Difference between revisions of "Pre-lecture videos"

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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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Revision as of 07:34, 24 October 2015

Video link Video contents
Week 1 [1] Power functions - when is xn>xm 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 x0.
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 ax.
[35] Inverse functions and logarithm, applications of logs.
Week 9 [36] Differential equations for growth and decay.
[37] A differential equation for human population growth.
[38] Exponential growth and decay, intro to differential equations, population growth and/or other examples.
[39] Solving differential equations of the type dy/dt=a−by.
[40] Solving differential equations of the type dy/dt=a−by.
LEK Newton's Law of Cooling (Murder Mystery example).
Week 10 Complete and/or review above topics.
[41], [42] Solving differential equations approximately using Euler's Method.
[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 [45] Geometry of change: (I) Slope fields.
[46] Geometry of change: (II) State space.
[47] The Logistic equation (state space and slope field).
[48] The Logistic equation (state space and slope field).
[49] Disease dynamics
[50] Disease dynamics
Week 12 Review of differential equations and/or complete above topics.
[51], [52] Introduction to Trigonometric Functions and review of trigonometric identities.
[53] (LEK),EC Trigonometric Functions and cyclic processes, phase, amplitude, etc. (fitting a sin or cos to a cyclic process), Inverse trig functions.
Week 13 [54] Derivatives of trig functions, related rates examples.
[55][56] The Escape Response and trigonometric related rates.
Second order ODEs. Complete and/or review trig.
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