the ultimate cheat sheet for math & physics · pdf fileimplicit differentiation ... visually...
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CopyrightWeSolveThemLLC 1
TheUltimateCheatSheetforMath&PhysicsPreview
TableofContentsAlgebra..............................................................................................................................................2Arithmetic......................................................................................................................................................................................................2Exponents......................................................................................................................................................................................................3
Trigonometry.....................................................................................................................................4DoubleAngleFormulas...........................................................................................................................................................................4HalfAngleFormulas..................................................................................................................................................................................5SumandDifferenceFormulas..............................................................................................................................................................6
Precalculus.........................................................................................................................................7EquationofaLine......................................................................................................................................................................................7EquationofParabola................................................................................................................................................................................7EquationofCircle.......................................................................................................................................................................................7EquationofEllipse.....................................................................................................................................................................................7EquationofHyperbola.............................................................................................................................................................................7EquationofHyperbola.............................................................................................................................................................................7
Calculus..............................................................................................................................................8Tangentline..................................................................................................................................................................................................8Implicitdifferentiation............................................................................................................................................................................9
LinearAlgebra..................................................................................................................................10Rankofmatrixandpivots...................................................................................................................................................................10Lengthofavectorandtheunitvector...........................................................................................................................................11SolutionsofAugmentedMatrices....................................................................................................................................................12CoefficientMatrix....................................................................................................................................................................................12UniqueSolution.......................................................................................................................................................................................13InfiniteSolution.......................................................................................................................................................................................13NoSolution.................................................................................................................................................................................................13DifferentialEquations......................................................................................................................14First-OrderLinearNon-Homogeneous..........................................................................................................................................14OrderandLinearity................................................................................................................................................................................14ReductionofOrder.................................................................................................................................................................................15
Physics.............................................................................................................................................16Vectors.........................................................................................................................................................................................................16DotProduct................................................................................................................................................................................................16CrossProduct............................................................................................................................................................................................16MagnitudeorLengthofavector......................................................................................................................................................17ResultantVector......................................................................................................................................................................................17
QuickReference...............................................................................................................................19Arithmetic...................................................................................................................................................................................................19Exponential................................................................................................................................................................................................19Radicals.......................................................................................................................................................................................................19Fractions.....................................................................................................................................................................................................19Logarithmic................................................................................................................................................................................................19
CopyrightWeSolveThemLLC 2
QuadraticFormula..................................................................................................................................................................................20About:Thisbookcoversalltheformula,equationstipsandtricksanundergraduateSTEMmajorrequiresforAlgebra,Trigonometry,Precalculus,Calculus(alllevels/areas),LinearAlgebra,DifferentialEquations,andPhysics(Mechanics,E&M,Optics)ThebookisapplicabletoanySTEMstudentatanypointoftheircareer.Itcanactasareview,aguidedassistantandortoolforstudentsoutsideofcollege.
AlgebraArithmetic
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=
123 =
1231=12 13 =
12 3 =
16
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=
12
34 =
1 4 2 32 4 =
4 68
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=
1 23 4 =
(1+ 2)(3+ 4) =
2 14 3
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+
= + , 0 12 16
4 =124
164 = 3 4
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=
165 =
4 45 = 4
45
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CopyrightWeSolveThemLLC 3
=
1
=
234
=2134
=21 43 =
83
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=
12 165 =
125
165
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