Rewrite the article into an online course syllabus.

Calculus is a branch of mathematics that involves the study of rates of change. Before calculus was invented, all math was static: It could only help calculate objects that were perfectly still. But the universe is constantly moving and changing. No objects—from the stars in space to subatomic particles or cells in the body—are always at rest. Indeed, just about everything in the universe is constantly moving. Calculus helped to determine how particles, stars, and matter actually move and change in real time.

Calculus is used in a multitude of fields that you wouldn't ordinarily think would make use of its concepts. Among them are physics, engineering, economics, statistics, and medicine. Calculus is also used in such disparate areas as space travel, as well as determining how medications interact with the body, and even how to build safer structures. You'll understand why calculus is useful in so many areas if you know a bit about its history as well as what it is designed to do and measure.
Calculus was developed in the latter half of the 17th century by two mathematicians, Gottfried Leibniz and Isaac Newton. Newton first developed calculus and applied it directly to the understanding of physical systems. Independently, Leibniz developed the notations used in calculus. Put simply, while basic math uses operations such as plus, minus, times, and division (+, -, x, and ÷), calculus uses operations that employ functions and integrals to calculate rates of change.

Those tools allowed Newton, Leibniz, and other mathematicians who followed to calculate things like the exact slope of a curve at any point. The Story of Mathematics explains the importance of Newton's fundamental theorem of the calculus:

"Unlike the static geometry of the Greeks, calculus allowed mathematicians and engineers to make sense of the motion and dynamic change in the changing world around us, such as the orbits of planets, the motion of fluids, etc."
Using calculus, scientists, astronomers, physicists, mathematicians, and chemists could now chart the orbit of the planets and stars, as well as the path of electrons and protons at the atomic level.

system
ek online paathyakram paathyakram main lekh ko phir se likhen.

calculas ganit kii ek shakha he jisamen parivartan kii daron kaa adhyayan shaamil he.calculas kaa avishkaar karne se pehle, sabhi ganit sthir tha: yah keval un vastuon kii gananaa karne main madad kar saktaa tha jo puri tarah se abhi bhi the.lekin brahmad lagaataar aage bad rahaa he or badal rahaa he.koi vastu - antariksh main taron se lekar sharir main up -parmaanu kanon yaa koshikaon tak - hameshaa aaraam karti he.darasal, brahmad main har cheez ke bare main lagaataar aage bad rahaa he.calculas ne yah nirdhaarit karne main madad kii ki kaise kan, taare or padaarth vastav main vaastavik samay main chalate hai or badalte hai.

calculas kaa upyog un kshetron kii ek bheed main kiya jaataa he jo aap aamtaur par nahin sochate the ki isaki avadharanaon kaa upyog kiya jayega.inamen bhautikee, ejineering, arthshaastra, sankhyikee or chikitsa hai.calculas kaa upyog antariksh yatra ke rup main aise asmaan kshetron main bhi kiya jaataa he, saath hi yah bhi nirdhaarit kiya jaataa he ki dawaaen sharir ke saath kaise baatcheet karti hai, or yahaan tak ki surakshit sanrachanaon kaa nirmaan kaise karen.aap samajhenge ki pathari itane saare kshetron main upyogi kyon he yadi aap iske itihaas ke bare main thodaa jaanate hai or saath hi saath ise karne or maapne ke liye kya dizine kiya gaya he.
calculas ko 17 veen shatabdi ke uttarardh main do ganitagyon, gotfreed libniz or ishak newton dwaara viksit kiya gaya tha.newton ne pehle calculas viksit kiya or ise sidhe bhautik pranaaliyon kii samaj ke liye lagu kiya.swatantra rup se, Leibniz ne calculas main upyog kiye gaye notesan viksit kiye.sidhe shabdon main kahen, jabaki buniyadi ganit plus, mines, times or divijan (+, -, eks, or,) jaise sanchaalan kaa upyog karata he, calculas us sanchaalan kaa upyog karata he jo parivartan kii daron kii gananaa karne ke liye kaaryon or abhinn ko niojit karata he.

un upkarnon ne newton, libanise or anya ganitagyon ko anumati di, jinhone kisi bhi bindu par vakr kii sateek dhalaan jaisi chizon kii gananaa karne ke liye peechha kiya.ganit kii kahani newton ke kalkulas ke moulik prameya ke mahatv ko bataati he:

