Math Symbols 5 Rectangle 6 Square Root Symbol 7 Integral Symbol 8 Contour or Closed Line Integral 9 Infinity 10 Negative Infinity
The symbol ? (sigma) is generally used to denote a sum of multiple terms This symbol is generally accompanied by an index that varies to encompass all
31 mai 2000 · LaTeX Math Symbols Page 1 of 9 http://www math ubc ca/~cautis/tools/latexmath html reads “above” and _ “below” on an arrow pointing
21 jan 2007 · v s (vide supra) means “see above” (It is used to imply that more information can be found before the current point in a written work and is
Identical mathematical symbols and notation are used in different circumstances to convey very different A digit or letter placed above and slightly to
2 Some common mathematical symbols 2 3 Variables 4 4 The Greek alphabet 4 5 Some more symbols 5 6 Summary 5 www mathcentre ac uk
Appendix A Math symbol tables Greek letters Lowercase Providing hundreds of symbols for typesetting mathematics articles cited above
Reverse the inequality sign when mult/divide by a negative above is below that is equal to over shorter / smaller than exactly greater / larger than
use of these symbols, we now state properties (P1) - (P9) of chapter one Let N denote the Further statements about truth can be derived from the above
19 mai 2018 · Letter-based symbols:Many mathematical symbols are based on, group H (? can also be used for isomorphic, as described above )
![[PDF] THE SUMMATION SYMBOL [PDF] THE SUMMATION SYMBOL](https://pdfprof.com/EN_PDFV2/Docs/PDF_6/1323_6The_summation_symbol.pdf.jpg)
1323_6The_summation_symbol.pdf
THESUMMATIONSYMBOL
Summary
1.Simplesum..............................................................................................................................1
2.Doublesum..............................................................................................................................5
3.Doubleindex............................................................................................................................5
1. Simplesum
Thesymbolȭ(sigma)isgenerallyusedtodenoteasumof
multipleterms.Thissymbol isgenerallyaccompaniedbyanindexthatvariestoencompassalltermsthatmustbe consideredinthesum. Forexample,thesumof݊firstwholenumberscanberepresentedinthefollowing manner: ݅ ୀଵ ൌͳ ʹ ͵ ڮ
Moregenerally,theexpressionσݔ
ୀଵ representsthesumofnterms ݔ ଵ ݔ ଶ ݔ ଷ ڮ .
Example1
Givenݔ
ଵ ൌ͵ǡݔ ଶ ൌͷǡݔ ଷ ൌǡݔ ସ ൌʹܽ ହ ൌ.
Evaluateσݔ
ହୀଵandσݔ ସୀଶ .
Solution:
Inthefirstsum,theindex"i"variesfrom1to5.Wemustthereforeincludethe5 termsinthesum. ݔ ହ ୀଵ ൌݔ ଵ ݔ ଶ ݔ ଷ ݔ ସ ݔ ହ ൌ͵ͷʹൌʹ͵
Page2of6
Inthesecondcase,theindex"i"variesfrom2to4.Onlythetermsݔ ଶ
ǡݔ
ଷ andݔ ସ must thereforebeconsidered. ݔ ସ ୀଶ ൌݔ ଶ ݔ ଷ ݔ ସ ൌͷʹൌͳ͵ Whenweusethesummationsymbol,itisusefultorememberthefollowingrules: ܿ ୀଵ ൌܿ ୀଵ ܿ ୀଵ ൌ݊ܿ ሺݔ ݕ ሻ ୀଵ ൌݔ ୀଵ ݕ ୀଵ
Example2
Givenݔ
ଵ ൌ͵ǡݔ ଶ ൌͷǡݔ ଷ ൌǡݔ ସ ൌʹܽ ହ ൌetݕ ଵ ൌʹǡݕ ଶ ൌͺǡݕ ଷ ൌ͵ǡ ݕ ସ ൌͳܽ ହ ൌ.
