Difference between revisions of "Pre-lecture videos"
From UBCMATH WIKI
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!width=10%|Video link | !width=10%|Video link | ||
!width=75%|Video contents | !width=75%|Video contents | ||
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|- class="NewWeek OddWeek" | |- class="NewWeek OddWeek" | ||
|id="week1"|Week 1 | |id="week1"|Week 1 | ||
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|[https://www.educreations.com/lesson/view/power-functions/23591979/?s=T9jC77&ref=app] | |[https://www.educreations.com/lesson/view/power-functions/23591979/?s=T9jC77&ref=app] | ||
|Power functions - when is $x^n>x^m$ and where do they intersect. Introduction to even and odd functions. | |Power functions - when is $x^n>x^m$ and where do they intersect. Introduction to even and odd functions. | ||
|- class="OddWeek" | |- class="OddWeek" | ||
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| | | | ||
|[http://www.educreations.com/lesson/view/cell-size/23429678/?s=6FnDiS&ref=app] | |[http://www.educreations.com/lesson/view/cell-size/23429678/?s=6FnDiS&ref=app] | ||
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|- class="OddWeek" | |- class="OddWeek" | ||
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|[http://www.educreations.com/lesson/view/graphing-a-simple-polynomial/23126849/?s=W2B6ko&ref=app] | |[http://www.educreations.com/lesson/view/graphing-a-simple-polynomial/23126849/?s=W2B6ko&ref=app] | ||
|Sketching simple polynomials (y=x^3-ax). | |Sketching simple polynomials (y=x^3-ax). | ||
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|- class="NewWeek EvenWeek" | |- class="NewWeek EvenWeek" | ||
|id="week2"|Week 2 | |id="week2"|Week 2 | ||
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|[http://youtu.be/v13aqQaMaSE] | |[http://youtu.be/v13aqQaMaSE] | ||
|Approximating a rational function near the origin. | |Approximating a rational function near the origin. | ||
|- class="EvenWeek" | |- class="EvenWeek" | ||
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| | | | ||
|[http://youtu.be/cXYCX8YBEVw] | |[http://youtu.be/cXYCX8YBEVw] | ||
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|- class="EvenWeek" | |- class="EvenWeek" | ||
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| | | | ||
|[http://youtu.be/kuMWI8kL1wI] | |[http://youtu.be/kuMWI8kL1wI] | ||
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|- class="EvenWeek" | |- class="EvenWeek" | ||
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|- class="EvenWeek" | |- class="EvenWeek" | ||
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|[https://www.youtube.com/watch?v=-yXuSU_jHQ4&list=UUNHASevzeyPH-OZMax8iMAA] | |[https://www.youtube.com/watch?v=-yXuSU_jHQ4&list=UUNHASevzeyPH-OZMax8iMAA] | ||
|Average rate of change and secant lines. Instantaneous rate of change. | |Average rate of change and secant lines. Instantaneous rate of change. | ||
|- class="EvenWeek" | |- class="EvenWeek" | ||
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| | | | ||
|[https://www.youtube.com/watch?v=PT2XNveWFoI&list=UUNHASevzeyPH-OZMax8iMAA] | |[https://www.youtube.com/watch?v=PT2XNveWFoI&list=UUNHASevzeyPH-OZMax8iMAA] | ||
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|- class="EvenWeek" | |- class="EvenWeek" | ||
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|[https://www.youtube.com/watch?v=2Yn05jvl0vI&list=UUNHASevzeyPH-OZMax8iMAA] | |[https://www.youtube.com/watch?v=2Yn05jvl0vI&list=UUNHASevzeyPH-OZMax8iMAA] | ||
|Continuity - definition and examples of three types of discontinuities. | |Continuity - definition and examples of three types of discontinuities. | ||
|- class="EvenWeek" | |- class="EvenWeek" | ||
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| | | | ||
|[https://www.youtube.com/watch?v=z4ED7eiNhBM&list=UUNHASevzeyPH-OZMax8iMAA] | |[https://www.youtube.com/watch?v=z4ED7eiNhBM&list=UUNHASevzeyPH-OZMax8iMAA] | ||
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|- class="NewWeek OddWeek" | |- class="NewWeek OddWeek" | ||
