Difference between revisions of "Pre-lecture videos"

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|Geometry of change: (I) Slope fields.
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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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Revision as of 22:33, 6 November 2014

Date Video link Video contents
Week 1 Sept 3 [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.
Sept 5 [3] Sketching simple polynomials (y=x^3-ax).
Week 2 Sept 8 [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.
Sept 10 [7] Average rate of change and secant lines. Instantaneous rate of change.
[8] Definition of the derivative.
Sept 12 [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 Sept 15 [11] Derivatives: analytic, and geometric (zoom in on a point). Sketching $f'(x)$ given $f(x)$ (intro).
Sept 17-19 [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 Sept 22 [16] Equation of a Tangent line.
[17] Generic Tangent line and intro to Newton's method.
[18] Tangent lines and linear approximation.
Sept 24 [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.


Sept 26 [23] Concavity and inflection points.
Week 5 Sept 29
Sept 30 MIDTERM 1: 6-7 pm
Oct 1 EC Finish sketching functions. Introduce simple optimization problem(s).
Oct 3 More optimization examples including those with a constraint and those on bounded intervals. Distinction between absolute (global) and local minima and maxima.
Week 6 Oct 6 [24] Kepler's Wedding - A wine optimization problem. (Blooper alert: want to get most wine for given budget)
Oct 8 [25] Optimal Foraging.
Oct 10 [26],[27],[28] Least Squares - finding the mean of a data set. See also the Fitting data supplement to the course notes.
Week 7 Oct 13 THANKSGIVING - no classes.
Oct 15 See Oct 10 Least Squares - finding the best fitting line y=ax through a set of data points.
Oct 17 [29], [30] Chain Rule: examples, applications to optimization problems.
Week 8 Oct 20 [31][32] More Chain Rule: Related Rates and Implicit differentiation.
Oct 22 [33] Exponential functions: intro and motivation, derivative of exponential functions.
Oct 22 [34] Exponential functions: intro and motivation, derivative of exponential functions.
Oct 24 [35] Inverse functions and logarithm, applications of logs.
Week 9 Oct 27 [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.
Oct 29 [39] Solving differential equations of the type $dy/dt=a-by$.
Oct 29 [40] Solving differential equations of the type $dy/dt=a-by$.
Oct 31 LEK Newton's Law of Cooling (Murder Mystery example).
Week 10 Nov 3 Complete and/or review above topics.
Nov 4 MIDTERM 2: 6-7 pm
Nov 5 [41], [42] Solving differential equations approximately using Euler's Method.
Nov 7 [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 Nov 10 [45] Geometry of change: (I) Slope fields.
[46] Geometry of change: (II) State space.
Nov 11 Remembrance Day. University closed.
Nov 12 [47] The Logistic equation (state space and slope field).
[48] The Logistic equation (state space and slope field).
Nov 14 [49] Disease dynamics
[50] Disease dynamics
Week 12 Nov 17 Review of differential equations and/or complete above topics.
Nov 19 EC Introduction to Trigonometric Functions.
Nov 21 [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 Nov 24 WM Derivatives of trig functions, related rates examples.
Nov 26 [52] The Escape Response and trigonometric related rates.
Nov 28 Second order ODEs. Complete and/or review trig.
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