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所在平台: Udemy |
课程主页: https://www.udemy.com/course/a-bootcamp-to-complex-analysis/
课程评论：没有评论
Coursera 课程《复杂分析入门训练营》旨在为学员介绍复变函数理论。课程从复平面、复数的代数与几何性质入手，逐步深入到代数运算、拓扑学、复数动力学、朱利亚集，以及指数函数与虚数单位 i 的关系、解析函数等概念。 与实分析不同，复平面上的无穷趋近方式更加多样。课程的亮点是残数定理，它能够运用技术优势解决实分析无法处理的积分问题。复杂分析在科学、工程及工业领域有着广泛的实际应用。 课程共包含 5 个部分，40 个视频讲座，并配有嵌入式小测验供学员自我评估。为进阶学习者提供了可选的作业，这些作业旨在通过“记忆-理解-应用-评价-创造”的认知层次（布鲁姆分类法）来提升学员的技能，并鼓励学员动笔练习。 课程要求学员具备基本的代数、几何和微积分知识，但也适合初学者作为打下创造性应用基础的入门课程。 课程的学习成果包括：复数（CN）的定义、代数运算、拓扑学、复数动力学、复函数绘图、迭代与朱利亚集、极限与连续性、指数函数与复数（欧拉恒等式）、以及解析函数等。
This course A Bootcamp to Complex Analysis provides an introduction to the theory of complex functions of a complex variable. It opens by introducing the complex plane, followed by the algebra and geometry of complex numbers. Like in Real Analysis, we will make our way through algebraic processing, topology, complex dynamics, Julia sets, the relationship of exponential function and the imaginary unit i, analytic function etc. In this course, we are going to learn different concepts than the ones we have already learned in school as Real Analysis. In real numbers, we can approach infinity by either heading towards the right side or left side on the number scale while in the complex plane, we have infinite ways of approaching infinity. Likewise, with the aid of the Residue theorem, which is the pinnacle of this learning concept, with a technical advantage we shall be able to solve integrals that real analysis is not capable of. Complex analysis has real-life applications spread over all science subjects, all fields of engineering disciplines, and industrial applications too. The course is divided into 5 sections that are spread over 40 video lectures with embedded quizzes for self-assessment and self-evaluation.The optional homework/practice assignments are for advanced learners to take up their skills via stages: Remembering-Understanding-Application-Evaluation-Creation, the cognitive domain of Bloom's Taxonomy. Infact, a significant amount of your learning will happen while completing the homework assignments that will need pen and paper. We anticipate basic knowledge of algebra, geometry, and calculus. However, amateurs can also take this as a primary course for building a level of creative application.Course OutcomesDefinition of CN,It's algebraic processing,Topology,Complex Dynamics,Plotting of complex functions,Iteration - Julia Sets, Limit & Continuity,Exponential function and complex numbers - Euler's Identity,Analytic Functions.