|id="week3"|Week 3 | |id="week3"|Week 3 | ||
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|[https://www.youtube.com/watch?v=E-owZqDrTkE&list=UUNHASevzeyPH-OZMax8iMAA] | |[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). | |Derivatives: analytic, and geometric (zoom in on a point). Sketching $f'(x)$ given $f(x)$ (intro). | ||
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|- class="OddWeek" | |- class="OddWeek" | ||
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|[https://www.educreations.com/lesson/view/using-a-spreadsheet-to-graph-a-function-and-its-de/24158741/?s=5I7yPP&ref=app] NEW!! | |[https://www.educreations.com/lesson/view/using-a-spreadsheet-to-graph-a-function-and-its-de/24158741/?s=5I7yPP&ref=app] NEW!! | ||
|Using a spreadsheet to graph a function and its (approximate) derivative. | |Using a spreadsheet to graph a function and its (approximate) derivative. | ||
|- class="OddWeek" | |- class="OddWeek" | ||
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| | | | ||
|[https://www.youtube.com/watch?v=HNXv3bmMGZ0&index=2&list=UUNHASevzeyPH-OZMax8iMAA] | |[https://www.youtube.com/watch?v=HNXv3bmMGZ0&index=2&list=UUNHASevzeyPH-OZMax8iMAA] | ||
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|- class="OddWeek" | |- class="OddWeek" | ||
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| | | | ||
|[https://www.youtube.com/watch?v=twnyZasD-d4&index=3&list=UUNHASevzeyPH-OZMax8iMAA] | |[https://www.youtube.com/watch?v=twnyZasD-d4&index=3&list=UUNHASevzeyPH-OZMax8iMAA] | ||
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|- class="OddWeek" | |- class="OddWeek" | ||
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| | | | ||
|[https://www.youtube.com/watch?v=giENfOUvE08&list=UUNHASevzeyPH-OZMax8iMAA&index=1] | |[https://www.youtube.com/watch?v=giENfOUvE08&list=UUNHASevzeyPH-OZMax8iMAA&index=1] | ||
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|- class="NewWeek EvenWeek" | |- class="NewWeek EvenWeek" | ||
|id="week4"|Week 4 | |id="week4"|Week 4 | ||
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|[http://www.educreations.com/lesson/view/equation-of-a-tangent-line/23143393/?s=JD4d1l&ref=app] | |[http://www.educreations.com/lesson/view/equation-of-a-tangent-line/23143393/?s=JD4d1l&ref=app] | ||
|Equation of a Tangent line. | |Equation of a Tangent line. | ||
|- class="EvenWeek" | |- class="EvenWeek" | ||
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| | | | ||
|[http://www.educreations.com/lesson/view/generic-tangent-line-and-intro-to-newton-s-method/23145498/?s=Ha5C44&ref=app] | |[http://www.educreations.com/lesson/view/generic-tangent-line-and-intro-to-newton-s-method/23145498/?s=Ha5C44&ref=app] | ||
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|- class="EvenWeek" | |- class="EvenWeek" | ||
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| | | | ||
|[http://www.educreations.com/lesson/view/linear-approximation/23185994/?s=AN5Da8&ref=app] | |[http://www.educreations.com/lesson/view/linear-approximation/23185994/?s=AN5Da8&ref=app] | ||
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|- class="EvenWeek" | |- class="EvenWeek" | ||
| | | | ||
− | |||
|[http://youtu.be/teRQpllWtaI] | |[http://youtu.be/teRQpllWtaI] | ||
|Introduction to Newton’s method - how it works and the formula for successive estimates. | |Introduction to Newton’s method - how it works and the formula for successive estimates. | ||
|- class="EvenWeek" | |- class="EvenWeek" | ||
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| | | | ||
|[http://youtu.be/TcPb4zkWEfo] | |[http://youtu.be/TcPb4zkWEfo] | ||
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|- class="EvenWeek" | |- class="EvenWeek" | ||
− | |||
| | | | ||
|[http://youtu.be/9nRU0V_3vjw] | |[http://youtu.be/9nRU0V_3vjw] | ||
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|- class="EvenWeek" | |- class="EvenWeek" | ||
− | |||
| | | | ||
|[https://www.youtube.com/watch?v=sDSt0G6dpzg] | |[https://www.youtube.com/watch?v=sDSt0G6dpzg] | ||
