Pre-lecture videos

	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 $x_0$.
	[22]	Increasing, decreasing and critical points.
	[23]	Concavity and inflection points.
Week 5
	EC	Finish sketching functions. Introduce simple optimization problem(s).
		More optimization examples including those with a constraint and those on bounded intervals. Distinction between absolute (global) and local minima and maxima.
Week 6	[24]	Kepler's Wedding - A wine optimization problem. (Blooper alert: want to get most wine for given budget)
	[25]	Optimal Foraging.
	[26],[27],[28]	Least Squares - finding the mean of a data set. See also the Fitting data supplement to the course notes.
	See Oct 10	Least Squares - finding the best fitting line y=ax through a set of data points.
	[29], [30]	Chain Rule: examples, applications to optimization problems.
Week 8	[31][32]	More Chain Rule: Related Rates and Implicit differentiation.
	[33]	Exponential functions: intro and motivation, derivative of exponential functions.
	[34]	Exponential functions: intro and motivation, derivative of exponential functions.
	[35]	Inverse functions and logarithm, applications of logs.
Week 9	[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.
	[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.