"unaniyon kii sthir jyamiti ke vipareet, calculas ne ganitagyon or ejiniyaron ko hamaare aas -paas kii badalati duniya main gati or gatisheel parivartan kii samaj banane kii anumati di, jaise ki grahon kii kakshaon, taral padaarthon kii gati, aadi."
calculas, vaigyanikon, khagolavidon, bhautikavidon, ganitagyon or rasayanagyon kaa upyog karnaa ab grahon or sitaron kii kaksha ko chart kar saktaa he, saath hi saath parmaanu str par electronon or proton kaa maarg bhi ho saktaa he.
user
paathyakram sheershak: calculas ke liye ek parichay: brahmad main gatisheel parivartan kii khoj

paathyakram vivaran: ganit kii ek shakha, calculas ne brahmad main gatisheel pranaaliyon ko samajhane or vishleshan karne ke tareeke main kranti laa di.is online paathyakram main, ham calculas ke mul siddhanton main ghota lagaayenge or vibhinn kshetron, jaise bhautikee, ejineering, arthshaastra, sankhyikee or chikitsa jaise iske anuprayogon kaa pataa lagaayenge.up-parmaanu kanon ke vyavhaar kii bhavishyavaanee karne ke liye khagoleey nikaayon kii gati ko samajhane se, calculas hamaari badalati duniya ke rahasyon ko ujagar karne main mahatvapurn bhoomika nibhaataa he.is paathyakram ke madhyam se, aap calculas main ek thos aadhaar praapt karenge or vaastavik duniya ke paridrishyon main apni avadharanaon ko lagu karne ke liye kaushal viksit karenge.

paathyakram ke uddeshy:
1. gatisheel pranaaliyon ke adhyayan main calculas ke aitihaasik sandarbh or mahatv ko samajhen.
2. calculas kii moulik avadharanaon kaa anveshan karen, jisamen parivartan kii daron or kaaryon or abhinn angon kaa upyog shaamil he.
3. vaastavik duniya kii samasyaon kaa vishleshan karen or model or unhen hal karne ke liye calculas takneekon ko lagu karen.
4. bhautikee, ejineering, arthshaastra, sankhyikee or chikitsa jaise kshetron main pathari ke vividh anuprayogon main antardrushti praapt karen.
5. calculas-aadhaarit abhyaas or asinament ke madhyam se mahatvapurn soch or samasya samaadhaan kaushal viksit karen.
6. vaigyanik gyaan or takneekee navachaar ko aage badhaane main calculas kii bhoomika kii saraahna karen.

paathyakram kii ruparekha
modul 1: calculas kaa parichay
• aitihaasik prishthbhumi: gotfreed libniz or issa newton dwaara calculas kaa vikaas
• paaramparik sthitik ganit se calculas ko alag karnaa.
• gatisheel pranaaliyon main parivartan kii daron or iske mahatv kii avadharana.

modul 2: calculas kii buniyadi avadharanaen
• kaary or unke chitramay pratinidhitiv
• bhedbhaav: parivartan kii daron kii gananaa or ghatata kii dhalaan dhundhna.
ekikaran: kshetron kii gananaa or maatra kaa sanchay.

modul 3: calculas kaa anuprayog
• bhautikee: gati, balon or urja kaa vishleshan karnaa.
• ejineering: sanrachanaon or digining pranaaliyon kaa anukulan.
• arthshaastra: modelling aarthik vikaas or anukulan.
• sankhyikee: data rujhaanon or sambhaavna kaa vishleshan karnaa
• dawa: jaivik prakriyaaon or dawa kii baatcheet ko samajhnaa.

modul 4: unnat calculas vishay
• ucch-kram derevative or unke anuprayog
• anukulan: adhiktam or nunatam maan khojna
• vibhedak sameekaran: modelling gatisheel system
• bahukriyasheel pathari: kai char ke kaaryon kaa vishleshan karnaa

modul 5: vaastavik duniya main pathari
• cese study: antariksh yatra, chikitsa or buniyadi dhaanche ke vikaas main pathari ke vyaavhaarik anuprayog.
• bhavishya ke nirdesh: ubharate hue kshetra or vaigyanik pragati main pathari kii viksit bhoomika.