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|- class="EvenWeek" | |- class="EvenWeek" | ||
| | | | ||
− | |||
|[http://youtu.be/_bRBbdsV7Hs] | |[http://youtu.be/_bRBbdsV7Hs] | ||
|Concavity and inflection points. | |Concavity and inflection points. | ||
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|- class="NewWeek OddWeek" | |- class="NewWeek OddWeek" | ||
|id="week5"|Week 5 | |id="week5"|Week 5 | ||
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| | | | ||
| | | | ||
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|- class="OddWeek" | |- class="OddWeek" | ||
| | | | ||
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| | | | ||
|<span class="emphasize">'''MIDTERM 1: 6-7 pm'''</span> | |<span class="emphasize">'''MIDTERM 1: 6-7 pm'''</span> | ||
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|- class="OddWeek" | |- class="OddWeek" | ||
| | | | ||
− | |||
|EC | |EC | ||
|Finish sketching functions. Introduce simple optimization problem(s). | |Finish sketching functions. Introduce simple optimization problem(s). | ||
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|- class="OddWeek" | |- class="OddWeek" | ||
| | | | ||
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|More optimization examples including those with a constraint and those on bounded intervals. Distinction between absolute (global) and local minima and maxima. | |More optimization examples including those with a constraint and those on bounded intervals. Distinction between absolute (global) and local minima and maxima. | ||
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|- class="NewWeek EvenWeek" | |- class="NewWeek EvenWeek" | ||
|id="week6"|Week 6 | |id="week6"|Week 6 | ||
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|[http://www.educreations.com/lesson/view/kepler-s-wedding/23147433/?s=uq5ffc&ref=app] | |[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) | |Kepler's Wedding - A wine optimization problem. (Blooper alert: want to get most wine for given budget) | ||
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|- class="EvenWeek" | |- class="EvenWeek" | ||
| | | | ||
− | |||
|[http://www.educreations.com/lesson/view/optimal-foraging/23177297/?s=UledUg&ref=app] | |[http://www.educreations.com/lesson/view/optimal-foraging/23177297/?s=UledUg&ref=app] | ||
|Optimal Foraging. | |Optimal Foraging. | ||
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|- class="EvenWeek" | |- class="EvenWeek" | ||
| | | | ||
− | |||
|[http://youtu.be/MB5zGQuDK5s],[http://slesse.math.ubc.ca/Teaching/Screencasts/LinearRegression1.mov],[http://slesse.math.ubc.ca/Teaching/Screencasts/LinearRegression2.mov] | |[http://youtu.be/MB5zGQuDK5s],[http://slesse.math.ubc.ca/Teaching/Screencasts/LinearRegression1.mov],[http://slesse.math.ubc.ca/Teaching/Screencasts/LinearRegression2.mov] | ||
|Least Squares - finding the mean of a data set. See also the [[Course notes/Fitting data - least squares| Fitting data]] supplement to the course notes. | |Least Squares - finding the mean of a data set. See also the [[Course notes/Fitting data - least squares| Fitting data]] supplement to the course notes. | ||
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|- class="NewWeek OddWeek" | |- class="NewWeek OddWeek" | ||
|id="week7"|Week 7 | |id="week7"|Week 7 | ||
− | |||
| | | | ||
|THANKSGIVING - no classes. | |THANKSGIVING - no classes. | ||
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|- class="OddWeek" | |- class="OddWeek" | ||
| | | | ||
− | |||
|See Oct 10 | |See Oct 10 | ||
||Least Squares - finding the best fitting line y=ax through a set of data points. | ||Least Squares - finding the best fitting line y=ax through a set of data points. | ||
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|- class="OddWeek" | |- class="OddWeek" | ||
| | | | ||
− | |||
