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 Ⅰ是微积分系列的第一个Part，内容覆盖函数、极限、导数、洛必达法则、链式法则与积分等。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 🎯『MATH100』，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I》的人都非常有帮助。
- 📚 作业：同样是 Paul Dawkins 整理的课程作业习题。
- 📚 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《微积分学习终极笔记》，可以理解为 18页小抄表，重点和精华总结都在这里了~
说明1：课程没有对外发布直接的课件等资料。团队搜索和筛选了能找到的、最匹配的相关资源。
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 | The Velocity Problem - Part I: Numerically |
| L2 | The Velocity Problem - Part II: Graphically |
| L3 | A Tale of Three Functions - Intro to Limits Part I |
| L4 | A Tale of Three Functions - Intro to Limits Part II |
| L5 | What is an infinite limit? |
| L6 | Limit Laws - Breaking Up Complicated Limits Into Simpler Ones |
| L7 | Building up to computing limits of rational functions |
| L8 | Limits of Oscillating Functions and the Squeeze Theorem |
| L9 | Top 4 Algebraic Tricks for Computing Limits |
| L10 | A Limit Example Combining Multiple Algebraic Tricks |
| L11 | Limits are simple for continuous functions |
| L12 | Were you ever exactly 3 feet tall? The Intermediate Value Theorem |
| L13 | Example: When is a Piecewise Function Continuous? |
| L14 | Limits “at” infinity |
| L15 | Computing Limits at Infinity for Rational Functions |
| L16 | Infinite Limit vs Limits at Infinity of a Composite Function |
| L17 | How to watch math videos |
| L18 | Definition of the Derivative - Part I |
| L19 | Applying the Definition of the Derivative to 1/x |
| L20 | Definition of Derivative Example: f(x) = x + 1/(x+1) |
| L21 | The derivative of a constant and of x^2 from the definition |
| L22 | Derivative Rules: Power Rule, Additivity, and Scalar Multiplication |
| L23 | How to Find the Equation of a Tangent Line |
| L24 | The derivative of e^x. |
| L25 | The product and quotient rules |
| L26 | The derivative of Trigonometric Functions |
| L27 | Chain Rule: the Derivative of a Composition |
| L28 | Interpreting the Chain Rule Graphically |
| L29 | The Chain Rule using Leibniz notation |
| L30 | Implicit Differentiation - Differentiation when you only have an equation, not an explicit function |
| L31 | Derivative of Inverse Trig Functions via Implicit Differentiation |
| L32 | The Derivative of ln(x) via Implicit Differentiation |
| L33 | Logarithmic Differentiation - Example: x^sinx |
| L34 | Intro to Related Rates |
| L35 | Linear Approximations - Using Tangent Lines to Approximate Functions |
| L36 | The MEAN Value Theorem is Actually Very Nice |
| L37 | Relative and Absolute Maximums and Minimums - Part I |
| L38 | Relative and Absolute Maximums and Minimums - Part II |
| L39 | Using L’Hopital’s Rule to show that exponentials dominate polynomials |
| L40 | Applying L’Hopital’s Rule to Exponential Indeterminate Forms |
| L41 | Ex: Optimizing the Volume of a Box With Fixed Surface Area |
| L42 | Folding a wire into the largest rectangle - Optimization example |
| L43 | Optimization Example: Minimizing Surface Area Given a Fixed Volume |
| L44 | Tips for Success in Flipped Classrooms + OMG BABY!!! |
| L45 | What’s an anti-derivative? |
| L46 | Solving for the constant in the general anti-derivative |
| L47 | The Definite Integral Part I: Approximating Areas with rectangles |
| L48 | The Definite Integral Part II: Using Summation Notation to Define the Definite Integral |
| L49 | The Definite Integral Part III: Evaluating From The Definition |
| L50 | Reverse Riemann Sums - Finding the Definite Integral Given a Sum |
| L51 | Fundamental Theorem of Calculus 1 - Geometric Idea + Chain Rule Example |
| L52 | Fundamental Theorem of Calculus II |
| L53 | Intro to Substitution - Undoing the Chain Rule |
| L54 | Adjusting the Constant in Integration by Substitution |
| L55 | Substitution Method for Definite Integrals careful! |
| L56 | Back Substitution - When a u-sub doesn’t match cleanly! |
| L57 | Average Value of a Continuous Function on an Interval |
| L58 | Exam Walkthrough - Calc 1, Test 3 - Integration, FTC I/II, Optimization, u-subs, Graphing |
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