Verifythethreeprecedingruleswiththefollowingsums:
ܽ ହ ୀଵ ܾ ହ ୀଵ ܿ ݕ ሻ ହ ୀଵ
Page3of6
Solution:
ܽ ହ ୀଵ ൌͶݔ ଵ Ͷݔ ଶ Ͷݔ ଷ Ͷݔ ସ Ͷݔ ହ ൌͶൈ͵ͶൈͷͶൈͶൈʹͶൈ ൌͻʹ and
Ͷݔ
ହ ୀଵ
ൌͶൈሺ͵ͷʹሻൌͶൈʹ͵ൌͻʹ
b) Ͷ ହ ୀଵ ൌͶͶͶͶͶൌͷൈͶൌʹͲ c) ሺݔ ݕ ሻ ହ ୀଵ
ൌሺ͵ʹሻሺͷͺሻሺ͵ሻሺʹͳሻሺሻൌͶ͵
And ݔ ହ ୀଵ ݕ ହ ୀଵ ൌሺ͵ͷڮሻሺʹͺڮ
Attention:
Wemustneitherconfoundtheexpression
ݔ ଶ ୀଵ with ൭ ݔ ୀଵ ൱ ଶ
Page4of6
northeexpression ݔ ݕ ୀଵ with ൭ ݔ ୀଵ ൱൭ݕ ୀଵ ൱
Example3
Givenݔ
ଵ ൌ͵ǡݔ ଶ ൌͷǡݔ ଷ ൌǡݔ ସ ൌʹܽ ହ ൌandݕ ଵ ൌʹǡݕ ଶ ൌͺǡݕ ଷ ൌ͵ǡ ݕ ସ ൌͳܽ ହ ൌ. a) ݔ ଶ ൌݔ ଵଶ ݔ ଶଶ ݔ ଷଶ ݔ ସଶ ݔ ହଶ ൌ ହ ୀଵ ͵ ଶ ͷ ଶ ଶ ʹ ଶ ଶ ൌ ͳʹ͵ and ൭ ݔ ହ ୀଵ ൱ ଶ ൌሺ͵ͷʹሻ ଶ ൌʹ͵ ଶ ൌ ͷʹ ് ͳʹ͵ b) ݔ ݕ ൌݔ ଵ ݕ ଵ ݔ ଶ ݕ ଶ ݔ ଷ ݕ ଷ ݔ ସ ݕ ସ ݔ ହ ݕ ହହ ୀଵ ൌሺ͵ൈʹሻሺͷൈͺሻڮ ൌ ͶͲ ڮ and ൭ ݔ ୀଵ ൱൭ݕ ୀଵ ൱ൌሺ͵ͷڮሻൈሺʹͺڮ
Page5of6
2. Doublesum
Incertainsituations,usingadoublesummaybenecessary.Youmustthenapplythe definitionsuccessively.
Example
Givenݔ
1 ൌ ͵ǡݔ 2 ൌ ͷǡݔ 3 ൌ ͳܽ 1 ൌʹǡݕ 2 ൌ Ͷ Wewillusetheindexiforthetermsofݔandindexjforthetermsofݕ ݔ ݕ ଶ ୀଵଷ ୀଵ ൌሺݔ ݕ ଵ ݔ ݕ ଶ ሻ ଷ ୀଵ ൌݔ ଵ ݕ ଵ ݔ ଵ ݕ ଶ ݔ ଶ ݕ ଵ ݔ ଶ ݕ ଶ ݔ ଷ ݕ ଵ ݔ ଷ ݕ ଶ
ൌሺ͵ൈʹሻሺ͵ൈͶሻሺͷൈʹሻሺͷൈͶሻሺͳൈʹሻሺͳൈͶሻൌͷͶ
3. Doubleindex
Torepresentthedataofatableoramatrix,weoftenuseadoubleindexnotation,like ݔ wherethefirstindex(i)correspondstothenumberoftherowwherethedatais locatedandthesecond(j)tothecolumn.Forexample,thetermݔ 24
representsthedata thatissituatedattheintersectionofthe2 nd rowandthe4 th columnofthetableorthe matrix.
Example
Given ݔ ଵଵ ൌ Ͷݔ ଵଶ ൌ Ͷݔ ଵଷ ൌ ͳݔ ଵସ ൌͷ ݔ ଶଵ ൌ Ͳݔ ଶଶ ൌ ͵ݔ ଶଷ ൌ ͳݔ ଶସ ൌʹ ݔ ଷଵ ൌ ͳݔ ଷଶ ൌ Ͷݔ ଷଷ ൌ ʹݔ ଷସ ൌ͵ Tocarryoutthesumofthetermsofarow,wemustfixtheindexofthatrowandvary, forallpossiblevalues,theindexofthecolumn.Forexample: σ ݔ ଵସୀଵ ൌݔ ଵଵ ݔ ଵଶ ݔ ଵଷ ݔ ଵସ ൌʹͶͳͷൌͳʹ(sumofthefirstrow) σ ݔ ଶସୀଵ ൌݔ ଶଵ ݔ ଶଶ ݔ ଶଷ ݔ ଶସ ൌͲ͵ͳʹൌ(sumofthe2 nd row) Tocarryoutthesumofthetermsofacolumn,youmustfixtheindexofthiscolumnand vary,forallpossiblevalues,theindexoftherow.
Page6of6
Forexample:
σ ݔ ସଷୀଵ ൌݔ ଵସ ݔ ଶସ ݔ ଷସ ൌͷʹ͵ൌͳͲ(sumofthe4 th column) Tocarryoutthesumofalltermsofthetable,youmustvarybothindicesandusea doublesum: ݔ ସ ୀଵଷ ୀଵ ൌሺݔ ଵ ݔ ଶ ݔ ଷ ݔ ସ ሻ ଷ ୀଵ ൌݔ ଵଵ ݔ ଵଶ ݔ ଵଷ ݔ ଵସ ݔ ଶଵ ݔ ଶଶ ݔ ଶଷ ݔ ଶସ ݔ ଷଵ ݔ ଷଶ ݔ ଷଷ ݔ ଷସ ൌʹͶͳͲ͵ڮ