|[http://www.educreations.com/lesson/view/optimization-problem/14708865/?s=SmFwgM&ref=app], [https://www.youtube.com/watch?v=-1A7ZbO5dDY&feature=youtu.be] | |[http://www.educreations.com/lesson/view/optimization-problem/14708865/?s=SmFwgM&ref=app], [https://www.youtube.com/watch?v=-1A7ZbO5dDY&feature=youtu.be] | ||
|Chain Rule: examples, applications to optimization problems. | |Chain Rule: examples, applications to optimization problems. | ||
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|- class="NewWeek EvenWeek" | |- class="NewWeek EvenWeek" | ||
|id="week8"|Week 8 | |id="week8"|Week 8 | ||
− | |||
|[https://www.youtube.com/watch?v=CPIt13UItqI][https://www.youtube.com/watch?v=ERZAbNW3x0w] | |[https://www.youtube.com/watch?v=CPIt13UItqI][https://www.youtube.com/watch?v=ERZAbNW3x0w] | ||
|More Chain Rule: Related Rates and Implicit differentiation. | |More Chain Rule: Related Rates and Implicit differentiation. | ||
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|- class="EvenWeek" | |- class="EvenWeek" | ||
| | | | ||
− | |||
|[http://www.educreations.com/lesson/view/exponential-functions-and-doublings/23173031/?s=tzmKvB&ref=app] | |[http://www.educreations.com/lesson/view/exponential-functions-and-doublings/23173031/?s=tzmKvB&ref=app] | ||
|Exponential functions: intro and motivation, derivative of exponential functions. | |Exponential functions: intro and motivation, derivative of exponential functions. | ||
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|- class="EvenWeek" | |- class="EvenWeek" | ||
| | | | ||
− | |||
|[http://www.educreations.com/lesson/view/derivative-of-a-x/23176738/?s=hQQTNF&ref=app] | |[http://www.educreations.com/lesson/view/derivative-of-a-x/23176738/?s=hQQTNF&ref=app] | ||
|Exponential functions: intro and motivation, derivative of exponential functions. | |Exponential functions: intro and motivation, derivative of exponential functions. | ||
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|- class="EvenWeek" | |- class="EvenWeek" | ||
| | | | ||
− | |||
|[https://www.youtube.com/watch?v=qrEuGgjVuqI&feature=youtu.be] | |[https://www.youtube.com/watch?v=qrEuGgjVuqI&feature=youtu.be] | ||
|Inverse functions and logarithm, applications of logs. | |Inverse functions and logarithm, applications of logs. | ||
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|- class="NewWeek OddWeek" | |- class="NewWeek OddWeek" | ||
|id="week9"|Week 9 | |id="week9"|Week 9 | ||
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|[http://www.educreations.com/lesson/view/differential-equation-for-exponential-growth-and-d/23382026/?s=GyshbX&ref=app] | |[http://www.educreations.com/lesson/view/differential-equation-for-exponential-growth-and-d/23382026/?s=GyshbX&ref=app] | ||
|Exponential growth and decay, intro to differential equations, population growth and/or other examples. | |Exponential growth and decay, intro to differential equations, population growth and/or other examples. | ||
|- class="OddWeek" | |- class="OddWeek" | ||
− | |||
| | | | ||
|[http://youtu.be/5UFVLtEjUKo] | |[http://youtu.be/5UFVLtEjUKo] | ||
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|- class="OddWeek" | |- class="OddWeek" | ||
− | |||
| | | | ||
|[http://www.educreations.com/lesson/view/simple-differential-equation-problem/14300182/?s=GCrISn&ref=app] | |[http://www.educreations.com/lesson/view/simple-differential-equation-problem/14300182/?s=GCrISn&ref=app] | ||
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|- class="OddWeek" | |- class="OddWeek" | ||
| | | | ||
− | |||
|[http://www.educreations.com/lesson/view/solving-de-checking-that-a-function-is-a-solution/23384860/?s=qwZb1k&ref=app] | |[http://www.educreations.com/lesson/view/solving-de-checking-that-a-function-is-a-solution/23384860/?s=qwZb1k&ref=app] | ||
|Solving differential equations of the type $dy/dt=a-by$. | |Solving differential equations of the type $dy/dt=a-by$. | ||
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|- class="OddWeek" | |- class="OddWeek" | ||
| | | | ||
− | |||
|[http://www.educreations.com/lesson/view/solving-a-diffl-eq-dy-dt-a-by/23385476/?s=ObLqjR&ref=app] | |[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 $dy/dt=a-by$. | |Solving differential equations of the type $dy/dt=a-by$. | ||
