Math Formula.pptx

7/24/2019 Math Formula.pptx

1/101

MATH

Formula &

Formula and Table


2/101

Diferential Calculus


3/101

Trigonometric Function?

Curvature?

Radius o Curvature?

Limits?

Linearity o a unction?


4/101

Cal Tech 2ndDerivatives?

Cal Tech 1stDerivatives?

m!licit Derivatives?

"a#imum$ "inimum %Caltech ?

Cal Tech 'rdDerivatives?


5/101

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?


6/101

)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?


7/101

*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?


8/101

/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?


9/101

-artial Derivatives?


10/101

-arametric Function?

rror ?

)lo!e Tangent Line?

Rth Derivatives?

)lo!e ormal Line?


11/101

3vg4 instantaneous?

/elocity4 3cceleration?

Time Rates?

Flo( Rates?

Linearity?

3dvanced time rates?


12/101

ntegral Calculus


13/101

3rea *ounded by a Curved$)!ecialCase ?

Calculator Tech?

Length o 3rc4 -olar Curve and

!arametric e5uation?

"ean /alue Theorem?

Double ntegral?


14/101

0or. or )!ring?

0or. or cable?

"ean value Theorem?

0or. Done?

0or. Done in 6uids?


15/101

/olume o )olid Revolution?

Centroid?

-a!!us Theorem 1stand 2nd?

)urace 3rea?

"oment o nertia?


16/101

Diferential 5uation


17/101

7igher D 3u#iliary 5uation?

Cal Tech D /ersion 1?

Cal Tech D /ersion 2?

Cal Tech on87omogenous D?

Cal Tech all D?


18/101

9rder and Degree?

/ariable )e!arable?

#act?

Linear D Form and ntegrating

Factor?

*ernoulli D Form and ntegratingFactor?


19/101

-o!ulation :ro(th?

e(tons La( o Cooling?

"oments o nertia?

Logistic :ro(th?

"i#ing !roblem?


20/101

-o!ulation :ro(th?

Limitting velocity?


21/101

0rongs.ian?

3bel;s Formula?

Cauchy8Riemann 5uation?

uler8Cauchy 5uation?

Logistic 5uation?


22/101

Com!le# umber


23/101

th root?

Com!le# Form?

-o(er Raising?

Logarithm o com!le#?

Caltech ln4 log4 raise imaginary?


24/101

Trigonometric com!le# identities?

#!onential and Trigo?

"ulti!licative nverse?

7y!erbolic Function?


25/101

umerical "ethods


26/101

Tra!e,oidal "ethod?

e(ton Divide and Diference?

)im!sons Rule?

Taylor and "aclaurin )eries?


27/101

*isection "ethod?

e(ton;s "ethod?

-o(er )eries ?

Radius o Convergence?

uler "ethod Cal Tech?


28/101

La!lace Transorm


29/101

nverse La!lace?

La!lace Transorm?

ot inorm la!lace?


30/101

Fourier )eries


31/101

Fourier 5uation?

3


32/101

3dvance "ath


33/101

=8 Transorm ?

Dirac Delta$ >nit m!luse?

7eaviside$ >nit )te!?

Fourier Transorm?


34/101

Discrete "ath


35/101

-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


36/101

*oolean 3lgebra?

Logical lement?

Duality?

"interm?

Logic :ates?


37/101

?

)ubstitution o unction?

nverse o a unction?

Com!osition o a unction?


38/101

-robability and )tatistics


39/101

"edian?

uartile?

-ercentile?

R?

"ean?


40/101

"ode?

Range4 "idrange?

"ean Deviation?

uadratic "ean?)tandard Deviation4 )am!le

-o!ulation?


41/101

/ariance?

Coe+cient o /ariation?


42/101

"ean :rade given re5uency ?

ormal Curve?

-rinci!le o Counting?

-ermutation ?

Circular -ermutation?


43/101

*anana Formula?

Combination?

3#iom o -robability?

9R case ?

3t least one?


44/101

Continuous Distribution?

?

?

?

?


45/101

*inomial Distribution 9R bermouli?

"ultinomial?

7y!ergeometric?

-oisson Distribution ?

-robability Tree$ Conditional -rob?


46/101

3L:*R3


47/101

-ro!erties o #!onent?

-ro!erties o Logarithms?

-ro!erties o Radicals?

-ro!ortionality?


48/101

Coe+cient #!ansion?

)um o numerical coe+cient?

)um o #!onent Terms?

Constant Coe+cient o a term?


49/101

LC" & LCD?

:DC & :CF?

:eometric -rogression?

3rithmetic -rogression?

)!ecial Case 3rithmetic

-rogression?


50/101

n@nite :eometric?

Remainder Theory?

3rithmetic "ean?

Discriminant?


51/101

)um o Roots?

-roduct o Roots?

Roman umerals?

Factor Theorems?

Finding (hat ty!e o roots?


52/101

0or.?

Coin?

Time?

digits?


53/101

"i#ture?

3ge?

motion?

Dio!hantine?

"od and Fernat;s Lil Theorem?


54/101

"atri# and /ector


55/101

"atrices?

Trans!ose o "atri# ?

"inors?

