Teaching and Learning Algebra最新文献

Teaching and Learning Algebra Pub Date : 2016-08-01 DOI: 10.1142/9789814730402_0006

Ronda Sanders, X. Wu

{"title":"Sequences and Series","authors":"Ronda Sanders, X. Wu","doi":"10.1142/9789814730402_0006","DOIUrl":"https://doi.org/10.1142/9789814730402_0006","url":null,"abstract":"Command/Example Description seq(f(n), n=i..j); Examples: seq(1/n,n=1..10); a:=seq(k!,k=3..10); a[3]; a[8]; seq(b[m]=sin(m*Pi/2),m=0..8); pt:=seq([n,f(n)],n=1..8); pt[2]; It creates a finite sequence of values f(i), f(i+1), · · ·, and f(j), where f(n) is a maple function and i ≤ j are integers. A sequence of points on the graph of y = f(x) can be obtained using: > seq([n,f(n)], n=i..j); sum(f(n), n=i..j) Examples: sum(n^2, n=-1..10); sum((1/2)^n,n=0..infinity); sum(c/k^2,k=1..infinity); S:=n->sum(k,k=1..n); S(n); S(8); f:=x->sum(x^n/n!,n=0..infinity); f(x); f(1); f(-1); It creates and evaluates a finite or infinite sum, that is, series ∑j n=i f(n), where f(n) is a maple function or expression and i ≤ j can be integers, variables, or infinity. For a finite or convergent infinite series, it automatically evaluates the sum and returns a value or formula. If you don’t want the automatic evaluation, use Sum instead of sum. for n from i to j do...end do; Examples: for n from 5 to 10 do c[n]:=1/n end do; for n from 0 to 9 do d[2*n]:=1; d[2*n+1]:=0 end do; s[1]:=1; for n from 2 to 8 do s[n]:= s[n-1]+n end do; A typical for-loop (for and do statement) used in general programming languages. It executes whatever between ‘‘do’’ and ‘‘end do’’ repeatedly for a counted number of times (‘‘for n from i to j’’). It hence can be used to work with sequences in much more general ways than what the command seq could. • A link to the SequenceDrill maplet can be found on the course website:","PeriodicalId":118589,"journal":{"name":"Teaching and Learning Algebra","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133397479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 40

Developing Algebraic Skills 发展代数技能

Teaching and Learning Algebra Pub Date : 2016-02-25 DOI: 10.5040/9781350933972.ch-004

J. Golding

引用次数: 0

Functions and Graphs 函数与图

Teaching and Learning Algebra Pub Date : 1996-10-01 DOI: 10.1142/9781860943928_0002

P. Kent, P. Ramsden, J. Wood

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Learning and Teaching Algebra 代数的学习与教学

Teaching and Learning Algebra Pub Date : 1900-01-01 DOI: 10.5040/9781350933972.ch-001

E. Warren, Robyn Pierce

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Links to Geometry 几何链接

Teaching and Learning Algebra Pub Date : 1900-01-01 DOI: 10.5040/9781350933972.ch-009

引用次数: 0