Calculus	tutorial	for	beginners	pdf
                                                                                                               	
  How	can	i	teach	myself	calculus.	Easy	way	to	learn	calculus	for	beginners.	How	do	you	do	calculus	for	beginners.	How	do	i	teach	myself	calculus.	What	is	calculus	for	beginners.	
  Section	of	Mathematics	This	article	is	about	the	section	of	mathematics.	For	other	uses,	see	Calculation	(marking).	Part	of	a	series	of	papers	on	calculus	Main	Theorem	Leibniz	Integral	Rule	Limits	of	Functions	Continuity	Mean	Value	Theorem	Role	Theorem	Differential	Definitions	of	Functions	Derivative	(generalizations)	Differential	Infinitesimal
  Function	Concepts	of	Sum	Derivation	Notation	Second	Derivative	Implicit	Differentiation	Logarithmic	Differentiation	and	Regular	Coefficients	Identities	Sum	Chain	of	Products	Power	Factor	Rule	Löpital	General	formula	for	the	inverse	integral	of	Leibniz	Faa	di	Bruno	Reynolds	Lists	of	integrals	Integral	transformation	Definitions	Primitives	Integral
  (false)	Riemann	integral	Lebesgue	integration	Contour	integration	Integration	of	inverse	functions	Integration	of	cylinders	Partial	shellx	integration	(trigonometric,	tangent	half	angle,	Euler)	Euler	formula	Fractional	parts	Reordering	Reduction	Formulas	Differentiation	under	the	Integral	Sign	Risch	Algorithm	Geometry	Series	arithmetic-geometric
  Harmonic	Vec	productivity	Binomial	Teulor	Convergence	criteria	Ratio	Root	integral	Direct	comparison	Comparison	of	boundary	values	​​Alternative	series	Cauchy	condensation	Abelian	Dirichlet	vector	Gradient	divergence	Laplace	curl	Directed	derivation	Identity	theorems	Stokes	gradient	divergence	according	to	the	generalized	multidimensional
  Stokes-Green	formalisms	Definition	of	manifolds	Matrix	Derivatives	Definition	of	Matrix	Tensor	Outer	Derivative	Definition	of	Area	Integral	Area	Integral	Volume	Integral	Jacobi-Hessian	Advanced	Euclidean	Spatial	Calculus	Distribution	Limit	Subject	Fractional	Malyavin	Stochastic	Variation	Miscellaneous	Precalculus	History	Glossary	logical	analysis
  Algebra	Geometry	and	logical	analysis	and	decision	sciences	Relations	e	to	the	sciencesDepartment	of	Mathematics	This	article	is	about	the	branch	of	mathematics.	For	other	uses,	see	Calculation	(marking).	Part	of	a	series	of	articles	on	mathematical	analysis	Main	theorem	Leibniz	integral	rule	Limits	of	functions	Continuity	Mean	value	theorem	Role
  theorem	Definitions	of	differentials	Derivation	(generalizations)	Differential	infinitesimal	function	Sum	concepts	Derivative	notation	Second	derivative	Implicit	differentiation	Logarithmic	differentiations	and	associated	norms.	Sum	Product	chain	Power	factor	L'Hopital's	rule	Inverse	Leibniz	general	formula	Fedia	Bruno	Reynolds	integral	Lists	of
  integrals	Integral	transformation	Definitions	Primitives	Integral	(false)	Riemann	integral	Lebesgue	integration	Contour	integration	Inverse	function	integral	Partial	integration	Disks	Cylindrical	substitution	of	semicircles	angle,	Euler)	Euler's	formula	Fractions	Change	order	Reduction	formulas	Differentiation	under	the	integral	sign	Risch	algorithm
  Geometric	series	(arithmetic-geometer	Harmonic	Wec	performance	Binomial	Taylor	convergence	terms	Check	factor	Root	Integral	Direct	comparison	Boundary	comparison	Variable	series	Cauchy	condensation	Abel	Dirichlet	vector	gradient	divergence	Curl	directed	Laplace	derivation	identity	theorems	Gradient	Stokes	divergence	according	to	Stokes
  Tenometric	definitional	generalization	of	Green's	multivariate	integralism	Integral	area	Integral	Jacobi-Hessian	volume	Integral	Improve	brush	Euclidean	space	calculus	Partition	limit	Subject	Fraction	Mallaven's	stochastic	variation	Miscellaneous	precalculus	History	Glossary	Topic	list	integration	Bi	calculus	Mathematics	and	mathematics	and
