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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/algebra-ii
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课程名称：代数：从初级到高级 - 函数与应用 课程概述：完成本课程后，学生将学会如何成功地应用函数来对不同的数据和现实世界事件进行建模。本课程首先回顾函数的概念，然后提供多种常见和不常见的函数类型实例，适用于各种学科。通过代数和分析技术，分析公式、定义域、值域、图形、截距及基本行为。从这一核心函数集出发，通过算术运算和函数组合创建新函数，并将这些函数应用于解决现实问题。能够描绘多种不同类型的函数将帮助学生了解如何以及何时应用这些函数，并给予学生几何直观，以理解代数技术。本课程的技能和目标将提升学生的解题能力。 课程大纲： 模块一：函数简介 描述：当两个变量之间存在一个常量的增加或减少关系时，即为线性关系。线性函数具备独立变量变化时，依赖变量也会相应比例变化的特性。许多物理情况可以通过线性关系建模。在线性函数中加入形如 ax^2 的额外项，即可形成二次函数，其图形为抛物线。本模块将展示线性和二次函数及其应用的实例。 模块二：其他常见函数 描述：在上一模块中，我们介绍了函数的重要概念，并讨论了线性和二次函数。在本模块中，我们将讨论如何利用已知函数构建新的函数。一种方法是使用先前介绍的图形移动技术。这些方法得到了进一步的发展，并应用于新函数的构建。构建图形往往是解决问题的重要第一步。能够描绘的函数越多，解题能力就越强。 期末考试：函数与应用 描述：恭喜你完成课程，迎来了期末考试！本次期末评估将涵盖课程的所有内容。将此期末考试作为一个学习工具：证明你的知识并识别待改进的领域。在考试时，使用草稿纸，并尝试将任何公式表或外部资源作为工具，而非依赖。提交前检查答案。在考试后，回顾任何错误答案以找出自己的失误，努力区分“愚蠢”的错误和理解上的更本质错误。祝你好运！
Name:Module 1: Introduction to Functions
Description:A linear relationship between two variables occurs when there is a constant increase or constant decrease in one variable with respect to the other. Linear functions have the property that any chance in the independent variable results in a proportional change in the dependent variable. Many physical situations can be modeled using a linear relationship. Adding an extra term of the form ax^2 to a linear function creates a quadratic function, and its graph is the parabola. We will see examples of linear and quadratic functions and their applications in the sections that follow.
Name:Module 2: Other Common Functions
Description:In the last module we introduced the important concept of a function and considered the linear and quadratic functions. In this module, we discuss methods for building new functions from those that are already familiar to use. One method will use the graph shifting techniques already introduced. These methods are developed further and applied to new functions. Constructing a graph is often an important first step in solving a problem. The more functions you can picture, the better problem solver you will be.
Name:Final Exam: Functions and Applications
Description:Congratulations on reaching the final exam! This final assessment will be cumulative in nature, covering all aspects of the course. Use this final as a teaching tool: justify what you know and identify areas for improvement. Use scrap paper as you take this final. Try to use any formula sheets or outside resources as a tool and not a crutch. Check your answers before you submit. After the test, review any incorrect answers to find your mistakes. Try to separate "silly" mistakes from the more substantial mistakes in understanding. Good luck!
After completing this course, students will learn how to successfully apply functions to model different data and real world occurrences. This course reviews the concept of a function and then provide multiple examples of common and uncommon types of functions used in a variety of disciplines. Formulas, domains, ranges, graphs, intercepts, and fundamental behavior are all analyzed using both algebraic and analytic techniques. From this core set of functions, new functions are created by arithmetic operations and function composition. These functions are then applied to solve real world problems. The ability to picture many different types of functions will help students learn how and when to apply these functions, as well as give students the geometric intuition to understand the algebraic techniques. The skills and objectives from this course improve problem solving abilities.
