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MATHEMETICAL TOPIC(S)

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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

Cost of Power Lines

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 Contaimination

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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