Difference between revisions of "Pre-lecture videos"
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| − | + | !width=10%|Video link | |
| − | + | !width=75%|Video contents | |
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| − | |Week 1 | + | |id="week1"|Week 1 |
| − | + | |[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. | |
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| − | + | |[http://www.educreations.com/lesson/view/cell-size/23429678/?s=6FnDiS&ref=app] | |
| − | + | |Cell size and nutrient balance: cell volume and area and the role of power functions in describing cell size limitations. | |
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| − | |[http://www.educreations.com/lesson/view/ | + | |
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| − | + | |[http://www.educreations.com/lesson/view/graphing-a-simple-polynomial/23126849/?s=W2B6ko&ref=app] | |
| − | + | |Sketching simple polynomials (y=x^3-ax). | |
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|- class="NewWeek EvenWeek" | |- class="NewWeek EvenWeek" | ||
| − | |Week | + | |id="week2"|Week 2 |
| − | + | |[http://youtu.be/v13aqQaMaSE] | |
| − | + | |Approximating a rational function near the origin. | |
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| − | + | |[http://youtu.be/cXYCX8YBEVw] | |
| − | + | |Approximating a rational function for large x. Introduction to Hill functions. | |
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| − | |[http://youtu.be/ | + | |
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|- class="EvenWeek" | |- class="EvenWeek" | ||
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| − | | | + | |[http://youtu.be/kuMWI8kL1wI] |
| − | + | |Sketching Hill functions by hand and by Desmos ([[Videos and demos|see Hill functions demo]]). Comparing Hill functions with different parameter values. | |
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| − | | | + | |See video [1] above for an introduction to even and odd functions and also Sec 1.4 and Appendix C.4 of the OpenBook (a.k.a."Course Notes"). |
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| − | | | + | |[https://www.youtube.com/watch?v=-yXuSU_jHQ4&list=UUNHASevzeyPH-OZMax8iMAA] |
| − | + | |Average rate of change and secant lines. Instantaneous rate of change. | |
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| − | + | |[https://www.youtube.com/watch?v=PT2XNveWFoI&list=UUNHASevzeyPH-OZMax8iMAA] | |
| − | + | |Definition of the derivative. | |
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| − | | | + | |[https://www.youtube.com/watch?v=2Yn05jvl0vI&list=UUNHASevzeyPH-OZMax8iMAA] |
| − | + | |Continuity - definition and examples of three types of discontinuities. | |
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|- class="EvenWeek" | |- class="EvenWeek" | ||
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| − | + | |[https://www.youtube.com/watch?v=z4ED7eiNhBM&list=UUNHASevzeyPH-OZMax8iMAA] | |
| − | + | |Examples of computing the derivative of a function from the definition of the derivative. | |
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|- class="NewWeek OddWeek" | |- 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). | |
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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] |
| − | + | |Using a spreadsheet to graph a function and its (approximate) derivative. | |
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|- class="OddWeek" | |- class="OddWeek" | ||
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| − | + | |[https://www.youtube.com/watch?v=HNXv3bmMGZ0&index=2&list=UUNHASevzeyPH-OZMax8iMAA] | |
| − | + | |Derivatives of polynomials. | |
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|- class="OddWeek" | |- class="OddWeek" | ||
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| − | + | |[https://www.youtube.com/watch?v=giENfOUvE08&list=UUNHASevzeyPH-OZMax8iMAA&index=1] | |
| − | + | |Rules of differentiation: Product and quotient rules. | |
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|- class="NewWeek EvenWeek" | |- class="NewWeek EvenWeek" | ||
| − | |Week | + | |id="week4"|Week 4 |
| − | | | + | |[https://www.youtube.com/watch?v=twnyZasD-d4&index=3&list=UUNHASevzeyPH-OZMax8iMAA] |
| − | + | |Rules of differentiation: Antiderivatives of polynomials. | |
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|- class="EvenWeek" | |- class="EvenWeek" | ||
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| − | | | + | |[http://www.educreations.com/lesson/view/equation-of-a-tangent-line/23143393/?s=JD4d1l&ref=app] |
| − | + | |Equation of a Tangent line. | |
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|- 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] | |
| − | + | |Generic Tangent line and intro to Newton's method. | |
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| − | |[http://www.educreations.com/lesson/view/ | + | |
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| − | + | |[http://www.educreations.com/lesson/view/linear-approximation/23185994/?s=AN5Da8&ref=app] | |
| − | |[http:// | + | |Tangent lines and linear approximation. |
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|- class="EvenWeek" | |- class="EvenWeek" | ||
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| − | + | |[http://youtu.be/teRQpllWtaI] | |
