DESCRIPTION

EQUATION

Pythagorean Property - Sine and Cosine 

Sine Definition for a Right Triangle 

Cosine Definition for a Right Triangle 

Tangent Definition for a Right Triangle 

Double Angle Identity - Sine 

Double Angle Identity - Cosine 

Half Angle Identity - Sine 

Half Angle Identity - Cosine 

Sum and Difference of Angles Identity - Sine 

Sum and Difference of Angles Identity - Cosine 

Additive Identity Property 

Additive Inverse Property 

Associative Property of Addition 

Commutative Property of Addition 

Definition of Subtraction 

Multiplicative Identity 

Multiplicative Inverse 

Zero Multiplication Property 

Associative Property of Multiplication 

Definition of Division 

Square of a First Order Polynomial 

Polynomial FOIL operation 

Difference of Squares Factorization 

Sum of Cubes Factorization 

Difference of Cubes Factorization 

Second Order Polynomial Factorization 

Quadratic Formula 

Exponent Equal to Zero Rule 

Exponent Equal to One Rule 

Addition of Exponents Rule 

Distributive Property of Exponents 

Power Rule of Exponents 

Fractional Exponent to Fractional Root Relationship 

Definition of Square Root 

Negative Exponent Definition 

Subtraction of Exponents Rule 

Definition of a Logarithm 

Logarithm of One 

Logarithmic Identity Property 

Sum of Logarithms Property 

Difference of Logarithms Property 

Logarithm of an Exponential 

Logarithm Base Conversion 

SURD Multiplication 

SURD Division 

SURD Addition and Subtraction 

Integral of powers not equal to -1 

Integration by parts 

Integral of reciprocal 

Integral of cosine 

Integral of sine 

Integral of tangent 

Integral of cosecant 

Integral of secant 

Limit of Sine X over X as X Approaches Zero 

Limit of Tangent X over X as X Approaches Zero 

Area of a circle 

Area of an ellipse 

Area of an equilateral triangle 

Area of a parallelogram 

Area of a rectangle 

Area of a regular polygon 

Area of a rhombus 

Area of a sector 

Area of a square 

Area of a trapezoid 

Area of a triangle 

Volume of a cone 

Volume of a sphere 

Volume of a pyramid 

Volume of a cube 

Volume of a cuboid 

Volume of a cylinder 

Volume of a prism 

Ideal gas equation 

Surface area of a sphere 

Surface area of a cylinder 

Surface area of a cuboid 

Surface area of a cube 

Refractive index 

Einstein's relativistic mass-energy relation 

spring constant 

simple harmonic motion acceleration 

Adibiatic change 

Ampere's law 

Angular Momentum 

Beat frequency 

Charles' Law 

de Broglie wavelength 

Voltage equation 

Yukawa Potential 

Young's modulus 

Newton's Second Law (Force) 

Z-transform time domain convolution (z domain multiplication) property 

Z-transform linearity property 

Z-transform translation (time shift) property 

Z-transform multiplication by an exponential (z domain scaling) property 

Z-transform multiplication by a ramp (z domain differentiation) property 

Z-transform time domain multiplication (z domain convolution) property 

Z-transform initial value theorem 

Z-transform final value theorem. Valid only if polues of (z-1)X(z) are inside the unit circle. 

Z-transform of delta 

Z-transform of shifted delta 

Z-transform of unit step function 

Z-transform involving the unit step function 

Z-transform involving the unit step function 

Z-transform involving the unit step function 

Z-transform involving the unit step function and an exponential 

Z-transform involving the unit step function and an exponential 

Z-transform involving the unit step function and an exponential 

Z-transform involving the unit step function and an exponential 

Z-transform involving the unit step function and an exponential 

Z-transform involving the unit step function and an exponential 

Z-transform involving the unit step function and an exponential 

Z-transform involving the unit step function and an exponential 

Z-transform involving the unit step function and sine 

Z-transform involving the unit step function and cosine 

Z-transform involving the unit step function and cosine 

Z-transform involving the unit step function and sine 

Z-transform involving the unit step function and hyperbolic sine 

Z-transform involving the unit step function and hyperbolic cosine 

Laplace transform of Kroeneker delta function 

Laplace transform of unit step function times a constant (K) 

Laplace transform involving the unit step function 

Laplace transform involving the unit step function 

Laplace transform involving the unit step function and an exponential 

Laplace transform involving the unit step function and an exponential 

Laplace transform involving the unit step function and sine 

Laplace transform involving the unit step function and cosine 

Laplace transform involving the unit step function, cosine, and an exponential 

Laplace transform involving the unit step function, sine, and an exponential 

Laplace transform linearity property 

Laplace transform Nth time domain derivative property 

Laplace transform integral property 

Laplace transform time domain shifting property 

Laplace transform time domain scaling property 

Laplace transform time varying coefficient (s domain differentiation) property 

Laplace transform time domain linear convolution (s domain multiplication) property 

Laplace transform final value theorem (valid if poles of sX(s) are in left half of s plane). 

