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MATH
Formula &
Formula and Table
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Diferential Calculus
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Trigonometric Function?
Curvature?
Radius o Curvature?
Limits?
Linearity o a unction?
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Cal Tech 2ndDerivatives?
Cal Tech 1stDerivatives?
m!licit Derivatives?
"a#imum$ "inimum %Caltech ?
Cal Tech 'rdDerivatives?
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Largest rectangle that can be
inscribed in a semicircle?
Largest Rectangle inscribed in a
circle?
Largest rectangle that can be inscribbed in a triangle(ith one side lying on the base o the triangle$ right
triangle circumscribing a rectangle?
Largest rectangle that can beinscribbed in an elli!se?
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)ector (ith a given area but
minimum !erimeter?
Largest area o a triangle (ith a
given !erimeter?
Right triangle (ith ma#imum!erimeter or ma#imum area?
"a#imum length o lie segmenttangent to an elli!se?
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*est !ossible vie( that is hang in a
certain height?
"ost e+cient tra!e,oidal section?
-arallele!i!ed (ith ma#imumvolume?
Location o single sta.e at groundlevel to minimi,e length o (ire?
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/olume o largest cone /c that can
be inscribbed in a hemishere?
Ration o the (eight o heaviest cylinder 0c tothe (eight o the circumscribing s!here 0s?
Largest cylinder that can beinscribbed in a cone?
"a#imum /olume o right circular cylinderinscribbed in a s!here o raius R?
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-artial Derivatives?
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-arametric Function?
rror ?
)lo!e Tangent Line?
Rth Derivatives?
)lo!e ormal Line?
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3vg4 instantaneous?
/elocity4 3cceleration?
Time Rates?
Flo( Rates?
Linearity?
3dvanced time rates?
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ntegral Calculus
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3rea *ounded by a Curved$)!ecialCase ?
Calculator Tech?
Length o 3rc4 -olar Curve and
!arametric e5uation?
"ean /alue Theorem?
Double ntegral?
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0or. or )!ring?
0or. or cable?
"ean value Theorem?
0or. Done?
0or. Done in 6uids?
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/olume o )olid Revolution?
Centroid?
-a!!us Theorem 1stand 2nd?
)urace 3rea?
"oment o nertia?
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Diferential 5uation
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7igher D 3u#iliary 5uation?
Cal Tech D /ersion 1?
Cal Tech D /ersion 2?
Cal Tech on87omogenous D?
Cal Tech all D?
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9rder and Degree?
/ariable )e!arable?
#act?
Linear D Form and ntegrating
Factor?
*ernoulli D Form and ntegratingFactor?
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-o!ulation :ro(th?
e(tons La( o Cooling?
"oments o nertia?
Logistic :ro(th?
"i#ing !roblem?
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-o!ulation :ro(th?
Limitting velocity?
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0rongs.ian?
3bel;s Formula?
Cauchy8Riemann 5uation?
uler8Cauchy 5uation?
Logistic 5uation?
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Com!le# umber
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th root?
Com!le# Form?
-o(er Raising?
Logarithm o com!le#?
Caltech ln4 log4 raise imaginary?
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Trigonometric com!le# identities?
#!onential and Trigo?
"ulti!licative nverse?
7y!erbolic Function?
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umerical "ethods
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Tra!e,oidal "ethod?
e(ton Divide and Diference?
)im!sons Rule?
Taylor and "aclaurin )eries?
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*isection "ethod?
e(ton;s "ethod?
-o(er )eries ?
Radius o Convergence?
uler "ethod Cal Tech?
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La!lace Transorm
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nverse La!lace?
La!lace Transorm?
ot inorm la!lace?
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Fourier )eries
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Fourier 5uation?
3
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3dvance "ath
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=8 Transorm ?
Dirac Delta$ >nit m!luse?
7eaviside$ >nit )te!?
Fourier Transorm?
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Discrete "ath
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-ro!ositions
Formal Name Symbol Nickname
Negation Not
Conjunction ^ AND
Disjunction v O
!"clusive#O $ %O
im&lication ' (M)*(!S+(,-t.en/
0icon1itional 2 (FF
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*oolean 3lgebra?
Logical lement?
Duality?
"interm?
Logic :ates?
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?
)ubstitution o unction?
nverse o a unction?
Com!osition o a unction?
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-robability and )tatistics
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"edian?
uartile?
-ercentile?
R?
"ean?
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"ode?
Range4 "idrange?
"ean Deviation?
uadratic "ean?)tandard Deviation4 )am!le
-o!ulation?
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/ariance?
Coe+cient o /ariation?
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"ean :rade given re5uency ?
ormal Curve?
-rinci!le o Counting?
-ermutation ?
Circular -ermutation?
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*anana Formula?
Combination?
3#iom o -robability?
9R case ?
3t least one?
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Continuous Distribution?
?
?
?
?
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*inomial Distribution 9R bermouli?
"ultinomial?
7y!ergeometric?
-oisson Distribution ?
-robability Tree$ Conditional -rob?
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3L:*R3
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-ro!erties o #!onent?
-ro!erties o Logarithms?
-ro!erties o Radicals?
-ro!ortionality?
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Coe+cient #!ansion?
)um o numerical coe+cient?
)um o #!onent Terms?
Constant Coe+cient o a term?
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LC" & LCD?
:DC & :CF?
:eometric -rogression?
3rithmetic -rogression?
)!ecial Case 3rithmetic
-rogression?
