Difference between revisions of "Math100Videos"

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!width=65%|Video contents
 
!width=65%|Video contents
  
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|-  
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|- class="NewWeek OddWeek"
 
|Limits
 
|Limits
 
|Limits and tangent lines
 
|Limits and tangent lines
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| Limits at Infinity
 
| Limits at Infinity
 
|[https://youtu.be/PI5mlJpLBhw]
 
|[https://youtu.be/PI5mlJpLBhw]
−
| limits at infinity
+
| Limits at infinity
 +
 
  
 
|- class="NewWeek EvenWeek"
 
|- class="NewWeek EvenWeek"
−
|id="week2"|Week 2
+
| Continuity
 +
| Intro to Continuity
 +
|[https://youtu.be/tR5EkjCH9GU]
 +
| 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
 +
|[https://youtu.be/zDuCAB1fx-o]
 +
|Strategies for evaluating limits; continuity; Intermediate Value Theorem
 +
 
 +
</tr>
 +
<tr>
 +
<td> Extra: continuity </td>
 +
<td> <a href='100/video/dirichlet-video.mp4'>video</a><br>
 +
<a href='https://youtu.be/0ftIwSH9y4E'>YouTube</a></td>
 +
<td> 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.) </td>
 +
</tr>
 +
 
 +
<tr>
 +
<td rowspan=3> Derivatives </td>
 +
<td> Intro to Derivatives </td>
 +
<td> <a href='100/video/ReviewSept_21_15.mp4'>video</a><br>
 +
<a href='https://youtu.be/FOVKHhHIx90'>YouTube</a></td>
 +
<td> Introduction to derivatives: interpretations, derivatives at a point, derivatives of a function </td>
 +
</tr>
 +
<tr>
 +
<td> Graphing Derivatives </td>
 +
<td> <a href='100/video/deriv graphing.mp4'>video</a><br>
 +
<a href='https://youtu.be/pe43D7BPHQw'>YouTube</a></td>
 +
<td> 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. </td>
 +
</tr>
 +
<tr>
 +
<td> Tangent Lines </td>
 +
<td> <a href='100/video/ReviewSept23_15.mp4'>video</a><br>
 +
<a href='https://youtu.be/D5M8dE7W874'>YouTube</a></td>
 +
<td> Find the tangent line to a curve; calculate derivatives using simple rules.
 +
</td>
 +
</tr>
 +
<tr>
 +
<td rowspan=4> Differentiation </td>
 +
<td> Product and Quotient Rules </td>
 +
<td> <a href='100/video/ReviewSept25_15.mp4'>video</a><br>
 +
<a href='https://youtu.be/QHQp0PXS43E'>YouTube</a></td>
 +
<td> Derivatives of Products and Ratios
 +
</td>
 +
</tr>
 +
<tr>
 +
<td> Exponential </td>
 +
<td> <a href='100/video/Sept28.mp4'>video</a><br>
 +
<a href='https://youtu.be/Vzs646Y5lNA'>YouTube</a></td>
 +
<td> Product rule and derivatives of exponential functions
 +
</td>
 +
</tr>
 +
<tr>
 +
<td> Trigonometric </td>
 +
<td> <a href='100/video/ReviewSept30_15.mp4'>video</a><br>
 +
<a href='https://youtu.be/BnxDzjYynAQ'>YouTube</a></td>
 +
<td> Derivatives of trigonometric functions.
 +
</td>
 +
</tr>
 +
<tr>
 +
<td> Chain Rule </td>
 +
<td> <a href='100/video/chain.mp4'>video</a><br>
 +
<a href='https://youtu.be/kSL7atf0Omw'>YouTube</a></td>
 +
<td> Derivatives of compound functions.
 +
</td>
 +
</tr>
 +
<tr>
 +
<td> Review </td>
 +
<td> Inverse Functions </td>
 +
<td> <a href='100/video/inverses.mp4'>video</a><br>
 +
<a href='https://youtu.be/HiWYatEbNFw'>YouTube</a></td>
 +
<td> Inverse functions.
 +
</td>
 +
</tr>
 +
<tr>
 +
<td> Differentiation </td>
 +
<td> Logarithms </td>
 +
<td> <a href='100/video/logarithmic.mp4'>video</a><br>
 +
<a href='https://youtu.be/FMYIvZVzGlc'>YouTube</a></td>
 +
<td> 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><br>
 +
<a href='https://youtu.be/3LMjCwvqAqw'>YouTube</a></td>
 +
<td> Rates of Change
 +
