何求取函数的逆。 模块3：指数函数和对数函数 描述：在本模块中，我们将扩展函数的种类，学习在建模自然现象中出现的指数函数和对数函数。我们之前看到一对一函数具有逆函数，可以逆转函数过程。例如，函数 f(x) = x^3 的逆为 g(x) = x^(1/3)。现在我们将扩展这个过程，以求取指数函数的逆，即形如 f(x) = a^x 的函数，其中 a 为不等于一的正数。 模块4：对数的性质 描述：理解对数作为指数的概念能够揭示对数的重要代数性质。本模块将探讨这些性质及其在实际例子中的应用。
Name:Module 1: Basics and Common Functions
Description:Functions help to study the relationship between two or more variables. They are the basic quantitative tool used to visualize, analyze, and interpret these relationships. Studying functions is the first step in developing analytics skills for mathematical modeling. In this module, we develop the concept of a function and review important algebraic operations on functions used later in this course. We will also study the important features, like domain, range, and end behavior of graphs.
Name:Module 2: Equations of Lines, Quadratics, and More Functions
Description:In this module, we will study two common types of functions: linear and quadratic. We will learn how to identify common features of their graphs, and see how they can be used to model real world situations, particularly those involving revenue and cost. We will also further explore function compositions, and learn how to find the inverse of a function.
Name:Module 3: Exponential and Logarithmic Functions
Description:In this module, we expand our catalog of functions to study two new functions that arise when modelling natural phenomena: the exponential and logarithmic functions. In the last module, we saw that one-to-one functions have inverses, which reverse the function process. For example, the function f(x) = x^3 has as its inverse the function g(x) = x^(1/3). We now want to expand this process to find inverses for exponential functions - those of the form f(x) = a^x, where a is a positive number not equal to one.
Name:Module 4: Properties of Logarithms
Description:Understanding the logarithm as an exponent allows for important algebraic properties of the logarithm. In this module, we will explore these properties and their uses as we apply logarithms to real world examples.
This course helps to build the foundational material to use mathematics as a tool to model, understand, and interpret the world around us. This is done through studying functions, their properties, and applications to data analysis. Concepts of precalculus provide the set of tools for the beginning student to begin their scientific career, preparing them for future science and calculus courses. This course is designed for all students, not just those interested in further mathematics courses. Students interested in the natural sciences, computer sciences, psychology, sociology, or similar will genuinely benefit from this introductory course, applying the skills learned to their discipline to analyze and interpret their subject material. Students will be presented with not only new ideas, but also new applications of an old subject. Real-life data, exercise sets, and regular assessments help to motivate and reinforce the content in this course, leading to learning and mastery.
