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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/precalculus-periodic-functions
课程评论：没有评论
课程名称：预备微积分：周期函数 课程概述：本课程旨在建立使用数学作为工具以建模、理解和诠释周围世界的基础材料。通过学习函数及其性质和数据分析的应用，学生将掌握预备微积分的概念，为未来的科学和微积分课程打下基础。本课程适合所有学生，不仅限于有意进一步学习数学的学生。对自然科学、计算机科学、心理学、社会学等领域感兴趣的学生也将从本课程中获益，能够将所学技能应用于各自学科中进行分析和理解。通过真实数据、习题集和定期评估，本课程的内容得以激励和巩固，从而实现学习和掌握。 课程大纲： 1. **周期函数**：了解周期函数的概念，以及如何通过这些函数建模自然现象，如行星运动、星期与季节的变化等。 2. **直角三角形三角学**：学习正弦、余弦和正切等展现周期行为的函数，并通过直角三角形探讨其代数关系。 3. **正弦和余弦作为周期函数**：使用单位圆定义正弦和余弦，以扩展之前通过直角三角形引入的定义。 4. **正切及其他周期函数**：研究基本周期函数的商和倒数，并注意避免除以零的情况，以完整记录周期函数。 5. **（一些）周期函数的恒等式**：介绍常见恒等式以简化周期函数的运用，强调如何理解和推导更大的恒等式集合。 本课程通过引入新概念和应用，帮助学生掌握如何利用数学分析和解释不同学科的内容。
Name:Module 1: Periodic Functions
Description:In this course, we expand our collection of functions which we can use to model by studying periodic functions. Periodic functions are functions whose graphs repeat themselves after a certain point. It is natural to study periodic functions as many natural phenomena are repetitive or cyclical: the motion of the planets in our solar system, days of the week, seasons, and the natural rhythm of the heart. Thus, the functions introduced in this course add considerably to our ability to model physical processes. In this module, we begin by learning methods of measuring angles.
Name:Module 2: Right Triangle Trigonometry
Description:Many common phenomena have oscillatory or periodic behavior. To model this behavior requires an understanding of functions that exhibit periodic behavior like sine, cosine, and tangent. These functions are introduced using right triangles in this module, which then lets us explore their algebraic relations.
Name:Module 3: Sine and Cosine as Periodic Functions
Description:Sine and cosine are now introduced using the unit circle, which is the circle centered at the origin with radius one. This definition of our key periodic functions extends the definition originally introduced with right triangles.
Name:Module 4: The Tangent and Other Periodic Functions
Description:The most basic periodic functions, sine and cosine, were defined for all real numbers. We now study their quotients and reciprocals. However, care must be taken to ensure we do not divide by zero. In this module, we will complete our catalog of periodic functions
Name:Module 5: (Some) Identities of Periodic Functions
Description:In an effort to simplify the work involving our periodic functions, we introduce common identities. This dramatically increases their usefulness in applications. This module will emphasize the development of a small core of identities that are continually needed and can be used to determine a much larger collection. While the number of identities is small in this module, an understanding of these and how to derive others from them is essential for success as you continue your studies.
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.