</td>
 +
</tr>
 +
<tr>
 +
<td rowspan=2> Exponential change </td>
 +
<td> Rates of Change </td>
 +
<td> <a href='100/video/decay.mp4'>video</a><br>
 +
<a href='https://youtu.be/eblBM7tvRLY'>YouTube</a></td>
 +
<td> Exponential growth and decay, such as radioactive decay, compound interest, and population growth. Introduction to differential equations.
 +
</td>
 +
</tr>
 +
<tr>
 +
<td> Newton's Law of Cooling </td>
 +
<td> <a href='100/video/cooling.mp4'>video</a><br>
 +
<a href='https://youtu.be/ug3k4fqQfbU'>YouTube</a></td>
 +
<td> Exponential rates of change applied to cooling bodies.
 +
</td>
 +
</tr>
 +
<tr>
 +
<td> Related Rates </td>
 +
<td> Related Rates </td>
 +
<td> <a href='100/video/RelatedRates.mp4'>video</a><br>
 +
<a href='https://youtu.be/_G5dx3-J-uE'>YouTube</a></td>
 +
<td> Calculating the rate of change in systems with lots of interconnected changing parts.
 +
</td>
 +
</tr>
 +
<tr>
 +
<td rowspan=3> Polynomial Approximations </td>
 +
<td> First Approximations </td>
 +
<td> <a href='100/video/Approx1.mp4'>video</a><br>
 +
<a href='https://youtu.be/cYtRR2NVeY0'>YouTube</a></td>
 +
<td> Estimating the value of a function with a constant, linear, or quadratic approximation.
 +
</td>
 +
</tr>
 +
<tr>
 +
<td rowspan=2> Error Bounding </td>
 +
<td> <a href='100/video/sqrt.mp4'>video</a><br>
 +
<a href='https://youtu.be/QavL2wnf8qk'>YouTube</a></td>
 +
<td> Give an approximation of a function, and bound the error you introduced.
 +
</td>
 +
</tr>
 +
<tr>
 +
<td> <a href='100/video/ln.mp4'>video</a><br>
 +
<a href='https://youtu.be/VbjR6JF1OG4'>YouTube</a></td>
 +
<td> If you are given an error tolerance, which approximation should you use? </td>
 +
</tr>
 +
<tr>
 +
<td rowspan=3> Optimization </td>
 +
<td> Extrema </td>
 +
<td> <a href='100/video/maxmin.mp4'>video</a><br>
 +
<a href='https://youtu.be/pxMPYzEm_-o'>YouTube</a></td>
 +
<td> Finding maxima and minima of a function. </td>
 +
</tr>
 +
<tr>
 +
<td> Optimization </td>
 +
<td> <a href='100/video/opt1.mp4'>video</a><br>
 +
<a href='https://youtu.be/IxYA1IWs2R4'>YouTube</a></td>
 +
<td>  </td>
 +
</tr>
 +
<tr>
 +
<td> Optimization </td>
 +
<td> <a href='100/video/opt2.mp4'>video</a><br>
 +
<a href='https://youtu.be/E-20K2Mby60'>YouTube</a></td>
 +
<td>  </td>
 +
</tr>
 +
<tr>
 +
<td rowspan=2> MVT </td>
 +
<td> Rolle's Theorem </td>
 +
<td> <a href='100/video/Rolle.mp4'>video</a><br>
 +
<a href='https://youtu.be/WBvTXxzhg9A'>YouTube</a></td>
 +
<td> A differentiable function that takes the same value twice has a horizontal tangent line somewhere.
 +
</td>
 +
</tr>
 +
<tr>
 +
<td> Mean Value Theorem </td>
 +
<td> <a href='100/video/MVT.mp4'>video</a><br>
 +
<a href='https://youtu.be/3lardKQbD_I'>YouTube</a></td>
 +
<td> 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><br>
 +
<a href='https://youtu.be/XjuyNjKEAcg'>YouTube</a></td>
 +
<td>  </td>
 +
</tr>
 +
<tr>
 +
<td> Curve Sketching 2 </td>
 +
<td> <a href='100/video/sketch2.mp4'>video</a><br>
 +
<a href='https://youtu.be/m4GeiEsEzXk'>YouTube</a></td>
 +
<td>  </td>
 +
</tr>
 +
<tr>
 +
<td> Symmetry </td>
 +
<td> <a href='100/video/sketch3.mp4'>video</a><br>
 +
<a href='https://youtu.be/vYZF078-Zow'>YouTube</a></td>
 +
<td> Even and odd functions. </td>
 +
</tr>
 +
<tr>
 +
<td> L'Hospital's Rule </td>
 +
<td> L'Hospital's Rule </td>
 +
<td> <a href='100/video/lhospital.mp4'>video</a><br>
 +
<a href='https://youtu.be/VJ7DlV1vp8o'>YouTube</a>
 +
</td>
 +
<td>  </td>
 +
</tr>
 +
</table>
 +
 
