Become a Differential Equations Master

所在平台: Udemy

课程主页: https://www.udemy.com/course/differential-equations-master/

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课程简介

Coursera课程“成为微分方程大师”是一门旨在帮助学习者掌握微分方程知识的综合性课程。本课程共包含260个课时,提供视频和文字讲解,涵盖微分方程的方方面面。此外,课程还设有76个带答案的测验和9个额外的练习手册,以帮助学习者巩固所学知识。 课程内容结构清晰,共分为以下几个主要部分: * **一阶方程**: 包括线性方程、可分离方程和伯努利方程。 * **二阶方程**: 涵盖齐次和非齐次方程、待定系数法和参数变分法。 * **微分方程建模**: 涉及欧拉法、logistic方程、指数增长与衰减、串联电路、弹簧-质量系统。 * **级数解**: 包括幂级数解、非多项式系数和福罗贝尼乌斯定理。 * **拉普拉斯变换**: 涉及拉普拉斯变换与逆变换、二阶移位定理、狄拉克δ函数和卷积积分。 * **微分方程组**: 讲解如何求解具有实数和复数特征值的微分方程组,以及相轨迹、相图和矩阵指数。 * **高阶方程**: 包括非齐次方程、其拉普拉斯变换、高阶方程组及其级数解。 * **傅里叶级数**: 涵盖周期延拓、傅里叶级数收敛性、余弦级数、正弦级数和分段函数。 * **偏微分方程**: 涉及分离变量法与边值问题、热传导方程和拉普拉斯方程。 课程的每个部分都包含以下内容: * **视频**: 讲师将演示如何解决所有遇到的数学问题,从基础开始,详细解释问题设置、解题步骤、中间过程的技巧以及最终答案的简化。 * **笔记**: 提供课程精华内容,如同书籍的“精读笔记”,包含通过课程所需的一切关键信息。 * **测验**: 帮助学习者检验对特定主题的掌握程度。 * **练习手册**: 提供额外的练习题目,帮助学习者系统地复习和巩固已学内容。 此外,本课程还提供终身访问权限、Q&A区的友好支持、可下载的Udemy结业证书,并享有30天退款保证。讲师 Krista King 以其清晰的讲解、丰富的例题和易于理解的教学方法而受到学生好评。

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课程详情

HOW BECOME A DIFFERENTIAL EQUATIONS MASTER IS SET UP TO MAKE COMPLICATED MATH EASY:This 260-lesson course includes video and text explanations of everything from Differential Equations, and it includes 76 quizzes (with solutions!) and an additional 9 workbooks with extra practice problems, to help you test your understanding along the way. Become a Differential Equations Master is organized into the following sections:First order equations, including linear, separable, and Bernoulli equationsSecond order equations, including homogeneous and nonhomogeneous equations, undetermined coefficients, and variation of parametersModeling with differential equations, including Euler's method, the logistic equation, exponential growth and decay, electrical series, spring and mass systemsSeries solutions, including power series solutions, nonpolynomial coefficients, and Frobenius' TheoremLaplace transforms, including Laplace and inverse Laplace transforms, the Second Shifting Theorem, Dirac delta functions, and convolution integralsSystems of differential equations, including solving systems with real and complex Eigenvalues, trajectories and phase portraits, and the matrix exponentialHigher order equations, including nonhomogeneous equations, their Laplace transforms, systems of higher order equations, and their series solutionsFourier series, including periodic extensions, convergence of a Fourier series, Fourier cosine series and Fourier sine series, and piecewise functionsPartial differential equations, including separation of variables and boundary value problems, the heat equation, and Laplace's equationAND HERE'S WHAT YOU GET INSIDE OF EVERY SECTION:Videos: Watch over my shoulder as I solve problems for every single math issue you'll encounter in class. We start from the beginning.I explain the problem setup and why I set it up that way, the steps I take and why I take them, how to work through the yucky, fuzzy middle parts, and how to simplify the answer when you get it.Notes: The notes section of each lesson is where you find the most important things to remember. It's like Cliff Notes for books, but for math. Everything you need to know to pass your class and nothing you don't.Quizzes: When you think you've got a good grasp on a topic within a course, you can test your knowledge by taking one of the quizzes. If you pass, great! If not, you can review the videos and notes again or ask for help in the Q & A section.Workbooks: Want even more practice? When you've finished the section, you can review everything you've learned by working through the bonus workbook. The workbooks include tons of extra practice problems, so they're a great way to solidify what you just learned in that section.HERE'S WHAT SOME STUDENTS HAVE TOLD ME ABOUT MY COURSES:"King is a thorough teacher, her course is broken up into easily-digestible parts. Do some every day - and before you know it, you have a better understanding of math!" - KDH."Once again, just like with Krista King's other courses, I got to enjoy clear explanations, and multiple examples, and discovered an unsuspected passion for math within myself. Highly recommended!" - Juan C."Straight forward and time-saving - thank you!" - Luisa B.YOU'LL ALSO GET:Lifetime access to Become a Differential Equations MasterFriendly support in the Q & A sectionUdemy Certificate of Completion available for download30-day money back guaranteeEnroll today!I can't wait for you to get started on mastering Differential Equations.- Krista:)

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