Difference between revisions of "Pre-lecture videos"

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Revision as of 01:45, 6 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.
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.
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