 +
 
 +
 
 +
|- class="NewWeek EvenWeek"
 +
|
 
|[http://youtu.be/v13aqQaMaSE]
 
|[http://youtu.be/v13aqQaMaSE]
 
|Approximating a rational function near the origin.
 
|Approximating a rational function near the origin.
Line 73: Line 275:
 
|Examples of computing the derivative of a function from the definition of the derivative.
 
|Examples of computing the derivative of a function from the definition of the derivative.
  
−
|- class="NewWeek OddWeek"
 
−
|id="week3"|Week 3
 
−
|[https://www.youtube.com/watch?v=E-owZqDrTkE&list=UUNHASevzeyPH-OZMax8iMAA]
 
−
|Derivatives: analytic, and geometric (zoom in on a point). Sketching $f'(x)$ given $f(x)$ (intro).
 
−
 
−
|- class="OddWeek"
 
−
|
 
−
|[https://www.educreations.com/lesson/view/using-a-spreadsheet-to-graph-a-function-and-its-de/24158741/?s=5I7yPP&ref=app]
 
−
|Using a spreadsheet to graph a function and its (approximate) derivative.
 
−
 
−
|- class="OddWeek"
 
−
|
 
−
|[https://www.youtube.com/watch?v=HNXv3bmMGZ0&index=2&list=UUNHASevzeyPH-OZMax8iMAA]
 
−
|Derivatives of polynomials.
 
−
 
−
|- class="OddWeek"
 
−
|
 
−
|[https://www.youtube.com/watch?v=giENfOUvE08&list=UUNHASevzeyPH-OZMax8iMAA&index=1]
 
−
|Rules of differentiation:  Product and quotient rules.
 
−
 
−
|- class="NewWeek EvenWeek"
 
−
|id="week4"|Week 4
 
−
|[https://www.youtube.com/watch?v=twnyZasD-d4&index=3&list=UUNHASevzeyPH-OZMax8iMAA]
 
−
|Rules of differentiation:  Antiderivatives of polynomials.
 
−
 
−
|- class="EvenWeek"
 
−
|
 
−
|[http://www.educreations.com/lesson/view/equation-of-a-tangent-line/23143393/?s=JD4d1l&ref=app]
 
−
|Equation of a Tangent line.
 
−
 
−
|- class="EvenWeek"
 
−
|
 
−
|[http://www.educreations.com/lesson/view/generic-tangent-line-and-intro-to-newton-s-method/23145498/?s=Ha5C44&ref=app]
 
−
|Generic Tangent line and intro to Newton's method.
 