Laplace transform initial value theorem 

Laplace transform definition 

Z transform definition 

Discrete-Time Fourier linearity theorem 

Discrete-Time Fourier time shift property 

Discrete-Time Fourier frequency shift property 

Discrete-Time Fourier time reversal property 

Discrete-Time Fourier time reversal property; x(n) real 

Discrete-Time Fourier frequency differentiation property 

Discrete-Time Fourier time/space convolution property 

Discrete-Time Fourier windowing, modulation, frequency convolution property 

Discrete-Time Fourier transform - Parseval's Theorem 

Discrete-Time Fourier transform - Parseval's Theorem 

Discrete-Time Fourier transform of delta 

Discrete-Time Fourier transform of shifted delta 

Discrete-Time Fourier transform of a constant 

Discrete-Time Fourier transform of unit step function 

Discrete-Time Fourier transform of unit step function and exponential 

Discrete-Time Fourier transform of unit step function and exponential 

Discrete-Time Fourier transform of complex exponential 

Discrete-Time Fourier transform of a sinc sequence 

Discrete-Time Fourier transform of a boxcar sequence 

Discrete-Time Fourier transform definition 

Black Hole Entropy as derived by Stephen Hawking 

Time-independent, one-dimensional Schr 

Time-dependent, one-dimensional Schr 

Ohm's Law 

Bohr Radius 

Radii of stable orbits in the Bohr model 

Phase difference between the first and last waves for a single-slit diffraction pattern 

single-slit diffraction pattern points of zero intensity 

Superposition of standing waves on a string with both ends fixed 

Standing-wave function 

Energy transmitted by a harmonic wave 

Power transmitted by a harmonic wave 

Harmonic wave function 

Harmonic wave function 

Velocity at resonance frequency of a driven oscillator 

Amplitude of a driven oscillation 

Displacement of a driven oscillator 

Displacement of a slightly damped oscillator 

Kinetic energy of simple harmonic motion 

Potential energy of simple harmonic motion 

Total energy of simple harmonic motion 

Viscous flow 

Continuity equation 

Hydraulic lift 

Shear modulus defined 

Shear stress 

Stress 

Centripetal acceleration 

Instantaneous Acceleration 

Velocity 

Displacement 

Velocity 

Average acceleration 

Maxwell's equation - Faraday's law 

Maxwell's equation - Gauss's law 

Self inductance of a solenoid 

Magnetic flux defined 

EMF (Electromotive Force) defined 

Resistance 

Electric current 

Number density of charge carriers 

Current in a conducting strip 

Magnetic dipole moment of a current loop 

Capacitance of a cylindrical capacitor 

Capacitance of a parallel-plate capacitor 

Potential due to a line charge 

Change in potential 

Change in electrostatic potential energy for a point charge 

Gauss's law 

Electric flux defined 

Electric field on the axis of a ring charge 

Acceleration of a particle in an electric field 

Net power radiated by an object 

Radiation absorbed by an object 

Stefan-Boltzmann law 

Thermal resistance 

Thermal conduction 

Van der Waals equation 

Speed of sound waves in a fluid 

Phase constant of a driven oscillation 

Angular frequency for a damped oscillation 

Energy change in a damped oscillation 

Energy change in a damped oscillation 

Compressibility 

Bulk modulus defined 

Poynting vector 

Electric field and magnetic field relationship for an electromagnetic wave 

Wave equation for magnetic field 

Magnetic field inside a solenoid 

Biot-Savart law 

Torque on a current loop 

Magnetic force on a moving charge 

Rydberg constant 

Schwarzschild Black Hole Radius 

Black Hole Temperature 

Binomial Coefficient 

Binomial Equation 

Mean of Binomial Distribution 

Variance of Binomial Distribution 

Standard Normal Distribution 

Euler's Constant 

Gaussian Normal Distribution 

nth moment about point a 

Mean about zero 

Variance or second moment about the Mean 

Fisher Skewness 

Standard Deviation 

Sample Variance (Biased) 

Unbiased Estimator of Populatoin Sample Variance 

Standard Error 

Poisson Distribution 

Gamma Distribution 

Pythagorean Property - Tangent and Secant 

Pythagorean Property - Cotangent and Cosecant 

Reciprocal Property - Tangent and Cotangent 

Reciprocal Property - Sine and Cosecant 

Reciprocal Property - Cosine and Secant 

Quotient Property - Tangent, Sine, and Cosine 

Quotient Property - Tangent, Secant, and Cosecant 

Quotient Property - Cotangent, Cosecant, and Secant 

Quotient Property - Cotangent, Cosine, and Sine 

Odd Symmetry Property - Sine 

Odd Symmetry Property - Tangent 

Odd Symmetry Property - Cosecant 

Even Symmetry Property - Cosine 

Even Symmetry Property - Cotangent 

Even Symmetry Property - Secant 

Area of Arbitrary Triangle 

Law of Sines 

Law of Cosines 

Sum and Difference of Angles Identity - Tangent 

Cotangent Definition for a Right Triangle 

Cosecant Definition for a Right Triangle 

Secant Definition for a Right Triangle 

Distributive Property 

Derivative of a Constant 

Derivative of a Variable to the First Power 

Derivative of a Variable to the nth Power 

Derivative of an Exponential 

Derivative of an Arbitrary Base Exponential 

Derivative of a Natural Logarithm 

Derivative of Sine 

Derivative of Cosine 

Derivative of Tangent 

Derivative of Cotangent 

Derivative of Secant 

Derivative of Cosecant 

Derivative of Inverse Sine (Arcsine) 

