Difference between revisions of "Pre-lecture videos"

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|[http://youtu.be/kuMWI8kL1wI]
 
|[http://youtu.be/kuMWI8kL1wI]
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|Sketching Hill functions by hand and by Desmos ([[Online_interactive_tools|see Hill functions demo]]). Comparing Hill functions with different parameter values.
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|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 1.2.3 and Appendix C.D of the course notes.
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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=HNXv3bmMGZ0&index=2&list=UUNHASevzeyPH-OZMax8iMAA]
 
|[https://www.youtube.com/watch?v=HNXv3bmMGZ0&index=2&list=UUNHASevzeyPH-OZMax8iMAA]
 
|Derivatives of polynomials.
 
|Derivatives of polynomials.
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|[https://www.youtube.com/watch?v=twnyZasD-d4&index=3&list=UUNHASevzeyPH-OZMax8iMAA]
 
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|Rules of differentiation:  Antiderivatives of polynomials.
 
  
 
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|id="week4"|Week 4
 
|id="week4"|Week 4
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|[https://www.youtube.com/watch?v=twnyZasD-d4&index=3&list=UUNHASevzeyPH-OZMax8iMAA]
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|Rules of differentiation:  Antiderivatives of polynomials.
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|- class="EvenWeek"
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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.
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|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.  
  
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|id="week5"|Week 5
 
|[http://youtu.be/TcPb4zkWEfo]
 
|[http://youtu.be/TcPb4zkWEfo]
 
|Introduction to Newton’s method - how to carry it out with a spreadsheet.
 
|Introduction to Newton’s method - how to carry it out with a spreadsheet.
  
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|[http://youtu.be/9nRU0V_3vjw]
 
|[http://youtu.be/9nRU0V_3vjw]
 
|Introduction to Newton’s method - how to choose a good $x_0$.
 
|Introduction to Newton’s method - how to choose a good $x_0$.
  
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|- class="OddWeek"
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|id="week5"|Week 5
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|[https://www.youtube.com/watch?v=sDSt0G6dpzg]
 
|[https://www.youtube.com/watch?v=sDSt0G6dpzg]
 
|Increasing, decreasing and critical points.
 
|Increasing, decreasing and critical points.
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|Exponential functions: derivative of $a^x$.
 
|Exponential functions: derivative of $a^x$.
  
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|id="week9"|Week 9
 
|[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="OddWeek"
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|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]
 
|Differential equations for growth and decay.
 
|Differential equations for growth and decay.
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|[http://youtu.be/5UFVLtEjUKo]
 
|[http://youtu.be/5UFVLtEjUKo]
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|Exponential growth and decay, intro to differential equations, population growth and/or other examples.
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|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]
 
|[http://www.educreations.com/lesson/view/simple-differential-equation-problem/14300182/?s=GCrISn&ref=app]
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|Exponential growth and decay, intro to differential equations, population growth and/or other examples.
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|A simple differential equation problem.
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|[http://www.educreations.com/lesson/view/solving-de-checking-that-a-function-is-a-solution/23384860/?s=qwZb1k&ref=app]
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|Solving differential equations of the type $dy/dt=a-by$.
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|[http://www.educreations.com/lesson/view/solving-a-diffl-eq-dy-dt-a-by/23385476/?s=ObLqjR&ref=app]
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|Solving differential equations of the type $dy/dt=a-by$.
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|LEK
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|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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|[http://www.educreations.com/lesson/view/geometry-of-change-i/23430270/?s=pB3DZB&ref=app]
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|Complete and/or review above topics.
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|Geometry of change: (I) Slope fields.
  
 
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|[https://www.youtube.com/watch?v=Yga2chpiLtc], [http://slesse.math.ubc.ca/Teaching/Screencasts/EulersMethod.mov]
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|[http://www.educreations.com/lesson/view/geometry-of-change-ii/23430914/?s=T8tWAw&ref=app]
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|Solving differential equations approximately using Euler's Method.
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|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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|[http://www.educreations.com/lesson/view/geometry-of-change-i/23430270/?s=pB3DZB&ref=app]
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|[http://www.educreations.com/lesson/view/logistic-equation/23431216/?s=2GkGkB&ref=app]
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|Geometry of change: (I) Slope fields.
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|The Logistic equation I (state space and slope field).
  
 
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|[http://www.educreations.com/lesson/view/geometry-of-change-ii/23430914/?s=T8tWAw&ref=app]
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|[http://www.educreations.com/lesson/view/slope-field-for-a-differential-equation/14300653/?s=c6aBLN&ref=app]
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|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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|The Logistic equation II (state space and slope field).
  
 
|- class="NewWeek OddWeek"
 
|- class="NewWeek OddWeek"
 
|id="week11"|Week 11
 
|id="week11"|Week 11
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|[http://www.educreations.com/lesson/view/geometry-of-change-i/23430270/?s=pB3DZB&ref=app]
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|[http://www.educreations.com/lesson/view/solving-a-diffl-eq-dy-dt-a-by/23385476/?s=ObLqjR&ref=app].
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|Geometry of change: (I) Slope fields.
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|Solving differential equations of the type $dy/dt=a-by$.
  
 
|- class="OddWeek"
 
|- class="OddWeek"
 
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|[http://www.educreations.com/lesson/view/geometry-of-change-ii/23430914/?s=T8tWAw&ref=app]
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|[https://www.youtube.com/watch?v=Yga2chpiLtc]
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|Geometry of change: (II) State space.
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|Solving differential equations approximately using Euler's Method - theory.
  
 
|- class="OddWeek"
 
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|
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|[http://www.educreations.com/lesson/view/logistic-equation/23431216/?s=2GkGkB&ref=app]
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|[https://www.youtube.com/watch?v=z7Kbp8hl950]
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|The Logistic equation (state space and slope field).
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|Solving differential equations approximately using Euler's Method - spreadsheet.
  
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|- class="NewWeek EvenWeek"
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|id="week12"|Week 12
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|[http://www.educreations.com/lesson/view/slope-field-for-a-differential-equation/14300653/?s=c6aBLN&ref=app]
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|The Logistic equation (state space and slope field).
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|[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]
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|Disease dynamics  
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|Disease dynamics I
  
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|[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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|Disease dynamics  
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|Disease dynamics II
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|- class="NewWeek EvenWeek"
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|id="week12"|Week 12
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|Review of differential equations and/or complete above topics.
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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.
 
  
 
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Latest revision as of 13:17, 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.
Retrieved from "https://wiki.math.ubc.ca/mathbook/M102/index.php?title=Pre-lecture_videos&oldid=7803"