−
 
−
|- class="EvenWeek"
 
−
|
 
−
|[http://www.educreations.com/lesson/view/linear-approximation/23185994/?s=AN5Da8&ref=app]
 
−
|Tangent lines and linear approximation.
 
−
 
−
|- class="EvenWeek"
 
−
|
 
−
|[http://youtu.be/teRQpllWtaI]
 
−
|Introduction to Newton’s method - how it works and the formula for successive estimates.
 
−
 
−
|- class="NewWeek OddWeek"
 
−
|id="week5"|Week 5
 
−
|[http://youtu.be/TcPb4zkWEfo]
 
−
|Introduction to Newton’s method - how to carry it out with a spreadsheet.
 
−
 
−
|- class="OddWeek"
 
−
|
 
−
|[http://youtu.be/9nRU0V_3vjw]
 
−
|Introduction to Newton’s method - how to choose a good $x_0$.
 
−
 
−
|- class="OddWeek"
 
−
|
 
−
|[https://www.youtube.com/watch?v=sDSt0G6dpzg]
 
−
|Increasing, decreasing and critical points.
 
−
 
−
|- class="OddWeek"
 
−
|
 
−
|[http://youtu.be/_bRBbdsV7Hs]
 
−
|Concavity and inflection points.
 
−
 
−
|- class="OddWeek"
 
−
|
 
−
|[https://www.youtube.com/watch?v=wNMK92GVTO8]
 
−
|Largest area of a rectangle inscribed in a semicircle
 
−
 
−
|- class="OddWeek"
 
−
|
 
−
|[https://www.youtube.com/watch?v=JIQTPlBs154]
 
−
|Absolute Maximum and Minimum Values of a Function - Calculus I
 
−
 
−
|- class="NewWeek EvenWeek"
 
−
|id="week6"|Week 6
 
−
|[http://www.educreations.com/lesson/view/kepler-s-wedding/23147433/?s=uq5ffc&ref=app]
 
−
|Kepler's Wedding - A wine optimization problem. (Blooper alert: want to get most wine for given budget)
 
−
 
−
|- class="EvenWeek"
 
−
|
 
−
|[http://www.educreations.com/lesson/view/optimal-foraging/23177297/?s=UledUg&ref=app]
 
−
|Optimal Foraging.
 
−
 
−
|- class="NewWeek OddWeek"
 
−
|id="week7"|Week 7
 
−
|[http://youtu.be/MB5zGQuDK5s]
 
−
|Least Squares -  finding the best fitting line y=ax through a set of data points. See also the [[Course notes/Fitting data - least squares| Fitting data]] supplement to the course notes.
 
−
 
−
|- class="OddWeek"
 
−
|
 
−
|[https://www.youtube.com/watch?v=-1A7ZbO5dDY&feature=youtu.be]
 
−
|Chain Rule: general introduction with examples
 
−
 
−
|- class="OddWeek"
 
−
|
 
−
|[http://www.educreations.com/lesson/view/optimization-problem/14708865/?s=SmFwgM&ref=app]
 
−
|Chain Rule: an applications to optimization problems involving plovers and crocodiles.
 
−
 
−
|- class="NewWeek EvenWeek"
 
−
|id="week8"|Week 8
 
−
|[https://www.youtube.com/watch?v=CPIt13UItqI]
 
−
|Implicit differentiation.
 
−
 
−
|- class="EvenWeek"
 
−
|
 
−
|[https://www.youtube.com/watch?v=ERZAbNW3x0w]
 
−
|Related Rates.
 
−
 
−
|- class="EvenWeek"
 
−
|
 
−
|[http://www.educreations.com/lesson/view/exponential-functions-and-doublings/23173031/?s=tzmKvB&ref=app]
 
−
|Exponential functions and doubling.
 
