1. ffoYsl ùch / Vector Calculus. ;d;a;aúl ixLHd l=,lfha ixjD; m%dka;rhl isg ;s%udk wjldYhg w¾: oelajqkq ika;;sl Y%s;hlg jl%hla hehs lshkq,efns. A continuous function defined from the set of Real numbers into the 3-dimensional space is called a curve. ksoiqk. 1 by This represents a straight line from (0,1,0) to (1,1,2). ksoiqk. 2 by A circle in the Oxy plane. A closed curve. (0,1,0) iy (1,1,2) hd lrk ir, f¾Ldj fjs. Oxy ;,fha jQ jD;a;hls. ixjD; jl%hls.

2. jvd;a idOdrKj by f,i jl%hla w¾: oelajqkq,efns. ksoiqk. by fuhg fy,slaih(Helix)la hehs lshkq,efns. by; jl%h u; fmd¥,laIHhl msysgqus ffoYslh f,i jl%h bosrsm;a lrkq,efns.

3. fif¾-fmfka iQ;% / Serret-Frenet Formulae wjldY jl%h i,lkak. A jl%h u; wp,,laIHhla P Q s ΔsΔs úp,H,laIHhla s- pdm ¥r PQ f¾Ldfjka PQ chdh,efnk w;r Q,laIHh P lrd t<fTk úg th P ysoS iam¾Ylh (tangent) fjs" pdm ¥r hkq jl%hg P ysoS we|s iam¾Ylh jk w;r neúk a hkq P ysoS jl%hg we|s tall iam¾Ylh (unit tangent) fjs"

4. uÕska tall iam¾Ylh (unit tangent) ksrEmKh lrhs" tksid hkak s úIhfhys wjl,kfhka ys osYdjg m%Odk wNs,usnfha osYdj hehs lshk w;r uÕska tall m%Odk wNs,usnh (principal unit normal) ksrEmKh lrhs" P ys oS tall iam¾Ylh Q ys oS tall iam¾Ylh P Q

5. P Q b;d l=vd úg fus ksid jl%;d wrh (radius of curvature) jl%;djh (curvature) iudka;rhs ksid m<uq fif¾-fmfka iQ;%h

6. hehs w¾: olajkq,efns" hkq wmr wNs,usnh (binormal) fjs' igyk 1 2 hkq iqr;a moaO;shls' s úIhfhys wjl,kfhka 1 2 1 iy ka 2 fofjks fif¾-fmfka iQ;%h jHdj¾;kh (torsion)

7. ksid s úIhfhys wjl,kfhka f;fjks fif¾-fmfka iQ;%h hkakg uQ,sl ;%s;ajh (Fundamental Triad) hehs lshkq,efns"

8. fif¾-fmfka iQ;%

9. ;jo iyneúka fyda ksoiqk jl%h i|yd úiªu 5 ;jo

10. iy tall iam¾Ylh

12. fok,o jl%hla i|yd fiùu wjldY jl%h hehs.ksuq. mshjr 1 fidhkak" ;jo mshjr 2 fidhkak" túg,nd.; yel" iy

13. mshjr 3 fhoSfuka wmr wNs,usnh fidhkak" fidhkak" túg igyk mshjr 3 o;ajd ksjerosj iq¿ lr we;akus muKla hkak i;H fjs" ksoiqk i|yd

14. ksoiqk i|yd ;jo

18. fok,o jl%hla i|yd muKla fiùug hkak t úIhfhys wjl,kfhka ksid fuhska fidhd.; yel túg,efns"

19. ksoiqk i|yd ;jo iy ksid

20. ys wdfoaYfhka ksoiqk i|yd

21. iy ;jo ksid

22. ys wdfoaYfhka