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所在平台: Udemy |
课程主页: https://www.udemy.com/course/become-a-calculus-master-in-easy-way/
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## Coursera 课程精粹：轻松成为微积分大师 本课程旨在帮助您系统掌握微积分的核心概念和应用，让学习过程轻松易懂，化繁为简。 **课程亮点：** * **多维度深入学习：** 涵盖连续性与可导性、导数的应用、积分及其应用，以及微分方程的基本概念与解法。 * **核心概念梳理：** 深入讲解复合函数求导、链式法则、反三角函数与隐函数求导，以及指数、对数函数的概念。 * **导数的实际应用：** 探索导数在变化率、函数增减、切线法线、近似计算以及求极值（通过几何直觉和二阶导数测试）等方面的应用，并结合生活实例进行讲解。 * **积分的奥秘：** 将积分视为微分的逆运算，掌握代换法、分部积分法、部分分式法等多种积分技巧，并讲解定积分的概念、性质及其应用，包括计算曲线下的面积以及两条曲线之间的面积。 * **微分方程入门：** 学习微分方程的定义、阶数、次数，以及通解与特解的求法，重点掌握变量分离法和一阶齐次微分方程的解法。 **课程目标：** 通过本课程的学习，您将： * **系统掌握微积分理论：** 建立深厚的微积分理论基础，理解其内在逻辑。 * **熟练运用数学工具：** 掌握多种数学工具和技巧，能够解决实际问题。 * **提升逻辑思维能力：** 培养严谨的数学思维和逻辑推理能力。 * **为进一步学习打下坚实基础：** 为后续更高级的数学和科学课程做好充分准备。 无论您是希望巩固现有知识，还是希望零基础入门微积分，本课程都将是您的理想选择，助您轻松跨越微积分的学习障碍，成为真正的微积分大师！
In this course you will learn following topics:Calculus1. Continuity and DifferentiabilityContinuity and differentiability, derivative of composite functions, chain rule, derivative of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions.2. Applications of DerivativesApplications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).3. IntegralsIntegration as inverse process of differentiation.Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof).Basic properties of definite integrals and evaluation of definite integrals.4. Applications of the IntegralsApplications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only), Area between any of the two above said curves (the region should be clearly identifiable).5. Differential EquationsDefinition, order and degree, general and particular solutions of a differential equation.formation of differential equation whose general solution is given.Solution of differential equations by method of separation of variables, solutions of homogeneous differential equations of first order and first degree.All about Microeconomics for Student and TeacherLearn Microeconomics and get some help for your exams and knowledge purposeObjectives:· Understanding of some basic economic concepts and development of economic reasoning which the learners can apply in their day-to-day life as citizens, workers and consumers.· Realisation of learners' role in nation building and sensitivity to the economic issues that the nation is facing today.· Equipment with basic tools of economics and statistics to analyse economic issues. This is pertinent for even those who may not pursue this course beyond senior secondary stage.· Development of understanding that there can be more than one view on any economic issue and necessary skills to argue logically with reasoning.
