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所在平台: Udemy |
课程主页: https://www.udemy.com/course/a-complete-guide-to-integral-calculus-advanced-calculus/
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课程名称：全面的积分微积分指南（高级微积分） 课程概述： 本课程《全面的积分微积分指南（高级微积分）》在基础微积分的基础上，深入探讨多维函数的行为及其应用。课程重点是积分微积分，同时介绍一些关键的向量微积分概念，包括绿色定理、斯托克斯定理和散度定理等重要定理。该课程对于希望在现实问题解决中获得实际和理论理解的数学、物理、工程等领域的学生至关重要。 适合人群： 本课程特别适合正在学习高级微积分的大学生，或已经完成微积分III和线性代数的学生。同时也适合任何渴望深入探索多变量微积分应用的人，尤其是在需要微积分技术的领域。 课程内容： 此课程涵盖积分微积分，是完整高级微积分系列的第一部分。您将可以访问讲座视频、黑板笔记以及带答案的问题集。课程内容包括： - 两变量函数：探讨极坐标中的雅可比行列式、双重积分中的变量变换及其应用。 - 伽马函数与拉普拉斯变换：理解与伽马函数相关的关键积分、伽马函数本身及拉普拉斯变换。 - 三变量函数：学习柱面和球面坐标中的雅可比行列式、三重积分中的变换及其应用。 - 表面和表面积分：计算不同坐标系（笛卡尔、柱面和球面）中的表面面积并评估表面积分。 - 向量微积分、积分定理及多变量微积分的微分计算（完整课程中提供）。 课程亮点： - 终身访问《全面的积分微积分指南（高级微积分）》。 - 可下载的讲座视频和笔记，便于随时复习。 - 两个综合性问题集及解决方案，以巩固学习。 - 导师全程致力于您的成功和学习进步。 期待您加入课程！- 吉娜·周
How This Course WorksThis course, A Complete Guide to Integral Calculus (Advanced Calculus), builds upon foundational calculus to dive deeply into the behavior and applications of functions in multiple dimensions. Focusing on integral calculus, it also provides an introduction to key vector calculus concepts that follow in the complete series, including major theorems like Green's, Stokes', and the Divergence Theorem. This course is essential for students in mathematics, physics, engineering, and other fields who want a practical and theoretical understanding of multivariable calculus tools for real-world problem-solving.Who Should Take This Course?This course is ideal for university students currently enrolled in Advanced Calculus, or those who have completed Calculus III and Linear Algebra. It's also designed for anyone eager to explore multivariable calculus applications more deeply, especially in fields where calculus techniques are indispensable.Course OverviewThis course includes Integral Calculus, the first part of the complete Advanced Calculus series. You'll have access to lecture videos, whiteboard notes, and problem sets with solutions. Topics covered here include:Integral Calculus (Sections Included in This Course)Two-Variable Functions: Explore Jacobians in polar coordinates, variable changes in double integrals, and applications of double integrals.Gamma Function and Laplace Transform: Understand a key integral related to the Gamma function, the Gamma function itself, and the Laplace transform.Three-Variable Functions: Learn about Jacobians in cylindrical and spherical coordinates, transformations in triple integrals, and applications of triple integrals.Surface Area and Surface Integrals: Calculate surface areas and evaluate surface integrals in Cartesian, cylindrical, and spherical coordinates.Vector Calculus, Integral Theorems, and Differential Calculus of Several Variables (Available in the Complete Course)Vector and Scalar FieldsLine IntegralsFlux, Circulation, and Vector OperatorsIntegral TheoremsIntroduction to Partial Differential EquationsTopics in Differential Calculus of Several VariablesCourse ContentVideos: Each topic is introduced and explained thoroughly, with step-by-step examples, making complex problems manageable.Notes: Downloadable lecture notes for each section to allow for offline review and reinforcement.Assignments: Practice problem sets with solutions so you can check your work after attempting each problem yourself.Highlights of What's IncludedLifetime access to A Complete Guide to Integral Calculus (Advanced Calculus).Downloadable lecture videos and notes for anytime review.Two comprehensive problem sets with solutions to reinforce learning.An instructor committed to your success every step of the way.See you inside the course!- Gina Chou:)
