Pre-lecture videos

	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]	Go over midterm. Introduction to nonlinear ODEs, qualitative analysis.
Week 11	Nov 10	[44]	Geometry of change: (I) Slope fields, (II) State space .
		[45]	Geometry of change: (I) Slope fields, (II) State space .
	Nov 11		Remembrance Day. University closed.
	Nov 12	[46]	The Logistic equation (state space and slope field).
		[47]	The Logistic equation (state space and slope field).
	Nov 14	[48]	Disease dynamics
		[49]	Disease dynamics
Week 12	Nov 17		Review of differential equations and/or complete above topics.
	Nov 19	EC	Introduction to Trigonometric Functions.
	Nov 21	[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	Nov 24	WM	Derivatives of trig functions, related rates examples.
	Nov 26	[51]	The Escape Response and trigonometric related rates.
	Nov 28		Second order ODEs. Complete and/or review trig.