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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/precalculus-mathematical-modelling
课程评论：没有评论
课程名称：预备微积分：数学建模 概述：本课程旨在帮助学生建立基础知识，将数学作为工具来建模、理解和解释周围世界。通过研究函数及其特性，以及应用于数据分析的实用例子，学生将在这一过程中掌握预备微积分的基本概念，为未来的科学和微积分课程做好准备。该课程面向所有学生，不仅限于有意继续数学学习的学生。自然科学、计算机科学、心理学、社会学等领域的学生都将从这一入门课程中受益，将所学技能应用于各自的学科，以分析和解释相关材料。课程中将介绍新观念及其在旧学科中的新应用，借助真实数据、练习题和定期评估，激励和巩固学习内容，促进知识的掌握。 课程大纲： 模块1：线性建模 在这一模块中，学生将探讨如何创建、获取、检查和利用数据来影响日常生活。课程将重点介绍数据的可视化、大数据集的表现、不同的数据模型及其统计检测方法，以及如何有效沟通模型结果，避免过度推断或夸大结论。 模块2：指数建模 本模块介绍了指数函数，这是本课程及后续微积分课程中最重要的函数之一。学员将学习如何利用指数函数建模自然现象，如人口增长、疾病传播和药物在体内的消除等。 模块3：其他函数建模 在这一模块中，学生将使用多项式、周期性和幂函数等其他函数来建模特定行为。 模块4：维度分析 这一模块探讨了在工程和科学中，如何通过识别基本物理量（如长度、质量、时间和电荷）及其测量单位，分析不同物理量之间的关系。学生将学习维度分析，具体包括因子-标签方法，并将其应用于衡量爆炸强度。
Name:Module 1: Linear Modeling
Description:Data is all around us, Trillions of terabytes of data are generated and recorded daily by just using a smartphone, driving a car, or using a credit card. In this course, students examine how data is created, obtained, examined, and used to shape everyday life. To understand an analyze this data, researchers in diverse fields conjecture models based on their data. With more data, they modify and update the model accordingly. The model is then tested to validate results and conclusions. This module will help you to visualize large data sets, present different models for data, and statistics to measure how good the model is to the data. We will also focus on how to communicate the results of the models and common pitfalls to avoid overreaching or overstating your conclusions.
Name:Module 2: Exponential Modeling
Description:Perhaps the most important function of this course and your future courses in calculus, the exponential function is introduced to model many natural phenomena. For example, this function is used to measure population growth, the spread of a disease, and the elimination of drug from the body. Types of interest and present value calculations will require the understanding and use of the exponential functions. We will allow the exponential to have any positive base, but the natural exponential, that with e = 2.718.. will be our main object of study.
Name:Modeling with Other Functions
Description:In this module, we will use other functions to model specific behavior, such as polynomial, periodic and power functions.
Name:Module 4: Dimensional Analysis
Description:In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric charge) and units of measure (such as miles vs. kilometres, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed. In this module, we will study dimensional analysis, or more specifically the factor-label method and apply it to measure the strength of an explosion.
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.