−
 
−
|- class="EvenWeek"
 
−
|
 
−
|[http://www.educreations.com/lesson/view/derivative-of-a-x/23176738/?s=hQQTNF&ref=app]
 
−
|Exponential functions: derivative of $a^x$.
 
−
 
−
|- class="NewWeek OddWeek"
 
−
|id="week9"|Week 9
 
−
|[https://www.youtube.com/watch?v=qrEuGgjVuqI&feature=youtu.be]
 
−
|Inverse functions and logarithm, applications of logs.
 
−
 
−
|- class="OddWeek"
 
−
|
 
−
|[http://www.educreations.com/lesson/view/differential-equation-for-exponential-growth-and-d/23382026/?s=GyshbX&ref=app]
 
−
|Differential equations for growth and decay.
 
−
 
−
|- class="OddWeek"
 
−
|
 
−
|[http://youtu.be/5UFVLtEjUKo]
 
−
|A differential equation for human population growth.
 
−
 
−
|- class="OddWeek"
 
−
|
 
−
|[http://www.educreations.com/lesson/view/simple-differential-equation-problem/14300182/?s=GCrISn&ref=app]
 
−
|A simple differential equation problem.
 
−
 
−
|- class="NewWeek EvenWeek"
 
−
|id="week10"|Week 10
 
−
|[http://www.educreations.com/lesson/view/geometry-of-change-i/23430270/?s=pB3DZB&ref=app]
 
−
|Geometry of change: (I) Slope fields.
 
−
 
−
|- class="EvenWeek"
 
−
|
 
−
|[http://www.educreations.com/lesson/view/geometry-of-change-ii/23430914/?s=T8tWAw&ref=app]
 
−
|Geometry of change: (II) State space. This one is more relevant to the pre-lecture questions but you should watch both.
 
−
 
−
|- class="EvenWeek"
 
−
|
 
−
|[http://www.educreations.com/lesson/view/logistic-equation/23431216/?s=2GkGkB&ref=app]
 
−
|The Logistic equation I (state space and slope field).
 
−
 
−
|- class="EvenWeek"
 
−
|
 
−
|[http://www.educreations.com/lesson/view/slope-field-for-a-differential-equation/14300653/?s=c6aBLN&ref=app]
 
−
|The Logistic equation II (state space and slope field).
 
−
 
−
|- class="NewWeek OddWeek"
 
−
|id="week11"|Week 11
 
−
|[http://www.educreations.com/lesson/view/solving-a-diffl-eq-dy-dt-a-by/23385476/?s=ObLqjR&ref=app].
 
−
|Solving differential equations of the type $dy/dt=a-by$.
 
−
 
−
|- class="OddWeek"
 
−
|
 
−
|[https://www.youtube.com/watch?v=Yga2chpiLtc]
 
−
|Solving differential equations approximately using Euler's Method - theory.
 
−
 
−
|- class="OddWeek"
 
−
|
 
−
|[https://www.youtube.com/watch?v=z7Kbp8hl950]
 
−
|Solving differential equations approximately using Euler's Method - spreadsheet.
 
−
 
−
|- class="NewWeek EvenWeek"
 
−
|id="week12"|Week 12
 
−
|[http://www.educreations.com/lesson/view/disease-dynamics-i/23465001/?s=pJChZV&ref=app]
 
−
|Disease dynamics I
 
−
 
−
|- class="EvenWeek"
 
−
|
 
−
|[http://www.educreations.com/lesson/view/disease-dynamics-ii/23465479/?s=EG7QeI&ref=app]
 
−
|Disease dynamics II
 
−
 
−
|- class="EvenWeek"
 
−
|
 
−
|[https://www.youtube.com/watch?v=vg1hmGI2WDM], [https://www.youtube.com/watch?v=XZ6O4dWaeZ0]
 
−
|Introduction to Trigonometric Functions and review of trigonometric identities.
 
−
 
−
|- class="EvenWeek"
 
−
|
 
−
|[http://www.educreations.com/lesson/view/periodic-function/14693344/?s=kxJDte&ref=app] (LEK),EC
 
−
|Trigonometric Functions and cyclic processes, phase, amplitude, etc. (fitting a sin or cos to a cyclic process), Inverse trig functions.
 
