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所在平台: Udemy |
课程主页: https://www.udemy.com/course/learn-to-sketch-curves-using-calculus/
课程评论：没有评论
课程名称：学习使用微积分绘制曲线 课程概述：曲线绘制是数学问题解决中非常有用的工具，同时也是提高和检验代数理解能力的机会。随着你在学校和大学的学习，代数技能将逐渐受到考验。要成为一名优秀的数学家，你需要理解代数所表达的含义。曲线绘制常常是考试中考查的内容，并且由于需要掌握多种技术，这一主题可能比较具有挑战性。本课程旨在帮助学生掌握这些技术。 虽然计算机程序如Autograph、Desmos、Maple和Matlab可以绘制曲线，但理解曲线的行为依赖于对代数和微积分的理解。本课程将教授多种技术，使你能够成功绘制复杂函数并了解不同图形的行为。 课程结构：课程初期将学习图形变换和微分及其应用，新的概念不需要有先前的了解。我们将从微分的基础开始，讲解不同函数的导数，直至链式法则、乘法法则和商法则。 接下来是曲线绘制部分，我们将学习多种不同的技术： 1. 线性图形：确定图形与坐标轴的交点，处理不同形式的线性方程。 2. 二次图形：学习因式分解、使用二次公式、了解判别式及如何完成平方。 3. 立方及高次多项式：学习余数定理和因式定理，进行多项式除法。 4. 有理函数：了解渐近线及如何判断图形在大正或负x值的行为。 5. 三角函数：学习单位圆上的sin(x)、cos(x)和tan(x)，绘制余弦、正割和余割等变换的三角曲线。 6. 指数和对数函数：学习e^x和对数的基本知识，了解对数法则以及如何解决包含指数和对数的方程。 7. 模函数：学习模函数的图形特征以及y=f(x)和y=f(x)的区别。 每个部分都是从零基础介绍，包括多个示例和练习题。同时，课程中有多次测验来检验理解程度。如有任何问题，欢迎参与讨论并寻求帮助。课程提供100多节讲座和13小时的内容，非常适合学习微积分课程或A-Level数学的学生，或是希望在进入大学相关的数学本科课程前检验和提高数学能力的学习者。
Curve Sketching is an incredibly useful tool in mathematical problem solving, as well as an opportunity to improve and test your algebraic understanding.As you study mathematics through school and college to degree level, your algebraic skills will be increasingly tested. In order to become a strong mathematician, you need to understand what the algebra is telling you. Curve Sketching is often examinable and can be a challenging topic to master due to the multitude of techniques that need to be learnt. This course is here to help.Computer programs like Autograph, Desmos, Maple and Matlab can all plot curves, but understanding why a curve behaves the way it does relies on your understanding of algebra and calculus. Using techniques that we will learn on this course, you will be able to successfully sketch complicated functions and learn about the behaviour of different graphs.The course is structured so that you will learn about Graph Transformations and Differentiation and its uses in the initial sections. You will not need to have met these concepts before. I go through Differentiation from its basics, through the derivatives of different functions, and up to the Chain Rule, Product Rule and Quotient Rule.We then start Sketching, and within this we will learn many different techniques along the way.Linear Graphs:Find where the graph crosses the coordinate axes.Learn how to deal with different forms of Linear equations.Quadratic Graphs: Learn methods of Factorising.Learn how to use the Quadratic Formula.Learn about the Discriminant and what it tells us.Learn how to Complete the Square.Cubics and Higher Polynomials:Learn about the Remainder Theorem and the Factor Theorem.Learn how to perform and use Polynomial Division.Rational Functions:Learn about Asymptotes and how to determine how each section of the graph behaves.Learn how to determine how a graph behaves for large positive or negative values of x.Trigonometric Functions:Learn about sin(x), cos(x) and tan(x) from the Unit Circle.Learn how to sketch cosec(x), sec(x) and cot(x).Learn how to sketch transformations of each trigonometric curve.Exponential and Logarithmic Functions:Learn about e^x and be introduced to Logarithms.Learn about the Laws of Logarithms.Learn how to solve equations involving Exponentials and Logarithms.Modulus Functions:Learn about x and how to sketch a host of graphs involving the Modulus Function. Learn about the difference between y = f(x) and y = f(x).Each of these sections is introduced from scratch and involves several worked examples and exercises for you to complete. There are several quizzes to try along the way to test your understanding, and if there are any problems please do not hesitate to start a discussion and ask for help. With over 100 lectures and 13 hours of content, this course is perfect for anybody studying a Calculus course or A-Level Mathematics, or for those wanting to test and improve their mathematical ability before tackling a Mathematics-related undergraduate degree course at university.
