TITLE |
MATHEMETICAL TOPIC(S) |
RELETED SUBJECT AREA(S) |
KEYWORDS |
---|---|---|---|
computing logarithm | Physical | Henderson-Hasselbalch Equation, pH-value, Base-10 Logarithm | |
natural exponential function and natural logarithm | Physical | Arrehenius Equation, Inverse Functions, Intercepts | |
concavity of a function | Biological | Allee Effect, Critial Points, Second Derivative Test | |
surveying problem | Physical | Gravity, Perpendicular Lines, Vectors | |
cross sections of a solid | Biological | CT Scan, Cone, Cylinder | |
optimization | Physical | Closed and Bounded Intervals, Fremat's Theorem | |
trigonometry in problem solving |
Physical |
Eclipse, Parameterization, Translation | |
Taylor polynomials | Biological | Alleles, remainder terms, Linear Approximation | |
algebraic tangency | Biological | Poiseuille's Law, Flux, Linear Approximation | |
derivative and antiderivatives of hyperbolic functions | Physical | Tension, Taylor Polynomial, Taylor Series | |
substitution, area of surface of revolution | Physical | Substitution in Integration, Antiderivatives | |
area of a surface of revolution | Physical | area, rotation | |
integral mean value theorem |
Agricultural |
Soil Moisture, Piecewise, Riemann Sum | |
first order differential equations | Biological | Prey and Predator, Per Capita Changes | |
implicit differentiation | Biological | BMI, Product Rule, Quotient Rule | |
difference quotient, average rate of change | Biological | Difference Quotient, Average Rate of Change | |
trigonometry in problem solviing | Physical | Newton, Cartesian Coordinates, Change of Coordinates | |
exponential growth models | Biological | Carbon Dating, Half-Life, Decay Rate | |
Fermat's Extreme Value Theorem |
Physical | Implicit Differentiation, Implicit Functions | |
asymptotic behavior of exponential function |
Biological | Gompertz Function, Horizontal Asymptote, Exponential Function | |
implicit differentiation | Biological | Keratocyte, Tangent to Ellipse, Orthogonal Direction | |
sketching functions |
Physical | Autocatalytic, Reaction Concavity, Extreme Value | |
first order initial value problems |
Physical | Law of Cooling, Antiderivative | |
motion in a plane | Physical | Centripedal Acceleration, Tangential Acceleration, Normal Acceleration | |
monotonicity of a function | Biological | Allee Model, Logistic Equation, Per Capita Growth Rate | |
linear scaling problems | Biological | Punnett Squares, Ratio, Proportion | |
linear scaling problems |
Physical | Mixture, Rate, Ratio | |
slope of a line, two-points form | Physical | Celsius, Fahrenheit, Linear Function | |
optimization | Physical | Critical Points, extrema | |
optimization | Physical | Critical Points, extrema | |
range of a piecewise defined function |
Mathematical | Partition, Domain | |
graphical representation of sinusoidal functions | Biological | Periodic Functions, Periods of a Function | |
optimization | Biological | Surge Function, Indeterminant Form, l'Hôpital Rule | |
reflection | Mathematical | Parabola, Translation, Reflection | |
sine and cosine functions | Physical | Bragg's Law, Diffraction, Reflection | |
distance between two points | Physical | Polar Coordinates, Cartesian Coordinates, Distance | |
first order initial value problems |
Physical |
Gravity, Antiderivative |
|
Riemann integrals as a limit |
Physical |
Coulomb's Law, Sequence of Partial Sums |
|
Riemann integrals as a limit | Physical | Coulomb's Law, Sequence of Partial Sums | |
distance and angles | Physical | Coulomb's Law, Polar Coordinates, Cartesian Coordinates | |
quadratic formula | Physical | Reversible Reaction, Quadratic Equations, Quadratic Formula | |
difference quotient, average rate of change | Physical | John Paul Stapp, Average Velocity, Average Acceleration | |
linear scaling problems | Mathematical | Ratio | |
sketching functions |
Biological |
Functional Response, Asymptote, Inflection |
|
domain of composite functions | Biological | Quadratic Functions, Range, Domain | |
basic rules of differentiation | Biological | Quotient Rule, Horizontal Asymptote | |
basic rules of differentiation | Biological | Functional Response, Type II, Functional Response, Type III, Quotient Rules | |
first order initial value problems | Physical | Resisting Force, Acceleration, Asymptote | |
nonlinear scaling | Biological | Bacteria, Power Functions, | |
antiderivative | Biological | Antiderivative, Per Capita Growth Rate | |
derivative of exponential function and logarithm | Biological | von Bertalanffy Function, Asymptote, Logarithmic Equations | |
graph of quadratic functions | Biological | Hardy-Weinberg Principle, Transformation, | |
limits of indeterminate forms | Physical | Einstein Solid Model, l'Hôptial Rule, | |
inverse proportion, nonlinear scaling | Physical | Ideal Gas, Inverse Proportion, Nonlinear Scaling | |
