Microtutorial Videos

TITLE	MATHEMETICAL TOPIC(S)	RELETED SUBJECT AREA(S)	KEYWORDS
A Buffered Solution	computing logarithm	Physical	Henderson-Hasselbalch Equation, pH-value, Base-10 Logarithm
A Model for Chemical Kinetics	natural exponential function and natural logarithm	Physical	Arrehenius Equation, Inverse Functions, Intercepts
A Sketch of Allee Effect	concavity of a function	Biological	Allee Effect, Critial Points, Second Derivative Test
Acceleration of a Skier	surveying problem	Physical	Gravity, Perpendicular Lines, Vectors
An Oval Shaped Tumor	cross sections of a solid	Biological	CT Scan, Cone, Cylinder
Angle of Vision	optimization	Physical	Closed and Bounded Intervals, Fremat's Theorem
Annular Solar Eclipse	trigonometry in problem solving	Physical	Eclipse, Parameterization, Translation
Approximating Genetic Drift	Taylor polynomials	Biological	Alleles, remainder terms, Linear Approximation
Approximation of Blood Flow	algebraic tangency	Biological	Poiseuille's Law, Flux, Linear Approximation
Approximation of Hanging Cables	derivative and antiderivatives of hyperbolic functions	Physical	Tension, Taylor Polynomial, Taylor Series
Area of a Satellite Dish	substitution, area of surface of revolution	Physical	Substitution in Integration, Antiderivatives
Area of a Tunnel	area of a surface of revolution	Physical	area, rotation
Average Soil Moisture	integral mean value theorem	Agricultural	Soil Moisture, Piecewise, Riemann Sum
Bobcats and Rabbits	first order differential equations	Biological	Prey and Predator, Per Capita Changes
Body Mass Index	implicit differentiation	Biological	BMI, Product Rule, Quotient Rule
California Population	difference quotient, average rate of change	Biological	Difference Quotient, Average Rate of Change
Car Accident	trigonometry in problem solviing	Physical	Newton, Cartesian Coordinates, Change of Coordinates
Carbon Dating	exponential growth models	Biological	Carbon Dating, Half-Life, Decay Rate
Carousel	Fermat's Extreme Value Theorem	Physical	Implicit Differentiation, Implicit Functions
Carrying Capacity of Tumors	asymptotic behavior of exponential function	Biological	Gompertz Function, Horizontal Asymptote, Exponential Function
Cell Motility	implicit differentiation	Biological	Keratocyte, Tangent to Ellipse, Orthogonal Direction
Chemical Reaction and Logistic Equation	sketching functions	Physical	Autocatalytic, Reaction Concavity, Extreme Value
Chilled Soda	first order initial value problems	Physical	Law of Cooling, Antiderivative
Circular Motion	motion in a plane	Physical	Centripedal Acceleration, Tangential Acceleration, Normal Acceleration
Competition and Cooperation	monotonicity of a function	Biological	Allee Model, Logistic Equation, Per Capita Growth Rate
Computing Punnett Squares	linear scaling problems	Biological	Punnett Squares, Ratio, Proportion
Concentration of a Mixture	linear scaling problems	Physical	Mixture, Rate, Ratio
Confined Particles
Conversion of Temperature	slope of a line, two-points form	Physical	Celsius, Fahrenheit, Linear Function
Cost of Power Line	optimization	Physical	Critical Points, extrema
Cross Section of a Salad Bowl	range of a piecewise defined function	Mathematical	Partition, Domain
Daylight	graphical representation of sinusoidal functions	Biological	Periodic Functions, Periods of a Function
Design a Drug	optimization	Biological	Surge Function, Indeterminant Form, l'Hôpital Rule
Design a Flying Saucer	reflection	Mathematical	Parabola, Translation, Reflection
Diffraction in Crystals	sine and cosine functions	Physical	Bragg's Law, Diffraction, Reflection
Displacement of a Hockey Puck	distance between two points	Physical	Polar Coordinates, Cartesian Coordinates, Distance
