LibreOffice-Suite-Math/C2/Derivatives-Differential-Equations-Integral-Equations-Logarithms/Khasi

Time	Narration
00:01	Ngi pdiangsngewbha ia phi sha ka “Spoken Tutorial” halor ka LibreOffice Math
00:05	Ha kane ka jinghikai, ngin sa nang kumno ban thoh: Derivatives and Differential equations Integral equations bad Formulae with Logarithms.
00:17	Na kabynta kane, to ngin plie nyngkong ia ka nuksa jong ngi Writer document kaba ngi la shna ha ka jinghikai ba hashuwa "MathExample1.odt".
00:29	Hangne, to ngin peit sha page kaba khatduh jong ka document bad nion Control, Enter ban leit sha ka page kaba thymmai
00:37	Mynta, type: “Derivatives and Differential Equations: ”bad nion ia u Enter key arsien.
00:45	Mynta, to ngin phai sha ka Math da kaba click Insert menu, nangta Object bad nangta pat Formula.
00:54	Shuwa ba ngin iaid shakhmat, to ngin pynheh ia ka font-size sha ka 18 point.
01:00	Pynkylla ia ka ka Alignment sha ka Left
01:03	Bad pynrung newlines bad ki lain ba suda hapdeng jong kawei pa kawei ka nuksa jong ngi na ka bynta ban lah ban pule bha.
01:11	To mynta ngin ia peit kumno ban thoh ia ki derivatives bad differential equations.
01:19	Math ka ai iaka lad kaba suk ban thoh ia ki formulae lane equations.
01:25	Ngi shu hap ban niew iaki kum ki fraction bad pyndonkam ia ka mark up over.
01:33	Kum ka nuksa-ban thoh ia ka total derivative, df by dx, ka mark up ka dei "df over dx" hapoh ka Formula Editor Window.
01:50	Ba bud, na kabynta ka partial derivative,ngi lah ban pyndonkam ia ka kyntien ‘partial’ bad ka markup ka long kum: del f over del x.
02:02	Ngi hap ban pyndonkam ki curly brackets haba ngi pyndonkam ka mark-up ‘partial’.
02:08	Phin iohi ia u ‘del’ symbol n aka bynta ka ‘partial derivatives’ ha ka ‘Writer gray box’.
02:14	Sa kawei pat ka nuksa hangne: Newton’s second law of motion
02:21	Kaba batai ia ka jingiadei hapdeng ka acceleration bad ka force.
02:26	F is equal to m a.
02:30	Ia kane lah ban thoh kum kiba bun ki differential equation kum: F of t is equal to m into d squared x over d t squared.
02:45	Phin iohi ba ngi la pyndonkam da ki babun ki sets jong ki curly brackets ban iathuh ia ka rukom long ka jingtreikam.
02:56	Bad ka equation ka long kumba la pyni ha ka screen.
03:01	Hangne kadei kawei pat ka nuksa jong ka differential equation.
03:05	Newton’s law of cooling.
03:08	Lada u theta jong u t u dei u temperature jong ka object ha ka time t, te ngi lah ban thoh ia ka differential equation:
03:18	d of theta over d of t is equal to minus k into theta minus S
03:30	Ha kaba u ‘S’ u dei u temperature jong ka mariang sawdong.
03:35	Phin iohi ia ka equation ha ka ‘Writer gray box’.
03:39	To ngin ‘save’ ia ka kam jong ngi mynta. Leit sha ka ‘File’ bad click ha ka ‘save’.
03:45	Mynta, to ngin peit kumno ban thoh ‘Integral equations’.
03:50	To ngin leit sha ka page kaba thymmai da kaba click laisien suki suki, shabar ka ‘Writer gray box’.
03:58	Bad nangta nion ‘Control, Enter’.
04:03	Type: ‘Integral Equations:’
04:06	Bad nion ‘Enter’ arsien.
04:11	Mynta, to ngin leit sha ka ‘Math’ na ka ‘Insert>Object’ menu;
04:17	Pynheh ia ka ‘Font size’ sha ka ’18 point’.
04:22	Bad pynkylla ia ka ‘Allignment’ sha ka ‘left’.
04:25	Ban thoh ia ka ‘integral’ symbol, ngi donkam ban pyndonkam tang ia u mark-up ‘int’ hapoh ka ‘Formula Editor Window’.
04:35	Te, kaba la ai ba u function 'f' jong u variable ba shisha 'x' bad ka interval 'a, b' jong u line bashisha halor u x-axis, ka definite integral lathoh ia ka kum Integral from a to b f of x dx