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|- class="OddWeek" | |- class="OddWeek" | ||
| | | | ||
− | |||
|LEK | |LEK | ||
|Newton's Law of Cooling (Murder Mystery example). | |Newton's Law of Cooling (Murder Mystery example). | ||
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|- class="NewWeek EvenWeek" | |- class="NewWeek EvenWeek" | ||
|id="week10"|Week 10 | |id="week10"|Week 10 | ||
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| | | | ||
|Complete and/or review above topics. | |Complete and/or review above topics. | ||
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|- class="EvenWeek" | |- class="EvenWeek" | ||
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− | |||
| | | | ||
|<span class="emphasize">'''MIDTERM 2: 6-7 pm'''</span> | |<span class="emphasize">'''MIDTERM 2: 6-7 pm'''</span> | ||
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|- class="EvenWeek" | |- class="EvenWeek" | ||
| | | | ||
− | |||
|[https://www.youtube.com/watch?v=Yga2chpiLtc], [http://slesse.math.ubc.ca/Teaching/Screencasts/EulersMethod.mov] | |[https://www.youtube.com/watch?v=Yga2chpiLtc], [http://slesse.math.ubc.ca/Teaching/Screencasts/EulersMethod.mov] | ||
|Solving differential equations approximately using Euler's Method. | |Solving differential equations approximately using Euler's Method. | ||
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|- class="EvenWeek" | |- class="EvenWeek" | ||
| | | | ||
− | |||
|[http://www.educreations.com/lesson/view/geometry-of-change-i/23430270/?s=pB3DZB&ref=app] | |[http://www.educreations.com/lesson/view/geometry-of-change-i/23430270/?s=pB3DZB&ref=app] | ||
|Geometry of change: (I) Slope fields. | |Geometry of change: (I) Slope fields. | ||
|- class="EvenWeek" | |- class="EvenWeek" | ||
− | |||
| | | | ||
|[http://www.educreations.com/lesson/view/geometry-of-change-ii/23430914/?s=T8tWAw&ref=app] | |[http://www.educreations.com/lesson/view/geometry-of-change-ii/23430914/?s=T8tWAw&ref=app] | ||
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|- class="NewWeek OddWeek" | |- class="NewWeek OddWeek" | ||
|id="week11"|Week 11 | |id="week11"|Week 11 | ||
− | |||
|[http://www.educreations.com/lesson/view/geometry-of-change-i/23430270/?s=pB3DZB&ref=app] | |[http://www.educreations.com/lesson/view/geometry-of-change-i/23430270/?s=pB3DZB&ref=app] | ||
|Geometry of change: (I) Slope fields. | |Geometry of change: (I) Slope fields. | ||
|- class="OddWeek" | |- class="OddWeek" | ||
− | |||
| | | | ||
|[http://www.educreations.com/lesson/view/geometry-of-change-ii/23430914/?s=T8tWAw&ref=app] | |[http://www.educreations.com/lesson/view/geometry-of-change-ii/23430914/?s=T8tWAw&ref=app] | ||
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|- class="OddWeek" | |- class="OddWeek" | ||
| | | | ||
− | |||
| | | | ||
|Remembrance Day. University closed. | |Remembrance Day. University closed. | ||
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|- class="OddWeek" | |- class="OddWeek" | ||
| | | | ||
− | |||
|[http://www.educreations.com/lesson/view/logistic-equation/23431216/?s=2GkGkB&ref=app] | |[http://www.educreations.com/lesson/view/logistic-equation/23431216/?s=2GkGkB&ref=app] | ||
|The Logistic equation (state space and slope field). | |The Logistic equation (state space and slope field). | ||
|- class="OddWeek" | |- class="OddWeek" | ||
− | |||
| | | | ||
|[http://www.educreations.com/lesson/view/slope-field-for-a-differential-equation/14300653/?s=c6aBLN&ref=app] | |[http://www.educreations.com/lesson/view/slope-field-for-a-differential-equation/14300653/?s=c6aBLN&ref=app] | ||
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|- class="OddWeek" | |- class="OddWeek" | ||
| | | | ||
− | |||
|[http://www.educreations.com/lesson/view/disease-dynamics-i/23465001/?s=pJChZV&ref=app] | |[http://www.educreations.com/lesson/view/disease-dynamics-i/23465001/?s=pJChZV&ref=app] | ||