Dropping a Phone	first order initial value problems	Physical	Gravity, Antiderivative
Electric Force of a Bent Wire	Riemann integrals as a limit	Physical	Coulomb's Law, Sequence of Partial Sums
Electric Force of a Straight Wire	Riemann integrals as a limit	Physical	Coulomb's Law, Sequence of Partial Sums
Electrostatic Forces	distance and angles	Physical	Coulomb's Law, Polar Coordinates, Cartesian Coordinates
Equilibrium Concentration	quadratic formula	Physical	Reversible Reaction, Quadratic Equations, Quadratic Formula
Extreme Acceleration	difference quotient, average rate of change	Physical	John Paul Stapp, Average Velocity, Average Acceleration
Fencing a Farm	linear scaling problems	Mathematical	Ratio
Food Consumption	sketching functions	Biological	Functional Response, Asymptote, Inflection
Food Contamination	domain of composite functions	Biological	Quadratic Functions, Range, Domain
Foraging	basic rules of differentiation	Biological	Quotient Rule, Horizontal Asymptote
Functional Response	basic rules of differentiation	Biological	Functional Response, Type II, Functional Response, Type III, Quotient Rules
Genetic Drift
Gravity Against Resisting Force	first order initial value problems	Physical	Resisting Force, Acceleration, Asymptote
Growing Bacteria	nonlinear scaling	Biological	Bacteria, Power Functions,
Growing Bananas	antiderivative	Biological	Antiderivative, Per Capita Growth Rate
Growth of Common Dolphins	derivative of exponential function and logarithm	Biological	von Bertalanffy Function, Asymptote, Logarithmic Equations
Hardy-Weinberg Analysis	graph of quadratic functions	Biological	Hardy-Weinberg Principle, Transformation,
Heat Capacity	limits of indeterminate forms	Physical	Einstein Solid Model, l'Hôptial Rule,
Ideal Gas	inverse proportion, nonlinear scaling	Physical	Ideal Gas, Inverse Proportion, Nonlinear Scaling
Illusion of Hanging Cables	derivative and antiderivatives of hyperbolic functions	Physical	Tension, Catenary, Parabola
Index of Healthy Hearts	domain and range of an inverse function	Biological	Cardiac Index, Inverse Proportion,
Inside a Hydrogen Atom*	antiderivatives of the products and sums of polynomial, sine, cosine, and exponential functions	Physical	Bohr Radius, Probability Density Function, Fundamental Theorem of Calculus I
Inside a Hydrogen Atom*	definite integrals	Physical	Bohr Radius, Spherical Symmetry, Probability Density
Integration of the Logistic Model	antiderivative of rational functions	Biological	Carrying Capacity, Inverse Function Theorem, Partial Fractions
Intercepting a Boat	linear motion and collision	Physical	Equation of Motion, Constant Velocity, Parametric form
Invasive Species	monotonicity of a function	Biological	Invasive Species, Per Capita Growth Rate
Laminar Blood	Riemann integrals of monomials	Biological	Poiseuille's Law, Laminar Flow
Law of Mass Action	fundamental theorem of calculus	Physical	Law of Mass Action, Fundamental Theorem of Calculus I, Fundamental Theorem of Calculus II
Learning Ski Jumping	algebraic tangency	Physical	Tangent Line, Linear Approximation, Polynomials
Lineweaver-Burk Plot	slope-intercept form of a line	Biological	Lineweaver-Burk, Michaelis-Menton, y-intercept
Logging	limits of recursively defined sequences	Biological	Biomass, Recursive Formula
Logistic Equation of Population Dynamics	first order differential equations	Biological	Logistic Functions, Exponential growth, Approximation
Logistic Functions	sketching functions	Mathematical	Logistic Functions, Critical Points, Concavity
Maximizing Chemotherapy	optimization	Biological	Chemotherapy, Critical Points, Fremat's Theorem
Melting Ice Cube	Taylor polynomials	Physical	remainder terms
Metabolizing Medicine	range of a piecewise defined function	Biological	Slope, Piecewise Linear Function