Coactor %)igned "inor?

3dAoint $ 3dAugate?


56/101

igen /ector?

igen /alues ?

Dot -roduct?

Cross -roduct?

"agnitude o /ector?


57/101

B#B matri#?


58/101

Trigo

/alue o angle in ach


59/101

/alue o angle in achuadrant?

dentities?

Calculator )ynta#?

3m!litude?

Reerence3ngle?


60/101

-eriod?

3rea o Triangle $ 5uilateral ?

Triangle inscribed?

Triangle scribed?

Triangle Circumscribing ?


61/101

Cosine La(?

Conversed )ine ?

Conversion Degree to "ils?

Direction o 3ngle?

/ersed )ine ?


62/101

Reerence 3ngle?

3ngle )um?

*earing?

Triangle ne5uality?


63/101

Reerence 3ngle?

)um and Diference angle tangent?

"edian?

3ltitude?

3ngle *isector?


64/101

)!herical Trigonometry


65/101

La( o )ine?

La( o Cosine side?

La( o Cosine 3ngle?


66/101

3rea o )!herical triangle?

Time 3!!?

3rea o 5uilateral Triangle?


67/101

-lane :eometry


68/101

umber o Diagonal?

nterior 3ngle?

3rea o a Rhombus?


69/101

3rea o !arallelogram?

3rea o Tra!e,oid?

3rea o Tra!e,ium

-olygon Circumscribing a


70/101

-olygon Circumscribing acircle?

-olygon inscribe a circle?

:iven one side o !olygon


71/101

Cyclic uadrilateral nscribed?

Cyclic uadrilateral Circumscribing?

3rc length?

3rea & Circumerence o


72/101

3rea & Circumerence oCircle?

3rea o a sector?

Central -eri!heral angle ?

-tolemy;s Theorem ?

3rea o a segment?

)ubtended )emi 3rc nscribed


73/101

)ubtended )emi 3rc nscribed

angle?

nscribed angle subtended by the

diameter o circle?

Chord theorem?


74/101

)ecant Theorem?

Tangent )ecant Theorem?

3rea o a -entagram?


75/101

)olid :eometry


76/101

/olume o regular solid?

/ l & 3 - ll l i d?


77/101

-risms and Cylinder?

Frustum?

/olume & 3rea o -arallel!i!ed?

Truncated -rism?

-yramid and Cone?

i id


78/101

-rismatoid?

)!here?

/olume )!herical Cone?

=one?

)!herical )egment?


79/101

/olume )!herical )ector?

/olume )!herical -yramid?

/olume )!herical 0edge?

/ l lli id?


80/101

/olume lli!soid?

/olume -rolate )!heroid?

/olume 9blate )!heroid?

/olume 0asher?

)imilarity?

/ l d 3 T ?


81/101

/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 ?


82/101

)olid "odelling?

Dimension o Cube?

Conoid?

)!herical )egment t(o bases?


83/101

3nalytic :eometry


84/101

Distance *et 2 !oints?

)lo!e?

Distance *et -oint and Line?

Distance *et -arallel Line?

inclination?


85/101

3ngle bet(een t(o line?

inclination?

3rea o -olygon by Coordinates?

Line 5uation?

Line Division and mid!oint?


86/101

3ngle o rotation?

: o Conic?

dentiying conics by ccentricity?

*y Discriminant?


87/101

Circle )tandard 5uation?

*y 5uation?

Center or Circle4 lli!se andhy!erbola?

- b l : ) d d i ?


88/101

-arabola Latus Rectum?

-arabola :4 )atandard5uation?

-arabola ccentricity?

3rea o -arabola?

5uation o )ymmetry 3#is?


89/101

lli!se -ythagorean ?

lli!se ) !art Dra( elli!se ?

lli!se ccentricity4 2nd4 'rd?

lli!se Latus Rectum?


90/101

-erigee?

3!ogee ?

lli!se 3rea?

lli!se -erimeter?

lli!se 6atness$ 2nd6atness?


91/101

7y!erbola -ythagorean ?

7y!erbola 5uation and Dra(?

7y!erbola eccentricity?

3ssym!tote?


92/101

Caltech -arabola !roblem?

Caltech lli!se !roblem?

-olar Curve?


93/101

)!ace :eometry

Distance bet(een a !oint and a


94/101

Distance bet(een a !oint and a!lane?

3ngle *et(een -lane?

3rea o 9ctant?


95/101

Coordinate )ystem

Cal Tech Coordinates system


96/101

Cylindrical

)!herical

Cal Tech Coordinates system-olar8Rectangular Coordinates?

Rectangular -olar /ice /ersa?

Cartesian$ Rectangular$ 9rthogonal


97/101

/ector 3nalysis


98/101

Dot -roduct )calar?

>nit /ector?

Cross -roAect /ector?

:iven /ector ?


99/101

Divergence o a /ector?

:radient o a )calar?

La!lacian o a scalar?

Com!onent /ector %)calar-roAection?


100/101

3rea o a Triangle?

/ector -roAection?

/ector Diferentiation?

/olume o -arallel!i!ed?


101/101

:reen;s Theorem?

3rc Length?

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Math Formula.pptx