|Disease dynamics | |Disease dynamics | ||
|- class="OddWeek" | |- class="OddWeek" | ||
− | |||
| | | | ||
|[http://www.educreations.com/lesson/view/disease-dynamics-ii/23465479/?s=EG7QeI&ref=app] | |[http://www.educreations.com/lesson/view/disease-dynamics-ii/23465479/?s=EG7QeI&ref=app] | ||
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|- class="NewWeek EvenWeek" | |- class="NewWeek EvenWeek" | ||
|id="week12"|Week 12 | |id="week12"|Week 12 | ||
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| | | | ||
|Review of differential equations and/or complete above topics. | |Review of differential equations and/or complete above topics. | ||
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|- class="EvenWeek" | |- class="EvenWeek" | ||
| | | | ||
− | |||
|[https://www.youtube.com/watch?v=vg1hmGI2WDM], [https://www.youtube.com/watch?v=XZ6O4dWaeZ0] | |[https://www.youtube.com/watch?v=vg1hmGI2WDM], [https://www.youtube.com/watch?v=XZ6O4dWaeZ0] | ||
|Introduction to Trigonometric Functions and review of trigonometric identities. | |Introduction to Trigonometric Functions and review of trigonometric identities. | ||
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|- class="EvenWeek" | |- class="EvenWeek" | ||
| | | | ||
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|[http://www.educreations.com/lesson/view/periodic-function/14693344/?s=kxJDte&ref=app] (LEK),EC | |[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. | |Trigonometric Functions and cyclic processes, phase, amplitude, etc. (fitting a sin or cos to a cyclic process), Inverse trig functions. | ||
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|[http://youtu.be/mdYuQ2NDVgA] | |[http://youtu.be/mdYuQ2NDVgA] | ||
|Derivatives of trig functions, related rates examples. | |Derivatives of trig functions, related rates examples. | ||
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|[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] | |[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. | |The Escape Response and trigonometric related rates. | ||
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|Second order ODEs. Complete and/or review trig. | |Second order ODEs. Complete and/or review trig. | ||
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Revision as of 16:10, 8 September 2015
Video link | Video contents | |
---|---|---|
Week 1 | [1] | Power functions - when is $x^n>x^m$ and where do they intersect. Introduction to even and odd functions. |
[2] | Cell size and nutrient balance: cell volume and area and the role of power functions in describing cell size limitations. | |
[3] | Sketching simple polynomials (y=x^3-ax). | |
Week 2 | [4] | Approximating a rational function near the origin. |
[5] | Approximating a rational function for large x. Introduction to Hill functions. | |
[6] | 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. | ||
[7] | Average rate of change and secant lines. Instantaneous rate of change. | |
[8] | Definition of the derivative. | |
[9] | Continuity - definition and examples of three types of discontinuities. | |
[10] | Examples of computing the derivative of a function from the definition of the derivative. | |
Week 3 | [11] | Derivatives: analytic, and geometric (zoom in on a point). Sketching $f'(x)$ given $f(x)$ (intro). |
[12] NEW!! | Using a spreadsheet to graph a function and its (approximate) derivative. | |
[13] | Derivatives of polynomials. | |
[14] | Rules of differentiation: Antiderivatives of polynomials. | |
[15] | Rules of differentiation: Product and quotient rules. | |
Week 4 | [16] | Equation of a Tangent line. |
[17] | Generic Tangent line and intro to Newton's method. | |
[18] | Tangent lines and linear approximation. | |
[19] | Introduction to Newton’s method - how it works and the formula for successive estimates. | |
[20] | Introduction to Newton’s method - how to carry it out with a spreadsheet. | |
[21] | Introduction to Newton’s method - how to choose a good $x_0$. | |
[22] | Increasing, decreasing and critical points.