| − | |[http://youtu.be/ | + | |Introduction to Newton’s method - how it works and the formula for successive estimates. |
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| − | | | + | |id="week5"|Week 5 |
| − | + | |[http://youtu.be/TcPb4zkWEfo] | |
| − | + | |Introduction to Newton’s method - how to carry it out with a spreadsheet. | |
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| − | + | |[http://youtu.be/9nRU0V_3vjw] | |
| − | + | |Introduction to Newton’s method - how to choose a good $x_0$. | |
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| − | | | + | |[https://www.youtube.com/watch?v=sDSt0G6dpzg] |
| − | + | |Increasing, decreasing and critical points. | |
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| + | |[http://youtu.be/_bRBbdsV7Hs] | ||
| + | |Concavity and inflection points. | ||
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| − | | | + | |[https://www.youtube.com/watch?v=wNMK92GVTO8] |
| − | + | |Largest area of a rectangle inscribed in a semicircle | |
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| − | | | + | |[https://www.youtube.com/watch?v=JIQTPlBs154] |
| − | + | |Absolute Maximum and Minimum Values of a Function - Calculus I | |
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| − | |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) |
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| − | | | + | |[http://www.educreations.com/lesson/view/optimal-foraging/23177297/?s=UledUg&ref=app] |
|Optimal Foraging. | |Optimal Foraging. | ||
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| − | |Week 7 | + | |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. |
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| − | | | + | |[https://www.youtube.com/watch?v=-1A7ZbO5dDY&feature=youtu.be] |
| − | + | |Chain Rule: general introduction with examples | |
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| − | + | |[http://www.educreations.com/lesson/view/optimization-problem/14708865/?s=SmFwgM&ref=app] | |
| − | + | |Chain Rule: an applications to optimization problems involving plovers and crocodiles. | |
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| − | |[http://www.educreations.com/lesson/view/optimization-problem/14708865/?s=SmFwgM&ref=app] | + | |
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| − | |Week 8 | + | |id="week8"|Week 8 |
| − | | | + | |[https://www.youtube.com/watch?v=CPIt13UItqI] |
| − | | | + | |Implicit differentiation. |
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|- class="EvenWeek" | |- class="EvenWeek" | ||
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| − | | | + | |[https://www.youtube.com/watch?v=ERZAbNW3x0w] |
| − | + | |Related Rates. | |
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| − | | | + | |[http://www.educreations.com/lesson/view/exponential-functions-and-doublings/23173031/?s=tzmKvB&ref=app] |
| − | + | |Exponential functions and doubling. | |
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| + | |- class="EvenWeek" | ||
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| − | | | + | |[http://www.educreations.com/lesson/view/derivative-of-a-x/23176738/?s=hQQTNF&ref=app] |
| + | |Exponential functions: derivative of $a^x$. | ||
|- class="NewWeek OddWeek" | |- class="NewWeek OddWeek" | ||
| − | | | + | |id="week9"|Week 9 |
| − | + | |[https://www.youtube.com/watch?v=qrEuGgjVuqI&feature=youtu.be] | |
| − | + | |Inverse functions and logarithm, applications of logs. | |
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| − | + | |[http://www.educreations.com/lesson/view/differential-equation-for-exponential-growth-and-d/23382026/?s=GyshbX&ref=app] | |
| − | + | |Differential equations for growth and decay. | |
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| − | |[http://www.educreations.com/lesson/view/ | + | |
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|- class="OddWeek" | |- class="OddWeek" | ||
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| − | | | + | |[http://youtu.be/5UFVLtEjUKo] |
| − | + | |A differential equation for human population growth. | |
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| − | | | + | |- class="OddWeek" |
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| − | | | + | |[http://www.educreations.com/lesson/view/simple-differential-equation-problem/14300182/?s=GCrISn&ref=app] |
| + | |A simple differential equation problem. | ||
|- class="NewWeek EvenWeek" | |- class="NewWeek EvenWeek" | ||
| − | |Week 10 | + | |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. | |
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|- class="EvenWeek" | |- class="EvenWeek" | ||
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| − | | | + | |[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. | |
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|- class="EvenWeek" | |- class="EvenWeek" | ||
| | | | ||
| − | + | |[http://www.educreations.com/lesson/view/logistic-equation/23431216/?s=2GkGkB&ref=app] | |
| − | + | |The Logistic equation I (state space and slope field). | |
| − | + | ||
| − | + | ||
| − | |[http:// | + | |
| − | | | + | |
|- class="EvenWeek" | |- 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). | |
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| − | |[http://www.educreations.com/lesson/view/ | + | |
