Difference between revisions of "Pre-lecture videos"

From UBCMATH WIKI
Jump to: navigation, search
Line 181: Line 181:
 
|Exponential functions: derivative of $a^x$.
 
|Exponential functions: derivative of $a^x$.
  
−
|- class="EvenWeek"
+
|- class="NewWeek OddWeek"
−
|
+
|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.
  
−
|- class="NewWeek OddWeek"
+
|- class="OddWeek"
−
|id="week9"|Week 9
+
|
 
|[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.
Line 210: Line 210:
 
|[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 $dy/dt=a-by$.
−
 
−
|- class="OddWeek"
 
−
|
 
−
|LEK
 
−
|Newton's Law of Cooling (Murder Mystery example).
 
  
 
|- class="NewWeek EvenWeek"
 
|- class="NewWeek EvenWeek"
 
|id="week10"|Week 10
 
|id="week10"|Week 10
−
|
 
−
|Complete and/or review above topics.
 
−
 
−
|- 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.
  
−
|- class="EvenWeek"
 
−
|
 
−
|[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="NewWeek OddWeek"
 
|- class="NewWeek OddWeek"
Line 244: Line 225:
 
|
 
|
 
|[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]
−
|Geometry of change: (II) State space.
+
|Geometry of change: (II) State space. This one is more relevant to the pre-lecture questions but you should watch both.
  
 
|- 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 I (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]
−
|The Logistic equation (state space and slope field).
+
|The Logistic equation II (state space and slope field).
  
−
|- class="OddWeek"
+
|- class="NewWeek EvenWeek"
−
|
+
|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  
+
|Disease dynamics I
  
−
|- class="OddWeek"
+
|- class="EvenWeek"
 
|
 
|
 
|[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  
+
|Disease dynamics II
−
 
+
−
|- class="NewWeek EvenWeek"
+
−
|id="week12"|Week 12
+
−
|
+
−
|Review of differential equations and/or complete above topics.
+
  
 
|- class="EvenWeek"
 
|- class="EvenWeek"
Line 290: Line 266:
 
|[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.  
−
 
−
|- class="OddWeek"
 
−
|
 
−
|
 
−
|Second order ODEs. Complete and/or review trig.
 
  
 
|}
 
|}

Revision as of 01:45, 30 October 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] 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 $dy/dt=a-by$.
[40] Solving differential equations of the type $dy/dt=a-by$.
Week 10 [41], [42] Solving differential equations approximately using Euler's Method.


Week 11 [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.
[45] The Logistic equation I (state space and slope field).
[46] The Logistic equation II (state space and slope field).
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.
Retrieved from "https://wiki.math.ubc.ca/mathbook/M102/index.php?title=Pre-lecture_videos&oldid=5784"