04:58	Ngi la pyndonkam ia u mark-up ‘int’ ban pyni ia ka ‘integral’ symbol.
05:04	Ban batai shai ia ka ‘limits’-‘a’ bad ‘b’, ngi la pyndonkam ia u mark-up ‘from bad ‘to’.
05:13	Phin iohi ia ka formula ha ka ‘Writer gray box’.
05:17	Babud, to ngin thoh ia ka nuksa ‘double integral formula’ ban khein ia ka volume jong u cuboid.
05:26	Bad ka phormula ka dei kumba la pyni ha ka screen.
05:30	Kumba ngi la iohi, u mark up n aka bynta u ‘double integral’ u dei ‘iint’. Kaba suk..
05:38	Kumjuh ruh, ngi lah ban pyndonkam da u triple integral ban wad ia ka volume ne jingheh jong u cuboid.
05:46	Bad ka ‘mark up’ n aka bynta jong ka triple integral ka dei ‘iiint’.
05:52	Ngi lah ruh ban pyndonkam da ka ‘subscript mark up’ ban batai shai ia ka ‘Limits’ jong u ‘integral’.
06:00	Da kaba pyndonkam da ka ‘subscript’, ‘math’ ka buh ia ka jingthoh shatrai na kamon jong u integral.
06:06	Te, kine ki dei ki rukom ban thoh ia u integral formulae bad ki equations ha ka Math.
06:13	Mynta, to ngin peit kumno ban thoh formulae badonlang ka ‘logarithm’s.
06:19	To ngin thoh ia kine ha ka ‘Math gray box’ lane ‘Math object’ bathymmai.
06:24	Type ‘Logarithms: bad nion ‘Enter’ arsien.
06:29	Call Math sa shisien;
06:35	Bad pynkylla ia ka font sha ka ’18 point’
06:39	Bad ‘align’ iaki sha ka ‘Left’.
06:42	Ka formula kaba suk da kaba pyndonkam da ka ‘logarithm’ ka dei ‘log 1000 to the base 10 is equal 3’.
06:52	Phin iohi ia ka ‘mark up’ hangne.
06:55	Sa kawei pat ka nuksa hangne: ‘log 64 to the base 2 is equal to 6’.
07:03	To ngin thoh mynta ia ka ‘integral’ representation ne rukom ban thoh jong u ‘natural logarithm’.
07:10	Ka natural logarithm of t is equal to the integral of 1 by x dx from 1 to t.
07:20	Bad ka ‘mark up’ ka long kumba lapyni ha ka screen.
07:25	To ngin ‘save’ ia ki nuksa jong ngi.
07:29	Hangne ka dei ka assignment na kabynta jong phi:
07:31	Thoh ia kine ki ‘derivative’ formula:
07:35	d squared y by d x squared is equal to d by dx of ( dy by dx)
07:47	Pyndonkam da ki brackets kiba lah ban pynkylla.
07:51	Thoh ia kine ki integral:
07:53	Integral with limits 0 to 1 of {square root of x } dx.
08:04	Ba bud, thoh ia ka ‘double integral’ kumba pyni:
08:09	Double integral from T of { 2 Sin x – 3 y cubed + 5 } dx dy
08:23	Bad da kaba pyndonkam ia ka formula:
08:25	log x to the power of p to the base b is equal to p into log x to the base b
08:35	wad ne khein log 1024 to the base 2.
08:41	Format ia ka formulae jongphi.
08:43	Da kane ngi la poi sha kaba kut jong kane ka jinghikai halor ka rukom thoh ia ki ‘Differential’ bad ‘Integral equations’ bad ‘logarithms’ jong ka ‘Libre Office Math’.
08:52	Ban batai lyngkot, ngi la pue kumno ban thoh :* Derivatives bad Differential equations
08:58	Integral equations bad *Formulae with Logarithms.
09:02	“Spoken Tutorial”project ka dei ka bynta jong ka Talk to a Teacher
09:06	Ba la kyrshan da ka National Mission on Education lyngba ka ICT, MHRD, Sorkar jong ka India.
09:13	Ia kane ka project la pyniaid da ka http://spoken-tutorial.org.
09:18	Khambun ki jingtip halor kane ka juh ki don hakane ka link harum :http://spoken-tutorial.org\NMEICT-Intro.
09:24	La pynkylla sha ka ktien khasi da i Godwin pyrbot bad nga i John Heribert Nongkynrih. Ngan pynkut noh. Khublei naka bynta ba iasnohlang.

Contributors and Content Editors

Pratik kamble, Winz