|
所在平台: Coursera |
课程主页: https://www.coursera.org/learn/calculus-through-data-and-modelling-precalculus-review
课程评论：没有评论
课程名称：通过数据与建模的微积分：初等数学复习 课程概述：此课程采用以应用为导向的探究方式，研究单变量和多变量微积分所需的数学主题。该课程的统一主题是函数的研究，包括多项式函数、理性函数、指数函数、对数函数和三角函数。特别强调利用这些函数进行数据建模和分析。课程中将使用图形计算器和/或计算机作为重要工具。 课程大纲： 1. **指数和对数函数** 本模块将回顾初等数学中的一些关键概念。指数和对数函数在建模自然现象时常被使用，对于微积分也至关重要。在应用环境中，指数函数建模时独立变量的恒定变化会引起依赖变量的相同比例变化（即百分比增加或减少），这一现象广泛存在于自然和社会科学中，如自我繁殖的种群、复利积累的基金或不断增长的制造业专长。 2. **三角函数** 三角函数同样重要，是最常见的周期性或循环函数之一。常见现象表现出振荡或周期性行为，如海浪、声波乃至心跳的规律。这些现象可以通过基于熟悉的正弦和余弦函数的方程来建模。在此模块中，我们将学习如何应用和构建能够模拟循环行为的函数。 3. **空间中的向量** 在经典的欧几里得几何中，向量是具有相同大小和方向的定向线段的等价类。向量在抽象意义上及其应用中均有重要作用，尤其是在物理学中，欧几里得向量用于表示既有大小又有方向的物理量，而标量则没有方向。比如，速度、力和加速度都用向量表示。本模块将专注于研究在xy平面和“三维”空间中的向量。 4. **直线和平面的方程** 在继续研究多维解析几何的过程中，向量被应用于创建代数方程，以描述空间中的常见物体，如直线和平面。此模块将测试你可视化代数方程的能力，并通过进行代数运算来创建和控制这些物体在空间中的运动，为我们在更高维对象上的多变量微积分学习奠定坚实基础。 5. **初等数学复习期末考试** 此评估将帮助识别你基础材料中的强项和弱点，以便在单变量和多变量微分微积分的学习中取得成功。请将此评估作为追踪后续学习和寻找更多资源和示例的指南。 此课程为学习微积分打下坚实的基础，适合希望准备好进行更深入数学学习的学生。
Name:Exponential and Logarithmic Functions
Description:In this module, we will review some of the key concepts from Precalculus. Exponential and logarithmic functions arise often when modeling natural phenomena, and are important to Calculus. In applied settings, exponential functions model a relationship in which a constant change in the independent variable gives the same proportional change (i.e., percentage increase or decrease) in the dependent variable. This occurs widely in the natural and social sciences, as in a self-reproducing population, a fund accruing compound interest, or a growing body of manufacturing expertise. Thus, the exponential function also appears in a variety of contexts within physics, chemistry, engineering, mathematical biology, and economics.
Name:Trigonometric Functions
Description:Equally important are the trigonometric functions, some of the most well-known examples of periodic or cyclic functions. Common phenomena have an oscillatory, or periodic, behavior. This is observed through ocean waves, sound waves, or even the regular beating of your heart. All these phenomena can be modeled using equations based on the familiar sine and cosine functions. In this module, we will see how to apply and construct functions that permit us to model cyclic behavior.
Name:Vectors in Space
Description:In classical Euclidean geometry, vectors are an equivalence class of directed segments with the same magnitude (e.g., the length of the line segment (A, B)) and same direction (e.g., the direction from A to B). Vectors are used both in abstract sense as well as for applications, particularly in physics, Euclidean vectors are used to represent physical quantities that have both magnitude and direction, but are not located at a specific place, in contrast to scalars, which have no direction. For example, velocity, forces and acceleration are represented by vectors. In this module, we will study vectors specifically in the xy-plane and in "3D" space.
Name:Equations of Lines and Planes
Description:Continuing our study of multi-dimensional analytic geometry, vectors are now applied to create algebraic equations to describe common objects like lines and planes in space. This module will test your ability to visualize algebraic equations and to create movement and thus control of these objects in space by performing algebraic manipulations. This will create a solid foundation for our study of multivariable calculus on these higher dimensional objects.
Name:Precalculus Review Final Exam
Description:The assessment below will help to identify strengths as weaknesses in your foundational material in order to be successful in single and multivariable differentiable calculus. Use the assessment below as a guide as to where to follow up and seek out more resources and examples.
This course is an applications-oriented, investigative approach to the study of the mathematical topics needed for further coursework in single and multivariable calculus. The unifying theme is the study of functions, including polynomial, rational, exponential, logarithmic, and trigonometric functions. An emphasis is placed on using these functions to model and analyze data. Graphing calculators and/or the computer will be used as an integral part of the course.
