Math100Videos
| Topic | Video link | Video contents | |
|---|---|---|---|
| Limits | Limits and tangent lines | [1] | Average and Instantaneous Velocity; secant and tangent line; limit notation |
| One-sided limits | [2] | A simple example motivating one-sided limits | |
| Limits, continued | [3] | Sometimes limits don't exist; one-sided limits; calculating limits | |
| Limits at Infinity | [4] | Limits at infinity
| |
| Continuity | Intro to Continuity | [5] | Before we learn the formal definition of a continuous function, dwell a little on what it means for a function's limit to differ from its value at a point. Being used to this behaviour will help you build intuition about continuity. |
| Limits, Continuity, IVT | [6] | Strategies for evaluating limits; continuity; Intermediate Value Theorem | |
| Extra: continuity | [7] | Think you understand continuity? Test yourself with a graph that has no limit... anywhere. (This video goes beyond the course material. Think of it as recreational.) | |
| Derivatives | Intro to Derivatives | [8] | Introduction to derivatives: interpretations, derivatives at a point, derivatives of a function |
| Graphing Derivatives | [9] | Use the graph of a function to create the graph of its derivative. Review the interpretation of positive and negative derivatives, and get used to looking at a line and intuiting its slope. | |
| Tangent Lines | [10] | Find the tangent line to a curve; calculate derivatives using simple rules. | |
| Differentiation | Product and Quotient Rules | [11] | Derivatives of Products and Ratios |
| Exponential | [12] | Product rule and derivatives of exponential functions | |
| Trigonometric | [13] | Derivatives of trigonometric functions. | |
| Chain Rule | [14] | Derivatives of compound functions. | |
| Review | Inverse Functions | [15] | Inverse functions. |
| Differentiation | Logarithms | [16] | Logarithmic functions and logarithmic differentiation.
</td> </tr>
<tr>
<td> Rates of Change </td>
<td> Rates of Change </td>
<td> <a href='100/video/RatesofChange.mp4'>video</a> </td> </tr>
<tr>
<td rowspan=2> Exponential change </td>
<td> Rates of Change </td>
<td> <a href='100/video/decay.mp4'>video</a> </td> </tr>
<tr>
<td> Newton's Law of Cooling </td>
<td> <a href='100/video/cooling.mp4'>video</a> </td> </tr>
<tr>
<td> Related Rates </td>
<td> Related Rates </td>
<td> <a href='100/video/RelatedRates.mp4'>video</a> </td> </tr>
<tr>
<td rowspan=3> Polynomial Approximations </td>
<td> First Approximations </td>
<td> <a href='100/video/Approx1.mp4'>video</a> </td> </tr>
<tr>
<td rowspan=2> Error Bounding </td>
<td> <a href='100/video/sqrt.mp4'>video</a> </td> </tr>
<tr>
<td> <a href='100/video/ln.mp4'>video</a> </td> </tr>
<tr>
<td> Mean Value Theorem </td>
<td> <a href='100/video/MVT.mp4'>video</a> </td> </tr>
<tr>
<td rowspan=3> Curve Sketching </td>
<td> Curve Sketching 1 </td>
<td> <a href='100/video/sketch1.mp4'>video</a>
|
| [17] | Approximating a rational function near the origin. | ||
| [18] | Approximating a rational function for large x. Introduction to Hill functions. | ||
| [19] | Sketching Hill functions by hand and by Desmos (see Hill functions demo). Comparing Hill functions with different parameter values. | ||
| See video [1] above for an introduction to even and odd functions and also Sec 1.2.3 and Appendix C.D of the course notes. | |||
| [20] | Average rate of change and secant lines. Instantaneous rate of change. | ||
| [21] | Definition of the derivative. | ||
| [22] | Continuity - definition and examples of three types of discontinuities. | ||
| [23] | Examples of computing the derivative of a function from the definition of the derivative.
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