Motions with Constant Velocity	linear motion and collision	Physical	Equation of Motion, Constant Velocity, Parametric form
Normalizing Probability	antiderivatives of the products and sums of polynomial, sine, cosine, and exponential functions	Physical	Schrödinger Equation, Integration Constant, Probability Density
Orchard Planning	linear scaling problems	Mathematical	Units, Ratios
Overflowing a Mixture	asymptotic behavior of rational functions	Mathematical	Horizontal Asymptote, Rates
Parameters of Allee Effect	antiderivative of rational functions	Biological	Carrying Capacity, Inverse Function Theorem, Partial Fractions
Planning a County Fair	conversion between coordinate systems	Mathematical	Polar Coordinates, Cartesian Coordinates, Change of Coordinates
Probability and Hydrogen Atom	integration by parts	Physical	Quantum State, Probability Density
Pulling a Weight	implicit differentiation	Physical	Related Rate, Pythagorean Theorem
Radiation Law in Frequency	Integrability of continuous functions	Physical	Planck's Radiation Law, Left Continuity, Right Continuity
Rate of Dimerization	instantaneous rate of change	Physical	Dimerization, Average Rate, Instantenous Rate
Reading CT Scan	volume of a solid of revolution	Biological	CT Scan, Cone, Cylinder
Resistive Forces	exponential growth models	Physical	Resistive Force
Shadow of the Moon	area between graphs of functions	Physical	Ellipse, Decomposition, Areas
Shannon Index of Species Diversity	limits of indeterminate forms	Biological	Shannon Index, Conintuous Extension, l'Hôpital Rule
Soil Moisture	range of a piecewise defined function	Physical	Volumnetric Water Content, Slope, Piecewise Linear Function
South of the Equator	rotation and reflection	Physical	Involution, Rotation, Transformations
Surge Function	sketching functions	Biological	Surge Function, Inflection Points, Horizontal Asymptote
Temperature of a Day	graphical representation of sinusoidal functions	Mathematical	Periodic Functions, Amplitude, Period
The Halley's Comet	Taylor series	Physical	Halley's Comet, Relativistic Kinetic Energy, Kinetic Energy
The Shell of a Tunnel	trigonometric substitutions	Physical	Surface of Revolution, Cylindrical Shell, Area
The Trajectory of a Projectile	motion in a plane	Physical	Projectile, Horizontal Component, Vertical Component
The pH of Soft Drinks	exponential and logarithmic equations	Physical	pH Value, Base-10
Total Radiance	comparison tests	Physical	Planck's Radiation Law
Tracking a Skateboarder	motion in a plane	Physical	Projectile, Horizontal Component, Vertical Component
Tracking an F-22	implicit differentiation	Physical	Trigonometric Functions
Tropic of Cancer
Tumor Growth	exponential growth models	Biological	Gompertz Function
Unclog an Artery	perturbation of input values	Biological	Poiseuille's Law, Perturbation, Error Terms
Velocity	instantaneous rate of change	Physical	Velocity, Average Velocity, Instantenous Velocity
Vision of a Highway Patrol	implicit differentiation	Physical	Local Linear Approximation, Co-Varying Quantities
Volume of Pyramids		Physical	Recursive Expression, Summation Notation
Volume of an Oval Watermelon	volume of a solid of revolution	Mathematical	Oval, Cross sections
Wave Functions and Probability Density	graphical representation of sinusoidal functions	Physical	Schrödinger Equation, Wave Function, Periodicity
Wind Chill	tangent line as an approximation	Biological	Modeling, Linear Approximation
Working with Ideal Gas	Riemann integrals as a limit	Physical	Boyle's Law, Inverse Proportion, Work Done
Work Done	VIII.6.2	Physical	Hooke's Constant, Force Fields, Work Integrals

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