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|- class="NewWeek OddWeek" | |- 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 $dy/dt=a-by$. | |
| − | | | + | |
| − | + | ||
| − | |[http://www.educreations.com/lesson/view/ | + | |
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| − | | | + | |
|- class="OddWeek" | |- class="OddWeek" | ||
| | | | ||
| − | | | + | |[https://www.youtube.com/watch?v=Yga2chpiLtc] |
| − | + | |Solving differential equations approximately using Euler's Method - theory. | |
| − | | | + | |
| − | + | ||
| − | + | ||
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|- class="OddWeek" | |- class="OddWeek" | ||
| | | | ||
| − | + | |[https://www.youtube.com/watch?v=z7Kbp8hl950] | |
| − | + | |Solving differential equations approximately using Euler's Method - spreadsheet. | |
| − | + | ||
| − | + | ||
| − | |[ | + | |
| − | + | ||
| − | |- class=" | + | |- class="NewWeek EvenWeek" |
| − | | | + | |id="week12"|Week 12 |
| − | | | + | |[http://www.educreations.com/lesson/view/disease-dynamics-i/23465001/?s=pJChZV&ref=app] |
| − | |Disease dynamics | + | |Disease dynamics I |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | |- class=" | + | |- class="EvenWeek" |
| − | + | ||
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| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| | | | ||
| + | |[http://www.educreations.com/lesson/view/disease-dynamics-ii/23465479/?s=EG7QeI&ref=app] | ||
| + | |Disease dynamics II | ||
|- class="EvenWeek" | |- class="EvenWeek" | ||
| | | | ||
| − | | | + | |[https://www.youtube.com/watch?v=vg1hmGI2WDM], [https://www.youtube.com/watch?v=XZ6O4dWaeZ0] |
| − | |Introduction to Trigonometric Functions. | + | |Introduction to Trigonometric Functions and review of trigonometric identities. |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
|- class="EvenWeek" | |- 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. | |Trigonometric Functions and cyclic processes, phase, amplitude, etc. (fitting a sin or cos to a cyclic process), Inverse trig functions. | ||
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|- class="NewWeek OddWeek" | |- class="NewWeek OddWeek" | ||
| − | |Week 13 | + | |id="week13"|Week 13 |
| − | | | + | |[http://youtu.be/mdYuQ2NDVgA] |
| − | |Derivatives of trig functions, related rates examples. | + | |Derivatives of trig functions, related rates examples. |
| − | + | ||
| − | + | ||
| − | + | ||
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|- class="OddWeek" | |- 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 | + | |The Escape Response and trigonometric related rates. |
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|} | |} | ||
Latest revision as of 12:17, 12 September 2017
| 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 1.4 and Appendix C.4 of the OpenBook (a.k.a."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] | Using a spreadsheet to graph a function and its (approximate) derivative. | |
| [13] | Derivatives of polynomials. | |
| [14] | Rules of differentiation: Product and quotient rules. | |
| Week 4 | [15] | Rules of differentiation: Antiderivatives of polynomials. |
| [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. | |
| Week 5 | [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. | |
| [24] | Largest area of a rectangle inscribed in a semicircle | |
| [25] | Absolute Maximum and Minimum Values of a Function - Calculus I | |
| Week 6 | [26] | Kepler's Wedding - A wine optimization problem. (Blooper alert: want to get most wine for given budget) |
| [27] | Optimal Foraging. | |
| Week 7 | [28] | Least Squares - finding the best fitting line y=ax through a set of data points. See also the Fitting data supplement to the course notes. |
| [29] | Chain Rule: general introduction with examples | |
| [30] | Chain Rule: an applications to optimization problems involving plovers and crocodiles. | |
| Week 8 | [31] | Implicit differentiation. |
| [32] | Related Rates. | |
| [33] | Exponential functions and doubling. | |
| [34] | Exponential functions: derivative of $a^x$. | |
| Week 9 | [35] | Inverse functions and logarithm, applications of logs. |
| [36] | Differential equations for growth and decay. | |
| [37] | A differential equation for human population growth. | |
| [38] | A simple differential equation problem. | |
| Week 10 | [39] | Geometry of change: (I) Slope fields. |
| [40] | Geometry of change: (II) State space. This one is more relevant to the pre-lecture questions but you should watch both. | |
| [41] | The Logistic equation I (state space and slope field). | |
| [42] | The Logistic equation II (state space and slope field). | |
| Week 11 | [43]. | Solving differential equations of the type $dy/dt=a-by$. |
| [44] | Solving differential equations approximately using Euler's Method - theory. | |
| [45] | Solving differential equations approximately using Euler's Method - spreadsheet. | |
| Week 12 | [46] | Disease dynamics I |
| [47] | Disease dynamics II | |
| [48], [49] | Introduction to Trigonometric Functions and review of trigonometric identities. | |
| [50] (LEK),EC | Trigonometric Functions and cyclic processes, phase, amplitude, etc. (fitting a sin or cos to a cyclic process), Inverse trig functions. | |
| Week 13 | [51] | Derivatives of trig functions, related rates examples. |
| [52][53] | The Escape Response and trigonometric related rates. |