| |
[23] | Concavity and inflection points. | |
Week 5 | ||
MIDTERM 1: 6-7 pm | ||
EC | Finish sketching functions. Introduce simple optimization problem(s). | |
More optimization examples including those with a constraint and those on bounded intervals. Distinction between absolute (global) and local minima and maxima. | ||
Week 6 | [24] | Kepler's Wedding - A wine optimization problem. (Blooper alert: want to get most wine for given budget) |
[25] | Optimal Foraging. | |
[26],[27],[28] | Least Squares - finding the mean of a data set. See also the Fitting data supplement to the course notes. | |
Week 7 | THANKSGIVING - no classes. | |
See Oct 10 | Least Squares - finding the best fitting line y=ax through a set of data points. | |
[29], [30] | Chain Rule: examples, applications to optimization problems. | |
Week 8 | [31][32] | More Chain Rule: Related Rates and Implicit differentiation. |
[33] | Exponential functions: intro and motivation, derivative of exponential functions. | |
[34] | Exponential functions: intro and motivation, derivative of exponential functions. | |
[35] | Inverse functions and logarithm, applications of logs. | |
Week 9 | [36] | Exponential growth and decay, intro to differential equations, population growth and/or other examples. |
[37] | Exponential growth and decay, intro to differential equations, population growth and/or other examples. | |
[38] | Exponential growth and decay, intro to differential equations, population growth and/or other examples. | |
[39] | Solving differential equations of the type $dy/dt=a-by$. | |
[40] | Solving differential equations of the type $dy/dt=a-by$. | |
LEK | Newton's Law of Cooling (Murder Mystery example). | |
Week 10 | Complete and/or review above topics. | |
MIDTERM 2: 6-7 pm | ||
[41], [42] | Solving differential equations approximately using Euler's Method. | |
[43] | Geometry of change: (I) Slope fields. | |
[44] | Geometry of change: (II) State space. This one is more relevant to the pre-lecture questions but you should watch both. | |
Week 11 | [45] | Geometry of change: (I) Slope fields. |
[46] | Geometry of change: (II) State space. | |
Remembrance Day. University closed. | ||
[47] | The Logistic equation (state space and slope field). | |
[48] | The Logistic equation (state space and slope field). | |
[49] | Disease dynamics | |
[50] | Disease dynamics | |
Week 12 | Review of differential equations and/or complete above topics. | |
[51], [52] | Introduction to Trigonometric Functions and review of trigonometric identities. | |
[53] (LEK),EC | Trigonometric Functions and cyclic processes, phase, amplitude, etc. (fitting a sin or cos to a cyclic process), Inverse trig functions. | |
Week 13 | [54] | Derivatives of trig functions, related rates examples. |
[55][56] | The Escape Response and trigonometric related rates. | |
Second order ODEs. Complete and/or review trig. |