Derivative of Inverse Cosine (Arccosine) 

Derivative of Inverse Tangent (Arctangent) 

Derivative of Inverse Cosecant (Arccosecant) 

Derivative of Inverse Secant (Arcsecant) 

Derivative of Inverse Cotangent (Arccotangent) 

Derivative of Hyperbolic Sine 

Derivative of Hyperbolic Cosine 

Derivative of Hyperbolic Tangent 

Derivative of Hyperbolic Cotangent 

Derivative of Hyperbolic Secant 

Derivative of Hyperbolic Cosecant 

Product Rule of Differentiation 

Quotient Rule of Differentiation 

Chain Rule of Differentiation 

Fundamental Theorem for Derivatives 

Definition of a Derivative 

Fundamental Theorem of Integrals of Derivatives 

Gamma Function 

Equation of a Line 

Equation of a Circle 

Equation of a Sphere 

Equation of an Ellipsoid 

Equation of an Ellipse 

Superposition (Addition and Subtraction) of Sine of Angles 

Superposition (Addition) of Cosine of Angles 

Superposition (Subtraction) of Cosine of Angles 

Euler's Formula 

Cosine Definition as an Infinite Series 

Sine Definition as an Infinite Series 

Distance Between Two Points (2-D) 

Distance Between Two Points (3-D) 

Cartesian to Polar Coordinates (2-D) 

Eccentricity of an Ellipse 

Eccentricity of a Hyperbola 

Equation of a Hyperbola 

Equation of a Plane 

Equation of a Hyperboloid of One Sheet 

Equation of an Elliptic Cone 

Equation of an Elliptic Cylinder 

Equation of a Hyperboloid of Two Sheets 

Equation of an Elliptic Paraboloid 

Equation of a Hyperbolic Paraboloid 

Equation of a Parabola 

Cartesian to Spherical Coordinates (3-D) 

Cartesian to Cylindrical Coordinates (3-D) 

Cylindrical to Spherical Coordinates (3-D) 

Arithmetic Series - Sequential Integers 

Arithmetic Series - Sequential Odd Integers 

Arithmetic Series - Sequential Squared Integers 

Finite Geometric Series 

Infinite Geometric Series 

Perimeter of a Circle 

Perimeter of a Rectangle 

Perimeter of a Square 

Perimeter of a Triangle 

Perimeter of a Regular Polygon 

Spiral of Archimedes (Archimedean Spiral) in Polar Coordinates 

Arclength 

L'Hopital's Rule 

Limit of One over X to the nth Power 

Limit of Arctangent X as X Approaches Infinity 

Limit of Arctangent X as X Approaches Negative Infinity 

Limit of e to the X power as X Approaches Negative Infinity 

Entropy Change 

Enthalpy Change 

Gibb's Free Energy Change Defined 

Gibb's Free Energy Change in Terms of Enthalpy, Absolute Temperature, and Entropy 

Gibb's Free Energy Change in Terms of Gas Constant, Absolute Temperature, and Equilibrium Constant 

Gibb's Free Energy Change in Terms of Number of Moles, Faraday, and Standard Reduction Potential 

Reaction Quotient 

Electric Current 

Cell Voltage 

Relationship between Equilibrium Constant and Cell Voltage 

Molar Heat Capacity at Constant Pressure 

Partial Pressure of a Gas 

Total Gas Pressure as Sum of Partial Pressures 

Number of Moles 

Temperature in Kelvin from Degrees Celsius Conversion 

Combined Gas Law 

Density of a Material 

Root Mean Square Velocity of Gas Molecules 

Kinetic Energy per molecule 

Kinetic Energy per Mole 

Kinetic Energy per Mole 

Graham's Law of Effusion 

Molarity Defined 

Molality Defined 

Freezing Point Depression 

Boiling Point Elevation 

Osmotic Pressure 

Specific Heat Capacity to Heat Equation 

Acid Ionization Constant 

Base Ionization Constant 

Ion Product Constant for Water 

pH Defined 

pOH Defined 

pH and pOH Relationship 

Buffer Design Equation 

pOH and Base Ionization Equilibrium Constant Relationship 

pK_a Definition 

pK_b Definition 

Gas Pressure and Concentration Relationship 

Planck's Quantized (Quantum) Energy Equation 

Speed of Light to Wavelength and Frequency Relationship 

De Broglie Wavelength 

Linear Momentum 

Relationship between Energy and Principal Quantum Number 

Rydberg Equation 

van't Hoff equation