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n@nite :eometric?
Remainder Theory?
3rithmetic "ean?
Discriminant?
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)um o Roots?
-roduct o Roots?
Roman umerals?
Factor Theorems?
Finding (hat ty!e o roots?
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0or.?
Coin?
Time?
digits?
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"i#ture?
3ge?
motion?
Dio!hantine?
"od and Fernat;s Lil Theorem?
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"atri# and /ector
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"atrices?
Trans!ose o "atri# ?
"inors?
Coactor %)igned "inor?
3dAoint $ 3dAugate?
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igen /ector?
igen /alues ?
Dot -roduct?
Cross -roduct?
"agnitude o /ector?
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B#B matri#?
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Trigo
/alue o angle in ach
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/alue o angle in achuadrant?
dentities?
Calculator )ynta#?
3m!litude?
Reerence3ngle?
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-eriod?
3rea o Triangle $ 5uilateral ?
Triangle inscribed?
Triangle scribed?
Triangle Circumscribing ?
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Cosine La(?
Conversed )ine ?
Conversion Degree to "ils?
Direction o 3ngle?
/ersed )ine ?
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Reerence 3ngle?
3ngle )um?
*earing?
Triangle ne5uality?
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Reerence 3ngle?
)um and Diference angle tangent?
"edian?
3ltitude?
3ngle *isector?
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)!herical Trigonometry
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La( o )ine?
La( o Cosine side?
La( o Cosine 3ngle?
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3rea o )!herical triangle?
Time 3!!?
3rea o 5uilateral Triangle?
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-lane :eometry
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umber o Diagonal?
nterior 3ngle?
3rea o a Rhombus?
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3rea o !arallelogram?
3rea o Tra!e,oid?
3rea o Tra!e,ium
-olygon Circumscribing a
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-olygon Circumscribing acircle?
-olygon inscribe a circle?
:iven one side o !olygon
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Cyclic uadrilateral nscribed?
Cyclic uadrilateral Circumscribing?
3rc length?
3rea & Circumerence o
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3rea & Circumerence oCircle?
3rea o a sector?
Central -eri!heral angle ?
-tolemy;s Theorem ?
3rea o a segment?
)ubtended )emi 3rc nscribed
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)ubtended )emi 3rc nscribed
angle?
nscribed angle subtended by the
diameter o circle?
Chord theorem?
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)ecant Theorem?
Tangent )ecant Theorem?
3rea o a -entagram?
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)olid :eometry
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/olume o regular solid?
/ l & 3 - ll l i d?
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-risms and Cylinder?
Frustum?
/olume & 3rea o -arallel!i!ed?
Truncated -rism?
-yramid and Cone?
i id
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-rismatoid?
)!here?
/olume )!herical Cone?
=one?
)!herical )egment?
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/olume )!herical )ector?
/olume )!herical -yramid?
/olume )!herical 0edge?
/ l lli id?
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/olume lli!soid?
/olume -rolate )!heroid?
/olume 9blate )!heroid?
/olume 0asher?
)imilarity?
/ l d 3 T ?
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/olume and 3rea o a Torus?
/olume 0asher?
-roblem Triangular Trough ($5uilateral triangle edges?
Closed Cylindrical Tan.?
Cone Constructed rom a sector?
) lid " d lli ?
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)olid "odelling?
Dimension o Cube?
Conoid?
)!herical )egment t(o bases?
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3nalytic :eometry
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Distance *et 2 !oints?
)lo!e?
Distance *et -oint and Line?
Distance *et -arallel Line?
inclination?
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3ngle bet(een t(o line?
inclination?
3rea o -olygon by Coordinates?
Line 5uation?
Line Division and mid!oint?
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3ngle o rotation?
: o Conic?
dentiying conics by ccentricity?
*y Discriminant?
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Circle )tandard 5uation?
*y 5uation?
Center or Circle4 lli!se andhy!erbola?
- b l : ) d d i ?
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-arabola Latus Rectum?
-arabola :4 )atandard5uation?
-arabola ccentricity?
3rea o -arabola?
5uation o )ymmetry 3#is?
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lli!se -ythagorean ?
lli!se ) !art Dra( elli!se ?
lli!se ccentricity4 2nd4 'rd?
lli!se Latus Rectum?
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-erigee?
3!ogee ?
lli!se 3rea?
lli!se -erimeter?
lli!se 6atness$ 2nd6atness?
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7y!erbola -ythagorean ?
7y!erbola 5uation and Dra(?
7y!erbola eccentricity?
3ssym!tote?
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Caltech -arabola !roblem?
Caltech lli!se !roblem?
-olar Curve?
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)!ace :eometry
Distance bet(een a !oint and a
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Distance bet(een a !oint and a!lane?
3ngle *et(een -lane?
3rea o 9ctant?
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Coordinate )ystem
Cal Tech Coordinates system
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Cylindrical
)!herical
Cal Tech Coordinates system-olar8Rectangular Coordinates?
Rectangular -olar /ice /ersa?
Cartesian$ Rectangular$ 9rthogonal
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/ector 3nalysis
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Dot -roduct )calar?
>nit /ector?
Cross -roAect /ector?
:iven /ector ?
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Divergence o a /ector?
:radient o a )calar?
La!lacian o a scalar?
Com!onent /ector %)calar-roAection?
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3rea o a Triangle?
/ector -roAection?
/ector Diferentiation?
/olume o -arallel!i!ed?
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:reen;s Theorem?
3rc Length?