moolyankan ke tareekon:
1. moulik avadharanaon or samasya-samaadhaan kaushal kii samaj kaa pareekshan karne ke liye quiz or asinament.
2. pramukh vishyon kii samaj kaa akalan karne ke liye madhyavadhi pariksha.
3. antim pariyojna: ek vaastavik duniya kii samasya yaa paridrishy ke liye calculas siddhanton ko lagu karnaa.
4. sagaai or vichaaron ke aadan -pradaan ko protsaahit karne ke liye online charchaa or bhagidaari.

aavashyak sharten: bijganit or purv-calculas avadharanaon kii buniyadi samaj.

anushansit sansaadhan:
• james steward dwaara "calculas: arli trancendental"
• richard cortent or fritz jon dwaara "parichay or vishleshan kaa parichay"
• online tutorial or calculas platformon par abhyaas abhyaas
assistant
<|system|>
</s>
<|user|>
ek online paathyakram paathyakram main lekh ko phir se likhen.

calculas ganit kii ek shakha he jisamen parivartan kii daron kaa adhyayan shaamil he.calculas kaa avishkaar karne se pehle, sabhi ganit sthir tha: yah keval un vastuon kii gananaa karne main madad kar saktaa tha jo puri tarah se abhi bhi the.lekin brahmad lagaataar aage bad rahaa he or badal rahaa he.koi vastu - antariksh main taron se lekar sharir main up -parmaanu kanon yaa koshikaon tak - hameshaa aaraam karti he.darasal, brahmad main har cheez ke bare main lagaataar aage bad rahaa he.calculas ne yah nirdhaarit karne main madad kii ki kaise kan, taare or padaarth vastav main vaastavik samay main chalate hai or badalte hai.

calculas kaa upyog un kshetron kii ek bheed main kiya jaataa he jo aap aamtaur par nahin sochate the ki isaki avadharanaon kaa upyog kiya jayega.inamen bhautikee, ejineering, arthshaastra, sankhyikee or chikitsa hai.calculas kaa upyog antariksh yatra ke rup main aise asmaan kshetron main bhi kiya jaataa he, saath hi yah bhi nirdhaarit kiya jaataa he ki dawaaen sharir ke saath kaise baatcheet karti hai, or yahaan tak ki surakshit sanrachanaon kaa nirmaan kaise karen.aap samajhenge ki pathari itane saare kshetron main upyogi kyon he yadi aap iske itihaas ke bare main thodaa jaanate hai or saath hi saath ise karne or maapne ke liye kya dizine kiya gaya he.
calculas ko 17 veen shatabdi ke uttarardh main do ganitagyon, gotfreed libniz or ishak newton dwaara viksit kiya gaya tha.newton ne pehle calculas viksit kiya or ise sidhe bhautik pranaaliyon kii samaj ke liye lagu kiya.swatantra rup se, Leibniz ne calculas main upyog kiye gaye notesan viksit kiye.sidhe shabdon main kahen, jabaki buniyadi ganit plus, mines, times or divijan (+, -, eks, or,) jaise sanchaalan kaa upyog karata he, calculas us sanchaalan kaa upyog karata he jo parivartan kii daron kii gananaa karne ke liye kaaryon or abhinn ko niojit karata he.

un upkarnon ne newton, libanise or anya ganitagyon ko anumati di, jinhone kisi bhi bindu par vakr kii sateek dhalaan jaisi chizon kii gananaa karne ke liye peechha kiya.ganit kii kahani newton ke kalkulas ke moulik prameya ke mahatv ko bataati he:

"unaniyon kii sthir jyamiti ke vipareet, calculas ne ganitagyon or ejiniyaron ko hamaare aas -paas kii badalati duniya main gati or gatisheel parivartan kii samaj banane kii anumati di, jaise ki grahon kii kakshaon, taral padaarthon kii gati, aadi."
calculas, vaigyanikon, khagolavidon, bhautikavidon, ganitagyon or rasayanagyon kaa upyog karnaa ab grahon or sitaron kii kaksha ko chart kar saktaa he, saath hi saath parmaanu str par electronon or proton kaa maarg bhi ho saktaa he.</s>
<|assistant|>
paathyakram sheershak: calculas ke liye ek parichay: brahmad main gatisheel parivartan kii khoj

