the ultimate cheat sheet for math & physics · pdf fileimplicit differentiation ... visually...

Download The Ultimate Cheat Sheet for Math & Physics · PDF fileImplicit differentiation ... Visually Dot Product !⋅!=!!,!!⋅!!,!! =!!!!+!!!!!⋅!=!!,!!,!!⋅!!,!!,!! =!!!!+!!!!+!!!! Cross

If you can't read please download the document

Upload: buinhu

Post on 06-Feb-2018

241 views

Category:

Documents


0 download

TRANSCRIPT

  • 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

    = = 10 6 = 2 5 2 3 = 2 5 3 = 5 3 2_________________________________________________________________________________________________________________

    _

    =

    123 =

    1231=12 13 =

    12 3 =

    16

    __________________________________________________________________________________________________________________

    =

    12

    34 =

    1 4 2 32 4 =

    4 68

    __________________________________________________________________________________________________________________

    =

    1 23 4 =

    (1+ 2)(3+ 4) =

    2 14 3

    __________________________________________________________________________________________________________________

    +

    = + , 0 12 16

    4 =124

    164 = 3 4

    __________________________________________________________________________________________________________________

    =

    165 =

    4 45 = 4

    45

    __________________________________________________________________________________________________________________

  • CopyrightWeSolveThemLLC 3

    =

    1

    =

    234

    =2134

    =21 43 =

    83

    __________________________________________________________________________________________________________________

    =

    12 165 =

    125

    165

    __________________________________________________________________________________________________________________

    = =