Math100Videos
From UBCMATH WIKI
| 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. | |
| Logarithms | [16] | Logarithmic functions and logarithmic differentiation. | |
| Rates of Change | Rates of Change | [17] | Rates of Change |
| Exponential change | [18] | Exponential growth and decay, such as radioactive decay, compound interest, and population growth. Introduction to differential equations. | |
| Newton's Law of Cooling | [19] | Exponential rates of change applied to cooling bodies. | |
| Related Rates | [20] | Calculating the rate of change in systems with lots of interconnected changing parts.
| |
| Polynomial Approximations | First Approximations | [21] | Estimating the value of a function with a constant, linear, or quadratic approximation. |
| Error Bounding | [22] | Give an approximation of a function, and bound the error you introduced. | |
| [23] | If you are given an error tolerance, which approximation should you use? | ||
| Optimization | Extrema | [24] | Finding maxima and minima of a function. |
| Optimization | [25]
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| [26] | |||
| Mean Value Theorem | Rolle's Theorem | [27] | A differentiable function that takes the same value twice has a horizontal tangent line somewhere. |
| Mean Value Theorem | [28] | A differentiable function has a point where its instantaneous rate of change is equal to is average rate of change over an interval.
</td> </tr>
<tr>
<td rowspan=3> Curve Sketching </td>
<td> Curve Sketching 1 </td>
<td> <a href='100/video/sketch1.mp4'>video</a>
| |
| [29] | Approximating a rational function near the origin. | ||
| [30] | Approximating a rational function for large x. Introduction to Hill functions. | ||
| [31] | 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. | |||
| [32] | Average rate of change and secant lines. Instantaneous rate of change. | ||
| [33] | Definition of the derivative. | ||
| [34] | Continuity - definition and examples of three types of discontinuities. | ||
| [35] | Examples of computing the derivative of a function from the definition of the derivative.
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