paathyakram vivaran: ganit kii ek shakha, calculas ne brahmad main gatisheel pranaaliyon ko samajhane or vishleshan karne ke tareeke main kranti laa di.is online paathyakram main, ham calculas ke mul siddhanton main ghota lagaayenge or vibhinn kshetron, jaise bhautikee, ejineering, arthshaastra, sankhyikee or chikitsa jaise iske anuprayogon kaa pataa lagaayenge.up-parmaanu kanon ke vyavhaar kii bhavishyavaanee karne ke liye khagoleey nikaayon kii gati ko samajhane se, calculas hamaari badalati duniya ke rahasyon ko ujagar karne main mahatvapurn bhoomika nibhaataa he.is paathyakram ke madhyam se, aap calculas main ek thos aadhaar praapt karenge or vaastavik duniya ke paridrishyon main apni avadharanaon ko lagu karne ke liye kaushal viksit karenge.

paathyakram ke uddeshy:
1. gatisheel pranaaliyon ke adhyayan main calculas ke aitihaasik sandarbh or mahatv ko samajhen.
2. calculas kii moulik avadharanaon kaa anveshan karen, jisamen parivartan kii daron or kaaryon or abhinn angon kaa upyog shaamil he.
3. vaastavik duniya kii samasyaon kaa vishleshan karen or model or unhen hal karne ke liye calculas takneekon ko lagu karen.
4. bhautikee, ejineering, arthshaastra, sankhyikee or chikitsa jaise kshetron main pathari ke vividh anuprayogon main antardrushti praapt karen.
5. calculas-aadhaarit abhyaas or asinament ke madhyam se mahatvapurn soch or samasya samaadhaan kaushal viksit karen.
6. vaigyanik gyaan or takneekee navachaar ko aage badhaane main calculas kii bhoomika kii saraahna karen.

paathyakram kii ruparekha
modul 1: calculas kaa parichay
• aitihaasik prishthbhumi: gotfreed libniz or issa newton dwaara calculas kaa vikaas
• paaramparik sthitik ganit se calculas ko alag karnaa.
• gatisheel pranaaliyon main parivartan kii daron or iske mahatv kii avadharana.

modul 2: calculas kii buniyadi avadharanaen
• kaary or unke chitramay pratinidhitiv
• bhedbhaav: parivartan kii daron kii gananaa or ghatata kii dhalaan dhundhna.
ekikaran: kshetron kii gananaa or maatra kaa sanchay.

modul 3: calculas kaa anuprayog
• bhautikee: gati, balon or urja kaa vishleshan karnaa.
• ejineering: sanrachanaon or digining pranaaliyon kaa anukulan.
• arthshaastra: modelling aarthik vikaas or anukulan.
• sankhyikee: data rujhaanon or sambhaavna kaa vishleshan karnaa
• dawa: jaivik prakriyaaon or dawa kii baatcheet ko samajhnaa.

modul 4: unnat calculas vishay
• ucch-kram derevative or unke anuprayog
• anukulan: adhiktam or nunatam maan khojna
• vibhedak sameekaran: modelling gatisheel system
• bahukriyasheel pathari: kai char ke kaaryon kaa vishleshan karnaa

modul 5: vaastavik duniya main pathari
• cese study: antariksh yatra, chikitsa or buniyadi dhaanche ke vikaas main pathari ke vyaavhaarik anuprayog.
• bhavishya ke nirdesh: ubharate hue kshetra or vaigyanik pragati main pathari kii viksit bhoomika.

moolyankan ke tareekon:
1. moulik avadharanaon or samasya-samaadhaan kaushal kii samaj kaa pareekshan karne ke liye quiz or asinament.
2. pramukh vishyon kii samaj kaa akalan karne ke liye madhyavadhi pariksha.
3. antim pariyojna: ek vaastavik duniya kii samasya yaa paridrishy ke liye calculas siddhanton ko lagu karnaa.
4. sagaai or vichaaron ke aadan -pradaan ko protsaahit karne ke liye online charchaa or bhagidaari.

aavashyak sharten: bijganit or purv-calculas avadharanaon kii buniyadi samaj.

anushansit sansaadhan:
• james steward dwaara "calculas: arli trancendental"
• richard cortent or fritz jon dwaara "parichay or vishleshan kaa parichay"
• online tutorial or calculas platformon par abhyaas abhyaas</s>