derivative and antiderivatives of hyperbolic functions | Physical | Tension, Catenary, Parabola | |
domain and range of an inverse function | Biological | Cardiac Index, Inverse Proportion, | |
antiderivatives of the products and sums of polynomial, sine, cosine, and exponential functions | Physical | Bohr Radius, Probability Density Function, Fundamental Theorem of Calculus I | |
definite integrals | Physical | Bohr Radius, Spherical Symmetry, Probability Density | |
antiderivative of rational functions | Biological | Carrying Capacity, Inverse Function Theorem, Partial Fractions | |
linear motion and collision | Physical | Equation of Motion, Constant Velocity, Parametric form | |
monotonicity of a function | Biological | Invasive Species, Per Capita Growth Rate | |
Riemann integrals of monomials | Biological | Poiseuille's Law, Laminar Flow | |
fundamental theorem of calculus | Physical | Law of Mass Action, Fundamental Theorem of Calculus I, Fundamental Theorem of Calculus II | |
algebraic tangency | Physical | Tangent Line, Linear Approximation, Polynomials | |
slope-intercept form of a line | Biological | Lineweaver-Burk, Michaelis-Menton, y-intercept | |
limits of recursively defined sequences | Biological | Biomass, Recursive Formula | |
first order differential equations |
Biological |
Logistic Functions, Exponential growth, Approximation |
|
sketching functions | Mathematical | Logistic Functions, Critical Points, Concavity | |
optimization | Biological | Chemotherapy, Critical Points, Fremat's Theorem | |
Taylor polynomials | Physical | remainder terms | |
range of a piecewise defined function |
Biological |
Slope, Piecewise Linear Function |
|
linear motion and collision | Physical | Equation of Motion, Constant Velocity, Parametric form | |
antiderivatives of the products and sums of polynomial, sine, cosine, and exponential functions | Physical | Schrödinger Equation, Integration Constant, Probability Density | |
linear scaling problems |
Mathematical | Units, Ratios | |
asymptotic behavior of rational functions |
Mathematical |
Horizontal Asymptote, Rates |
|
antiderivative of rational functions | Biological | Carrying Capacity, Inverse Function Theorem, Partial Fractions | |
conversion between coordinate systems |
Mathematical |
Polar Coordinates, Cartesian Coordinates, Change of Coordinates |
|
integration by parts | Physical | Quantum State, Probability Density | |
implicit differentiation | Physical | Related Rate, Pythagorean Theorem | |
Integrability of continuous functions |
Physical |
Planck's Radiation Law, Left Continuity, Right Continuity |
|
instantaneous rate of change | Physical | Dimerization, Average Rate, Instantenous Rate | |
volume of a solid of revolution | Biological | CT Scan, Cone, Cylinder | |
exponential growth models | Physical | Resistive Force | |
area between graphs of functions |
Physical |
Ellipse, Decomposition, Areas |
|
limits of indeterminate forms |
Biological |
Shannon Index, Conintuous Extension, l'Hôpital Rule |
|
range of a piecewise defined function |
Physical |
Volumnetric Water Content, Slope, Piecewise Linear Function |
|
rotation and reflection |
Physical |
Involution, Rotation, Transformations |
|
sketching functions |
Biological |
Surge Function, Inflection Points, Horizontal Asymptote |
|
graphical representation of sinusoidal functions | Mathematical | Periodic Functions, Amplitude, Period | |
Taylor series | Physical | Halley's Comet, Relativistic Kinetic Energy, Kinetic Energy | |
trigonometric substitutions | Physical | Surface of Revolution, Cylindrical Shell, Area | |
motion in a plane | Physical |
Projectile, Horizontal Component, Vertical Component |
|
exponential and logarithmic equations | Physical | pH Value, Base-10 | |
comparison tests | Physical | Planck's Radiation Law | |
motion in a plane | Physical | Projectile, Horizontal Component, Vertical Component | |
implicit differentiation | Physical | Trigonometric Functions | |
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exponential growth models | Biological | Gompertz Function | |
perturbation of input values | Biological | Poiseuille's Law, Perturbation, Error Terms | |
instantaneous rate of change | Physical | Velocity, Average Velocity, Instantenous Velocity | |
implicit differentiation | Physical | Local Linear Approximation, Co-Varying Quantities | |
Physical | Recursive Expression, Summation Notation | ||
volume of a solid of revolution | Mathematical | Oval, Cross sections | |
graphical representation of sinusoidal functions | Physical | Schrödinger Equation, Wave Function, Periodicity | |
tangent line as an approximation | Biological | Modeling, Linear Approximation | |
Riemann integrals as a limit | Physical | Boyle's Law, Inverse Proportion, Work Done | |
VIII.6.2 | Physical | Hooke's Constant, Force Fields, Work Integrals |