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所在平台: Udemy |
课程主页: https://www.udemy.com/course/cambridge-international-a-level-maths-pure-2-3/
课程评论：没有评论
**课程名称：** CIE International A-Level 数学：纯数学 2/3 **课程概述：** 本课程全面涵盖剑桥国际 A-Level 数学考试 Papers 2 和 3（纯数学 2 和 3）的所有纯数学内容。它也适合任何对学习更高级纯数学感兴趣的人。 **主要学习内容：** * **代数：** 模函数及其方程和不等式的解法，多项式除法，余数定理和因子定理。 * **对数与指数函数：** 直观理解对数和指数函数，并学习如何应用它们解决各类问题，包括 $e^x$ 和自然对数。 * **三角学：** 学习三种新的三角函数（sec, cosec, cot）以及新的三角恒等式，包括二倍角公式。 * **微分：** 学习各种函数的微分方法，包括链式法则、乘积法则、商法则，以及隐函数和参数方程微分。 * **积分：** 学习用于积分的多种技巧，以处理目前所学的大部分函数。 * **方程的数值解：** 探索求解无解析解方程的近似方法，包括迭代法。 * **进阶代数：** 学习代数分式分解为部分分式，以及如何将二项式展开扩展到负指数和分数指数。 * **进阶积分：** 扩展积分技巧，学习逆链式法则、换元积分法和分部积分法。 * **向量：** 学习如何在三维空间中操作向量，以及直线方程和标量（点）积的应用。 * **微分方程：** 学习如何建立和求解微分方程，并了解其在实际中的应用。 * **复数：** 探索复数，包括阿甘图、极坐标形式、指数形式以及复数轨迹。 **适用人群：** * 学习剑桥国际 A-Level 数学课程的学生。 * Paper 3 考生将涵盖所有内容。 * Paper 2 考生将学习至“方程的数值解”部分。 **注意：** 本课程仅针对剑桥国际 A-Level 数学考试大纲，不适用于英国本土的考试大纲（如 Edexcel, OCR, AQA, MEI）。 **课程形式：** * **视频讲解：** 细致讲解每个主题的关键概念，并通过大量例题展示解题方法，指出常见误区。 * **随堂测验：** 每个小节后提供测验，巩固所学知识。测验题目多来自真实 A-Level 考题。 * **练习题：** 每章末提供精选的真实 A-Level 考题集，帮助巩固和应用所学内容。提供详细的评分标准。 **课程福利：** * 可获得可打印的 Udemy 结业证书。 * 在问答区获得支持，解决学习难题。 **讲师：** Woody
CIE International A-Level Maths is a course for anyone studying the Cambridge International A-Level Maths:This course covers all the pure content in Papers 2 and 3 (Pure Mathematics 2 and 3) of the Cambridge International A-Level Maths Course. It is also a great course for anyone interested in learning some more advanced pure maths.The main sections of the course are:- Algebra - we'll learn about the modulus function and how to solve equations and inequalities using it, as well as polynomial division, remainders and the factor theorem.- Logarithms and Exponentials Functions - we'll learn what these are, and how to use them to solve many different styles of problems. We'll also learn about e^x and the natural logarithm.- Trigonometry - we'll learn three new trig functions (sec, cosec and cot) as well as explore many new trigonometric identities, including double angles.- Differentiation - we'll learn how to different almost any function you can think of! We'll use the chain, product and quotient rules and also look at implicit and parametric differentiation.- Integration - we'll learn a range of techniques to integrate most functions we've seen so far.- Numerical Solutions to Equations - We'll explore ways of finding approximate solutions to equations with no analytical solutions, including iteration.- Further Algebra - we'll learn how to split algebraic fractions into partial fractions, and how to extend binomial expansion to include negative and fractional powers.- Further Integration - We'll extend what we've already covered, and look at reverse chain rule, substitution and integration by parts.- Vectors - we'll learn how to work with vectors in 3d and how to use the vector equation of straight lines and the scalar (dot) product.- Differential Equations - we'll explore how to set up and solve differential equations, and how to apply these in real world contexts.- Complex Numbers - we'll explore the fascinating world of complex numbers, including the argand diagram, polar and exponential forms, and complex loci.Those of you studying for Paper 3 will cover all of these section. If you're studying for Paper 2, you will study up to Numerical Solutions to Equations.Please note: This course is intended for people studying the Cambridge International A-Level Maths Syllabus, and not the UK syllabus (covered by Edexcel, OCR, AQA and MEI exam boards). If you are looking for these, check out my other courses on these!What you get in this course:Videos: Watch as I explain each topic, introducing all the key ideas, and then go through a range of different examples, covering all the important ideas in each. In these videos I also point out the most common misconceptions and errors so that you can avoid them.Quizzes: Each sub-section is followed by a short quiz for you to test your understanding of the content just covered. Most of the questions in the quizzes are taken from real A-Level past papers. Feel free to ask for help if you get stuck on these!Worksheets: At the end of each chapter I have made a collection of different questions taken from real A-Level past papers for you to put it all together and try for yourself. At the bottom of each worksheet is a full mark-scheme so you can see how you have done.This course comes with:· A printable Udemy certificate of completion.· Support in the Q & A section - ask me if you get stuck!I really hope you enjoy this course!Woody
