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所在平台: Udemy |
课程主页: https://www.udemy.com/course/advanced-calculus-of-higher-mathematics/
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**高级高等数学微积分课程总结 (Coursera)** 本课程旨在通过生动有趣的动画，帮助您快速掌握高等数学微积分的精髓。课程内容涵盖从基础概念、公式推导到图形和数值分析，辅以严谨的数学证明和大量的例题解析。 **课程特色：** * **视觉化学习：** 精心设计的动画和图表，使抽象概念变得直观易懂。 * **高效学习：** 视频节奏明快，内容精炼，帮助您在短时间内最大化知识吸收。 * **全面覆盖：** 深入讲解傅里叶级数（包括Parseval恒等式、谐波分析、复数形式）、傅里叶变换、Z变换以及幂级数（包括二项级数）等核心主题。 * **实践导向：** 大量经过详细解答的数值问题和相关示例，强化理解和应用能力。 **课程内容概览：** * **傅里叶级数：** 涵盖基础知识、公式推导、数学证明，以及Parseval恒等式和谐波分析的应用。 * **复数傅里叶级数：** 详细介绍基础、推导过程、数学证明及解题技巧。 * **傅里叶变换：** 讲解图像、正弦/余弦变换、卷积定理，并提供证明和解题方法。 * **Z变换：** 学习基础、收敛域、性质、公式推导、数学证明及逆变换解题。 * **幂级数：** 探索基础、收敛域、收敛半径、收敛区间、项的微分与积分，并包含二项级数的各种解法。 本课程是为那些厌倦冗长讲座，希望以高效、轻松的方式深入学习高等数学微积分的学生量身打造的理想选择。立即加入，开启您的快速学习之旅！
Learn Advanced Calculus of Higher Mathematics through animation. This course includes videos explanation starting right from introduction and basics, then takes graphical and numerical phase with formulas, verification and proofs both graphically and mathematically. At the end it carries plenty of solved numerical problems with the relevant examples. The lectures' videos are appealing, attractive, fancy (with some nice graphic designing), fast and take less time to walk you through the whole lecture. It's a prefect choice for students who feel boredom watching long lectures and wants things to finish them quickly with the maximum knowledge gain. So join me here and do it in a quick and easy way. This course covers the below list of topics:Parseval's Identity of Fourier SeriesIntroductionBasics and Equations, Mathematical ProofsProblem SolutionsHarmonic Analysis of Fourier SeriesIntroduction and BasicsDifferent orders of Harmonic seriesProblem SolutionsComplex Fourier Series Introduction and Basics Prerequisites Equations derivation Mathematical Proofs Problem SolutionsFourier TransformIntroduction and BasicsGraphsFourier Sine TransformFourier Cosine TransformConvolution theoremMathematical ProofsProblem SolutionsZ-TransformIntroduction and BasicsRegion of convergenceProperties of Z-TransformEquation DerivationMathematical ProofInverse Z-Transform Problem SolutionsPower SeriesIntroduction and BasicsRegion of convergenceRadius of convergenceInterval of convergenceDifferentiation of Power seriesIntegration of Power seriesEquation DerivationMathematical ProofsProblem SolutionsBinomial SeriesIntroduction and BasicsPrerequisitesMethods to solve binomial seriesFinite seriesInfinite seriesGeneral TermBinomial series as power seriesProblem Solutions