−
 
−
|- class="NewWeek OddWeek"
 
−
|id="week13"|Week 13
 
−
|[http://youtu.be/mdYuQ2NDVgA]
 
−
|Derivatives of trig functions, related rates examples.
 
−
 
−
|- class="OddWeek"
 
−
|
 
−
|[http://www.educreations.com/lesson/view/visual-angles/23504229/?s=0mhFFb&ref=app][https://www.educreations.com/lesson/view/visual-angles-part-2-escape-response/26980643/?s=YzbN0D&ref=app]
 
−
|The Escape Response and trigonometric related rates.
 
  
 
|}
 
|}

Revision as of 13:25, 18 August 2017


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

</tr> <tr> <td> Extra: continuity </td> <td> <a href='100/video/dirichlet-video.mp4'>video</a>
<a href='https://youtu.be/0ftIwSH9y4E'>YouTube</a></td> <td> 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.) </td> </tr>

<tr> <td rowspan=3> Derivatives </td> <td> Intro to Derivatives </td> <td> <a href='100/video/ReviewSept_21_15.mp4'>video</a>
<a href='https://youtu.be/FOVKHhHIx90'>YouTube</a></td> <td> Introduction to derivatives: interpretations, derivatives at a point, derivatives of a function </td> </tr> <tr> <td> Graphing Derivatives </td> <td> <a href='100/video/deriv graphing.mp4'>video</a>
<a href='https://youtu.be/pe43D7BPHQw'>YouTube</a></td> <td> 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. </td> </tr> <tr> <td> Tangent Lines </td> <td> <a href='100/video/ReviewSept23_15.mp4'>video</a>
<a href='https://youtu.be/D5M8dE7W874'>YouTube</a></td> <td> Find the tangent line to a curve; calculate derivatives using simple rules. 

</td>

</tr> <tr> <td rowspan=4> Differentiation </td> <td> Product and Quotient Rules </td> <td> <a href='100/video/ReviewSept25_15.mp4'>video</a>
<a href='https://youtu.be/QHQp0PXS43E'>YouTube</a></td> <td> Derivatives of Products and Ratios 

</td>

</tr> <tr> <td> Exponential </td> <td> <a href='100/video/Sept28.mp4'>video</a>
<a href='https://youtu.be/Vzs646Y5lNA'>YouTube</a></td> <td> Product rule and derivatives of exponential functions 

</td>

</tr> <tr> <td> Trigonometric </td> <td> <a href='100/video/ReviewSept30_15.mp4'>video</a>
<a href='https://youtu.be/BnxDzjYynAQ'>YouTube</a></td> <td> Derivatives of trigonometric functions. 

</td>

</tr> <tr> <td> Chain Rule </td> <td> <a href='100/video/chain.mp4'>video</a>
<a href='https://youtu.be/kSL7atf0Omw'>YouTube</a></td> <td> Derivatives of compound functions. 

</td>

</tr> <tr> <td> Review </td> <td> Inverse Functions </td> <td> <a href='100/video/inverses.mp4'>video</a>
<a href='https://youtu.be/HiWYatEbNFw'>YouTube</a></td> <td> Inverse functions. 

</td>

</tr> <tr> <td> Differentiation </td> <td> Logarithms </td> <td> <a href='100/video/logarithmic.mp4'>video</a>
<a href='https://youtu.be/FMYIvZVzGlc'>YouTube</a></td> <td> 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>
<a href='https://youtu.be/3LMjCwvqAqw'>YouTube</a></td> <td> Rates of Change 

</td>

</tr> <tr> <td rowspan=2> Exponential change </td> <td> Rates of Change </td> <td> <a href='100/video/decay.mp4'>video</a>
<a href='https://youtu.be/eblBM7tvRLY'>YouTube</a></td> <td> Exponential growth and decay, such as radioactive decay, compound interest, and population growth. Introduction to differential equations. 

