课程介绍
Trefor Bazett 教授在 Cincinnati 大学任教时，制作了两套完整的的数学课程（微积分、离散数学），上传网络后备受欢迎！课程覆盖核心知识要点，并借助可视化的方式做了生动讲解，是基础学习和查漏补缺的优先选择。
Calculus Ⅱ是其中的微积分系列Part 2，内容覆盖 定积分、级数、多元函数、偏导、泰勒展开、极坐标等，形象的可视化与活泼的授课方式，让你更好地掌握抽象的数学知识，为其他工科方向课程学习打好基础。
课程讲师 Trefor Bazett，2016-2019年任职于 University of Cincinnati，担任助理教授，系列课程也是那时制作完成！目前任职于University of Victoria，主要爱好是数学教育，同时对代数拓扑感兴趣。
课程资料 | 下载
扫描上方图片二维码，关注公众号并回复关键字 🎯『MATH101』，就可以获取整理完整的资料合辑啦！当然也可以点击 🎯 这里 查看更多课程的资料获取方式！
ShowMeAI 对课程资料进行了梳理，整理成这份完备且清晰的资料包：
- 📚 笔记：Paul Dawkins在 Lamar University 教授Calculus课程。这是他整理的课程笔记，对于任何想要学习或《微积分II》的人都非常有帮助。
- 📚 作业：同样是 Paul Dawkins 整理的《微积分II》作业习题。
- 📚 问题与解答：还是 Paul Dawkins 整理的常见问题和解答 (有解答!) 值得一看~
- 📚 拓展阅读材料：奉上两份 微积分小抄表，重点和精华总结都在这里了~
课程视频 | B站
ShowMeAI 将视频上传至B站，并增加了中英双语字幕，以提供更加友好的学习体验。点击页面视频，可以进行预览。推荐前往 👆 B站 观看完整课程视频哦！
本门课程，ShowMeAI 将部分章节进行了切分，按照主题形成更短小的视频片段，便于按照标题进行更快速的检索。切分后的视频清单列写在这里：
| 序号 | 视频清单 |
|---|---|
| L1 | Welcome to Calculus II |
| L2 | Intro to Integration By Parts — Examples: ∫xsinxdx & ∫arctan(x)dx |
| L3 | Two Tricky Integration By Parts Examples |
| L4 | Trigonometric Integrals - ∫sin^n(x)cos^m(x)dx via Pythagorean or Half-Angle Identities |
| L5 | Intro to Trigonometric Substitution - Ex: Deriving Area of Circle Formula |
| L6 | Trig Subs - How To Choose The Substitution & Deal With Indefinite Integrals |
| L7 | Deconstructing a messy integral - Trig subs & u-subs combined |
| L8 | Integration by Partial Fractions - Big Idea + First Example |
| L9 | Partial Fractions - Repeating and irreducible Quadratic Terms |
| L10 | Choosing what integration methods to use - Part I |
| L11 | Choosing what integration methods to use - Challenging Example! |
| L12 | MATH PROF vs TRICKY INTEGRALS |
| L13 | Improper Integrals: How to Integrate with Infinities, 2 ways! |
| L14 | Comparison Test for Improper Integrals |
| L15 | Arclength Formula - Derivation & Ex: Circumference of a Circle |
| L16 | Area of Surfaces of Revolution - Derivation & Example |
| L17 | Infinite Surface Area but Finite Volume!?!? Gabriel’s Horn |
| L18 | Intro to Sequences |
| L19 | Limits of Sequences, Limit laws & Function Representations |
| L20 | Intro to Series: What is 1/2+1/4+1/8+1/16+…? |
| L21 | Geometric Series - Convergence, Derivation, and Example |
| L22 | Harmonic Series - It diverges, but insanely slowly! |
| L23 | Integral Test - Derivation & 1st Example |
| L24 | Estimating the Remainder of a Series Approximation via the Integral Test |
| L25 | Comparison Test for Series |
| L26 | Limit Comparison Test for Series |
| L27 | Alternating Series Test - Intuition, Statement & Example |
| L28 | Alternating Series - Estimating the Remainder |
| L29 | The bizarre world of INFINITE rearrangements // Riemann Series Theorem |
| L30 | Absolute Convergence vs Conditional Convergence vs Convergence |
| L31 | Ratio & Root Tests - Geometric Series Generalized |
| L32 | Choosing Which Convergence Test to Apply to 8 Series |
| L33 | Solving Inequalities with Absolute Values |
| L34 | Power Series & Intervals of Convergence |
| L35 | Intro to Taylor Series: Approximations on Steroids |
| L36 | 3 Applications of Taylor Series: Integrals, Limits, & Series |
| L37 | Why Taylor Series actually work: The Taylor Inequality |
| L38 | Plotting Parametric Curves |
| L39 | Tangents to Parametric Curves - Multiple tangents at the same point!! |
| L40 | Area under a Parametric Curve - Formula, Derivation, & Example |
| L41 | Arclength of Parametric Curves |
| L42 | Intro to Polar Coordinates |
| L43 | Sketching Polar Curves |
| L44 | Areas in Polar Coordinates |
| L45 | Example: Area Inside Polar Curves |
| L46 | Why Exponential Growth?? Intro to Separable Differential Equations |
| L47 | Defining the Natural Logarithm as an Integral?!?!? |
| L48 | Intro to COMPLEX NUMBERS // Motivation, Algebraic Definition & Fundamental Theorem of Algebra Ep. 1 |
| L49 | The geometric view of COMPLEX NUMBERS |
| L50 | The Polar Form of COMPLEX NUMBERS // Finding the nth roots of -1 |
更多技术与课程清单 | 点击查看详细课程
