Math100Videos

The videos below were made by Elyse Yeager for her Math 100 class at UBC. Due to the substantial overlap between the content of Math 100 and Math 102, we include them here for your use. Keep in mind that different courses and textbooks use slightly different conventions.

Topic		Link	Video contents
Limits	Limits and tangent lines	[1]	Average and Instantaneous Velocity; secant and tangent line; limit notation
	One-sided limits	[2]	A simple example motivating one-sided limits
	Limits, continued	[3]	Sometimes limits don't exist; one-sided limits; calculating limits
	Limits at Infinity	[4]	Limits at infinity
Continuity	Intro to Continuity	[5]	Before we learn the formal definition of a continuous function, dwell a little on what it means for a function's limit to differ from its value at a point. Being used to this behaviour will help you build intuition about continuity.
	Limits, Continuity, IVT	[6]	Strategies for evaluating limits; continuity; Intermediate Value Theorem
	Extra: continuity	[7]	Think you understand continuity? Test yourself with a graph that has no limit... anywhere. (This video goes beyond the course material. Think of it as recreational.)
Derivatives	Intro to Derivatives	[8]	Introduction to derivatives: interpretations, derivatives at a point, derivatives of a function
	Graphing Derivatives	[9]	Use the graph of a function to create the graph of its derivative. Review the interpretation of positive and negative derivatives, and get used to looking at a line and intuiting its slope.
	Tangent Lines	[10]	Find the tangent line to a curve; calculate derivatives using simple rules.
Differentiation	Product and Quotient Rules	[11]	Derivatives of Products and Ratios
	Exponential	[12]	Product rule and derivatives of exponential functions
	Trigonometric	[13]	Derivatives of trigonometric functions.
	Chain Rule	[14]	Derivatives of compound functions.
	Review: Inverse Functions	[15]	Inverse functions.
	Logarithms	[16]	Logarithmic functions and logarithmic differentiation.
Rates of Change	Rates of Change	[17]	Rates of Change
	Exponential change	[18]	Exponential growth and decay, such as radioactive decay, compound interest, and population growth. Introduction to differential equations.
	Newton's Law of Cooling	[19]	Exponential rates of change applied to cooling bodies.
Related Rates		[20]	Calculating the rate of change in systems with lots of interconnected changing parts.
Polynomial Approximations	First Approximations	[21]	Estimating the value of a function with a constant, linear, or quadratic approximation.
	Error Bounding	[22]	Give an approximation of a function, and bound the error you introduced.
		[23]	If you are given an error tolerance, which approximation should you use?
Optimization	Extrema	[24]	Finding maxima and minima of a function.
	Optimization	[25]	Second derivative test; solving an optimization word problem
		[26]	Another optimization word problem
Mean Value Theorem	Rolle's Theorem	[27]	A differentiable function that takes the same value twice has a horizontal tangent line somewhere.
	Mean Value Theorem	[28]	A differentiable function has a point where its instantaneous rate of change is equal to is average rate of change over an interval.
Curve Sketching	Curve Sketching 1	[29]	Sketching a curve using its domain and asymptotes.
	Curve Sketching 2	[30]	Sketching a curve using the first two derivatives.
	Symmetry	[31]	Even and odd functions.
L'Hospital's Rule		[32]	Using l'Hospital's rule in a variety of situations