Difference between revisions of "Pre-lecture videos"

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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/solving-a-diffl-eq-dy-dt-a-by/23385476/?s=ObLqjR&ref=app].
+
|[http://www.educreations.com/lesson/view/geometry-of-change-i/23430270/?s=pB3DZB&ref=app]
−
|Solving differential equations of the type $dy/dt=a-by$ (same as [39]).
+
|Geometry of change: (I) Slope fields.
  
 
|- class="EvenWeek"
 
|- class="EvenWeek"
 
|
 
|
−
|[https://www.youtube.com/watch?v=Yga2chpiLtc]
+
|[http://www.educreations.com/lesson/view/geometry-of-change-ii/23430914/?s=T8tWAw&ref=app]
−
|Solving differential equations approximately using Euler's Method - theory.
+
|Geometry of change: (II) State space. This one is more relevant to the pre-lecture questions but you should watch both.
  
 
|- class="EvenWeek"
 
|- class="EvenWeek"
 
|
 
|
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|[https://www.youtube.com/watch?v=z7Kbp8hl950]
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|[http://www.educreations.com/lesson/view/logistic-equation/23431216/?s=2GkGkB&ref=app]
−
|Solving differential equations approximately using Euler's Method - spreadsheet.
+
|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"
 
|- 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/solving-a-diffl-eq-dy-dt-a-by/23385476/?s=ObLqjR&ref=app].
−
|Geometry of change: (I) Slope fields.
+
|Solving differential equations of the type $dy/dt=a-by$ (same as [39]).
  
 
|- class="OddWeek"
 
|- class="OddWeek"
 
|
 
|
−
|[http://www.educreations.com/lesson/view/geometry-of-change-ii/23430914/?s=T8tWAw&ref=app]
+
|[https://www.youtube.com/watch?v=Yga2chpiLtc]
−
|Geometry of change: (II) State space. This one is more relevant to the pre-lecture questions but you should watch both.
+
|Solving differential equations approximately using Euler's Method - theory.
  
 
|- class="OddWeek"
 
|- class="OddWeek"
 
|
 
|
−
|[http://www.educreations.com/lesson/view/logistic-equation/23431216/?s=2GkGkB&ref=app]
+
|[https://www.youtube.com/watch?v=z7Kbp8hl950]
−
|The Logistic equation I (state space and slope field).
+
|Solving differential equations approximately using Euler's Method - spreadsheet.
  
−
|- class="OddWeek"
+
|- class="OddWeek 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 EvenWeek"
+
 
|id="week12"|Week 12
 
|id="week12"|Week 12
 
|[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 I
 
|Disease dynamics I
  
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|- class="EvenWeek"
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|- class="OddWeek"
 
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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]
 
|Disease dynamics II
 
|Disease dynamics II
  
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|- class="EvenWeek"
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|- class="OddWeek"
 
|
 
|
 
|[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.
  
−
|- class="EvenWeek"
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|- class="OddWeek"
 
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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

Revision as of 15:56, 2 September 2016

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] 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 $x_0$.
Week 5 [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.
[39] Solving differential equations of the type $dy/dt=a-by$.
Week 10 [40] Geometry of change: (I) Slope fields.
[41] Geometry of change: (II) State space. This one is more relevant to the pre-lecture questions but you should watch both.
[42] The Logistic equation I (state space and slope field).
[43] The Logistic equation II (state space and slope field).
Week 11 [44]. Solving differential equations of the type $dy/dt=a-by$ (same as [39]).
[45] Solving differential equations approximately using Euler's Method - theory.
[46] Solving differential equations approximately using Euler's Method - spreadsheet.
Week 12 [47] Disease dynamics I
[48] Disease dynamics II
[49], [50] Introduction to Trigonometric Functions and review of trigonometric identities.
[51] (LEK),EC Trigonometric Functions and cyclic processes, phase, amplitude, etc. (fitting a sin or cos to a cyclic process), Inverse trig functions.
Week 13 [52] Derivatives of trig functions, related rates examples.
[53][54] The Escape Response and trigonometric related rates.
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