</td>

</tr> <tr> <td> Newton's Law of Cooling </td> <td> <a href='100/video/cooling.mp4'>video</a>
<a href='https://youtu.be/ug3k4fqQfbU'>YouTube</a></td> <td> Exponential rates of change applied to cooling bodies. 

</td>

</tr> <tr> <td> Related Rates </td> <td> Related Rates </td> <td> <a href='100/video/RelatedRates.mp4'>video</a>
<a href='https://youtu.be/_G5dx3-J-uE'>YouTube</a></td> <td> Calculating the rate of change in systems with lots of interconnected changing parts. 

</td>

</tr> <tr> <td rowspan=3> Polynomial Approximations </td> <td> First Approximations </td> <td> <a href='100/video/Approx1.mp4'>video</a>
<a href='https://youtu.be/cYtRR2NVeY0'>YouTube</a></td> <td> Estimating the value of a function with a constant, linear, or quadratic approximation. 

</td>

</tr> <tr> <td rowspan=2> Error Bounding </td> <td> <a href='100/video/sqrt.mp4'>video</a>
<a href='https://youtu.be/QavL2wnf8qk'>YouTube</a></td> <td> Give an approximation of a function, and bound the error you introduced. 

</td>

</tr> <tr> <td> <a href='100/video/ln.mp4'>video</a>
<a href='https://youtu.be/VbjR6JF1OG4'>YouTube</a></td> <td> If you are given an error tolerance, which approximation should you use? </td> </tr> <tr> <td rowspan=3> Optimization </td> <td> Extrema </td> <td> <a href='100/video/maxmin.mp4'>video</a>
<a href='https://youtu.be/pxMPYzEm_-o'>YouTube</a></td> <td> Finding maxima and minima of a function. </td> </tr> <tr> <td> Optimization </td> <td> <a href='100/video/opt1.mp4'>video</a>
<a href='https://youtu.be/IxYA1IWs2R4'>YouTube</a></td> <td> </td> </tr> <tr> <td> Optimization </td> <td> <a href='100/video/opt2.mp4'>video</a>
<a href='https://youtu.be/E-20K2Mby60'>YouTube</a></td> <td> </td> </tr> <tr> <td rowspan=2> MVT </td> <td> Rolle's Theorem </td> <td> <a href='100/video/Rolle.mp4'>video</a>
<a href='https://youtu.be/WBvTXxzhg9A'>YouTube</a></td> <td> A differentiable function that takes the same value twice has a horizontal tangent line somewhere. 

</td>

</tr> <tr> <td> Mean Value Theorem </td> <td> <a href='100/video/MVT.mp4'>video</a>
<a href='https://youtu.be/3lardKQbD_I'>YouTube</a></td> <td> 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>
<a href='https://youtu.be/XjuyNjKEAcg'>YouTube</a></td> <td> </td> </tr> <tr> <td> Curve Sketching 2 </td> <td> <a href='100/video/sketch2.mp4'>video</a>
<a href='https://youtu.be/m4GeiEsEzXk'>YouTube</a></td> <td> </td> </tr> <tr> <td> Symmetry </td> <td> <a href='100/video/sketch3.mp4'>video</a>
<a href='https://youtu.be/vYZF078-Zow'>YouTube</a></td> <td> Even and odd functions. </td> </tr> <tr> <td> L'Hospital's Rule </td> <td> L'Hospital's Rule </td> <td> <a href='100/video/lhospital.mp4'>video</a>
<a href='https://youtu.be/VJ7DlV1vp8o'>YouTube</a> </td> <td> </td> </tr> </table>


[7] Approximating a rational function near the origin.
[8] Approximating a rational function for large x. Introduction to Hill functions.
[9] 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.
[10] Average rate of change and secant lines. Instantaneous rate of change.
[11] Definition of the derivative.
[12] Continuity - definition and examples of three types of discontinuities.
[13] Examples of computing the derivative of a function from the definition of the derivative.


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