Pub Date : 2016-08-01DOI: 10.1142/9789814730402_0006
Ronda Sanders, X. Wu
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:
命令/示例说明seq(f(n)， n=i..j);例子:seq (1 / n, n = 1 . . 10);答:= seq (k !, k = 3 . . 10);[3];[8];seq (b [m] =罪(m *π/ 2),m = 0 . . 8);pt: = seq (n、f (n), n = 1 . . 8);pt [2];它创建一个有限序列的值f(i)， f(i+1)，···和f(j)，其中f(n)是一个枫函数，i≤j是整数。y = f(x)图上的点序列可以用:> seq([n,f(n)]， n=i..j);sum(f(n)， n=i..j)示例:sum(n²，n=-1..10);总和((1/2)^ n, n = 0 . .∞);总和(c / k ^ 2 k = 1 . .∞);S: = n - >总和(k, k = 1 . . n);S (n);(8);f: = x - >总和(x ^ n / n, n = 0 . .∞);f (x);f (1);f (1);它创建并计算一个有限或无限和，即级数∑j n=i f(n)，其中f(n)是一个枫函数或表达式，i≤j可以是整数、变量或无穷大。对于有限的或收敛的无穷级数，它自动求和并返回一个值或公式。如果不希望自动求值，请使用Sum而不是Sum。对于n从I到j做…结束;示例:for n从5到10 do c[n]:=1/n end do;对于n从0到9,do d[2*n]:=1;D [2*n+1]:=0;[1]: = 1;对于n从2到8,do s[n]:= s[n-1]+n end do;一般编程语言中使用的典型for循环(for和do语句)。它重复执行“do”和“end do”之间的任何内容，并计算次数(“for n from i to j”)。因此，它可以用比命令seq更通用的方式来处理序列。•在课程网站上可以找到SequenceDrill市场的链接:
{"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}
Pub Date : 2016-02-25DOI: 10.5040/9781350933972.ch-004
J. Golding
AIMSSEC. of QAIMs-E=Mathematical Thinking in the lower secondary classroom Mathematical Thinking in the lower secondary classroom Edited by Christine. Front Cover.
AIMSSEC。《初中课堂数学思维》由Christine编辑。封面。
{"title":"Developing Algebraic Skills","authors":"J. Golding","doi":"10.5040/9781350933972.ch-004","DOIUrl":"https://doi.org/10.5040/9781350933972.ch-004","url":null,"abstract":"AIMSSEC. of QAIMs-E=Mathematical Thinking in the lower secondary classroom Mathematical Thinking in the lower secondary classroom Edited by Christine. Front Cover.","PeriodicalId":118589,"journal":{"name":"Teaching and Learning Algebra","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122691365","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}
Pub Date : 1996-10-01DOI: 10.1142/9781860943928_0002
P. Kent, P. Ramsden, J. Wood
{"title":"Functions and Graphs","authors":"P. Kent, P. Ramsden, J. Wood","doi":"10.1142/9781860943928_0002","DOIUrl":"https://doi.org/10.1142/9781860943928_0002","url":null,"abstract":"","PeriodicalId":118589,"journal":{"name":"Teaching and Learning Algebra","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128773113","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}
Pub Date : 1900-01-01DOI: 10.5040/9781350933972.ch-009
{"title":"Links to Geometry","authors":"","doi":"10.5040/9781350933972.ch-009","DOIUrl":"https://doi.org/10.5040/9781350933972.ch-009","url":null,"abstract":"","PeriodicalId":118589,"journal":{"name":"Teaching and Learning Algebra","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124393823","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}
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