|
所在平台: Udemy |
课程主页: https://www.udemy.com/course/calculus-2-auk-aum/
课程评论：没有评论
Calculus 2 - AUK (منهج د. إلهام) 是一门课程，旨在全面探索积分微积分及其应用。课程建立在基础概念之上，发展对关键数学技术和定理的深刻理解。 **主要内容包括：** * **积分基础：** 区域与距离，涉及计算曲线下的面积和函数间的面积。 * **微积分基本定理：** 连接微分与积分，用于高效解决实际问题。 * **不定积分与净变化定理：** 学习数量的累积。 * **积分技巧：** 替换积分法、分部积分法、三角积分、三角替换法、部分分式分解积分法。 * **特殊积分：** 瑕积分，探讨积分应用于具有无穷极限或不连续性的函数。 * **几何应用：** 弧长计算。 * **序列与级数：** 引入无穷过程，包括积分判别法、交错级数判别法、比值和根值判别法等收敛性检验。 * **幂级数：** 泰勒级数和麦克劳林级数，用于函数逼近，为高等数学和科学研究奠定基础。 本课程为学习者提供了扎实的积分微积分知识和应用能力。
Course contentAreas and DistancesThe Fundamental Theorem of CalculusIndefinite Integrals and the Net Change TheoremThe Substitution RuleAreas Between CurvesIntegration by PartsTrigonometric IntegralsTrigonometric SubstitutionIntegration of Rational Functions by Partial Fractionsimproper integralArc LengthSequencesSeriesThe Integral TestAlternating SeriesAbsolute Convergence and the Ratio and Root TestsPower SeriesTaylor and Maclaurin SeriesThis course provides a comprehensive exploration of integral calculus and its applications, building on foundational concepts to develop a deep understanding of key mathematical techniques and theorems. The content begins with areas and distances, introducing integral concepts to calculate areas under curves and between functions. The Fundamental Theorem of Calculus is presented as a cornerstone, linking differentiation and integration to solve real-world problems efficiently.Learners will master indefinite integrals and explore the Net Change Theorem, which highlights the accumulation of quantities. The course delves into the Substitution Rule, a vital tool for simplifying complex integrals. Applications such as finding areas between curves, using integration by parts, and handling trigonometric integrals further enhance practical skills. Techniques like trigonometric substitution and partial fractions are introduced to solve challenging rational function integrals. The concept of improper integrals extends the applicability of integration to functions with infinite limits or discontinuities.The course also explores geometric applications, including arc length calculations. A transition to infinite processes is made through sequences and series, where students learn the Integral Test, Alternating Series Test, and convergence techniques such as the Ratio and Root Tests. Finally, the exploration of power series and Taylor and Maclaurin Series equips students with tools for approximating functions, laying the foundation for advanced mathematical and scientific studies.4o
