|
所在平台: Udemy |
课程主页: https://www.udemy.com/course/ace-calculus-3-in-16-hours-the-complete-course/
课程评论：没有评论
课程名称：16小时掌握微积分3（完整课程） 课程概述：本课程旨在介绍无限序列与级数、向量函数以及多变量函数的导数和积分。课程包含讲座视频、白板笔记以及练习题（附答案）。每个例子和证明的每个步骤都会详细展示。 课程内容： 1. 无限序列：序列的收敛性、序列的性质（单调性和有界性）。 2. 无限级数：特殊级数（几何级数、望远镜级数、调和级数）、六种收敛/发散测试（发散测试、积分测试、比较测试、极限比较测试、交替测试、比率测试和根测试）。 3. 幂级数：泰勒级数和麦克劳林级数、泰勒不等式、三种方法（直接计算、逐项求导/积分以及利用幂级数的求和、乘法和除法）。 4. 向量与空间几何：向量的运算（点积、投影和叉积）、三维空间中的直线和平面方程、三维曲面。 5. 向量函数：向量函数的导数和积分、弧长与曲率、弗雷内-塞雷特方程、空间运动（速度和加速度）。 6. 偏导数：多变量函数、偏导数的解释、切平面、线性近似、链式法则、差分法、梯度向量和方向导数、寻找多变量函数的极值、拉格朗日乘数法。 7. 多重积分：双黎曼求和、估算曲面下的体积、迭代/双重积分、一般区域的双重积分、极坐标下的双重积分、曲面面积。 每个部分的内容： - 视频：介绍和解释概念，展示解题技巧以及课堂中可能遇到的数学问题。 - 笔记：提供可下载的讲座笔记，让您即使没有互联网也能复习（鼓励上课时做自己的笔记）。 - 作业：观看示例后，自己动手解决问题！在检查答案之前务必诚实完成练习。如果需要，可以反复查看视频和笔记再进行练习。 课程亮点： - 关心您成功的讲师 - 终身访问“16小时掌握微积分3（完整课程）” - 可下载的讲座视频和笔记 - 每部分附有七个练习题集（附答案）以供更多练习 - 分步指南以帮助解决问题 期待在课程中见到您！- Gina :)
HOW THIS COURSE WORK:This course, Ace Calculus 3 in 16 Hours (The Complete Course), is intended to introduce student to the study of infinite sequences and series, vector functions, and derivatives and integrals for multivariable functions. The course includes videos, notes from whiteboard during lectures, and practice problem sets (with solutions!). I also show every single step in examples and proofs. The course is organized into the following topics:Section 2: Infinite SequencesConvergence of a sequenceProperties of a sequence: monotonic and boundedSection 3: Infinite SeriesSpecial series: geometric series, telescoping series, harmonic seriesSix convergence/divergence tests: test for divergence, integral test, comparison test, limit comparison test, alternating test, ratio test, and root testSection 4: Power SeriesTaylor series and Maclaurin seriesTaylor's inequalityThree methods: direct computation, use term-by-term differentiation/integration, and use summation, multiplication, and division of power seriesSection 5: Vectors and the Geometry of SpaceVectorsOperations of vectors: the dot product, projection, and cross productEquations of lines and planes in 3DSurfaces in 3DSection 6: Vector FunctionsDerivative and integral of vector functionsThe arc length and curvatureFrenet-Serret EquationsMotion in Space: Velocity and AccelerationSection 7: Partial DerivativesMultivariable functionsPartial derivativesInterpretations of partial derivativesTangent planesLinear approximationsChain ruleDifferentiationThe gradient vector and directional derivativesFinding extreme values of a multivariable functionLagrange multipliersSection 8: Multiple IntegralsDouble Riemann sumEstimating the volume under a surfaceIterated/double integralsDouble integral over general regionsDouble integrals in polar coordinatesSurface areaCONTENT YOU WILL GET INSIDE EACH SECTION:Videos: I start each topic by introducing and explaining the concept. I share all my solving-problem techniques using examples. I show a variety of math issue you may encounter in class and make sure you can solve any problem by yourself.Notes: In each section, you will find my notes as downloadable resource that I wrote during lectures. So you can review the notes even when you don't have internet access (but I encourage you to take your own notes while taking the course!).Assignments: After you watch me doing some examples, now it's your turn to solve the problems! Be honest and do the practice problems before you check the solutions! If you pass, great! If not, you can review the videos and notes again before moving on to the next section.THINGS THAT ARE INCLUDED IN THE COURSE:An instructor who truly cares about your successLifetime access to Ace Calculus 3 in 16 Hours (The Complete Course)HIGHLIGHTS:#1: Downloadable lectures so you can watch the videos whenever and wherever you are.#2: Downloadable lecture notes so you can review the lectures without having a device to watch/listen.#3: Seven problem sets at the end of each section (with solutions!) for you to do more practice.#4: Step-by-step guide to help you solve problems.See you inside the course!- Gina:)