  mathematics	fields	logistics	and	logic	geometry	geometry	geometry	number	analysis.	decision	sciences	Attitudes	towards	sciencesComputational	biology	Linguistics	Economics	Philosophy	Learning	portal	Calculus,	originally	called	calculus	of	infinitesimals	or	"infinites",	is	the	mathematical	study	of	constant	change,	just	as	geometry	is	the	science	of
  form	and	algebra	is	the	science	of	generalizations	of	arithmetic.	operation.	It	has	two	main	branches:	differential	and	integral	calculus;	the	former	refers	to	the	instantaneous	rates	of	change	and	slopes	of	the	curves,	and	the	latter	to	the	accumulation	of	magnitudes	and	areas	under	or	between	the	curves.	These	two	branches	are	connected	by	the
  fundamental	theorem	of	calculus	and	use	the	basic	notions	of	convergence	of	infinite	sequences	and	infinite	series	to	a	well-defined	limit.	Infinitesimal	calculus	was	independently	developed	in	the	late	17th	century	by	Isaac	Newton	and	Gottfried	Wilhelm	Leibniz.	More	recent	work,	including	the	codification	of	the	idea	of	​​boundaries,	has	placed	this
  development	on	a	more	solid	conceptual	basis.	Today,	numbers	are	widely	used	in	science,	technology,	and	the	social	sciences.[4]	Etymology	In	mathematics	education,	the	number	refers	to	elementary	calculus	courses	that	are	mainly	devoted	to	the	study	of	functions	and	limits.	The	word	calculus	is	Latin	for	"little	pebble"	(a	diminutive	of	limestone,
  meaning	"stone"),	a	meaning	that	is	still	retained	in	today's	medicine.	Since	such	pebbles	were	used	for	counting	distances,	counting	votes,	and	arithmetic	on	the	abacus,	the	word	came	to	mean	a	method	of	counting.	In	this	sense,	it	was	used	in	English	at	least	as	early	as	1672,	a	few	years	before	the	publications	of	Leibniz	and	Newton.[6]	In	addition
  to	calculus	and	integral	calculus,	the	term	is	also	used	for	specific	methods	of	calculus	and	related	theories	that	attempt	to	model	a	certain	concept	in	mathematical	terms.	Examples	of	this	convention	include	propositional	calculus,	Ricci	calculus,	differential	calculuslambda	calculus	and	process	calculus.	In	addition,	the	term	"number"	has	various
  uses	in	ethics	and	philosophy	for	systems	such	as	the	luck	number	and	Bentham's	ethical	number.	History	Main	article:	History	of	calculus	Modern	calculus	was	developed	in	17th-century	Europe	by	Isaac	Newton	and	Gottfried	Wilhelm	Leibniz	(independently,	first	published	around	the	same	time),	but	elements	of	it	appeared	in	ancient	Greece,	then
  in	China	and	the	Middle	East,	and	even	later	in	medieval	Europe	and	India.	Ancient	Ancestors	Egypt	Calculation	of	volume	and	area,	one	of	the	purposes	of	integral	calculus,	can	be	found	on	the	Egyptian	Muscovite	Papyrus	(c.	1820	BC),	but	the	formulas	are	simple	instructions	with	no	indication	of	how	they	were	derived.	[7]	[8]	Greece	See	also:
  Greek	mathematics	Archimedes	used	an	exhaustive	method	of	calculating	the	area	under	a	parabola	in	his	work	The	Square	of	a	Parabola.	When	the	ancient	Greek	mathematician	Eudoxus	of	Cnidus	(c.	390–337	BC)	laid	the	foundations	for	integral	calculus	and	anticipated	the	concept	of	limits,	he	devised	an	exhaustive	method	of	proving	formulas	for
  the	volumes	of	cones	and	pyramids.	In	the	Hellenistic	period,	this	method	was	developed	by	Archimedes	(c.	287	-	c.	212	BC),	who	combined	it	with	the	concept	of	indivisibles	-	a	precursor	to	infinitesimals	-	which	allowed	him	to	solve	several	problems	that	the	Today	integral	solves.	number.	In	"The	Method	of	Mechanical	Theorems",	he	describes,	for
  example,	the	calculation	of	the	center	of	gravity	of	a	full	hemisphere,	the	center	of	gravity	of	a	truncated	circular	paraboloid,	and	the	area	of	​​the	area	bounded	by	the	parabola	and	one	of	its	secants.	China	The	exhaustion	method	was	later	independently	discovered	in	China	by	Liu	Hui	in	the	3rd	century	AD	to	find	the	area	of	​​a	circle.	In	the	5th
  century	AD,	Zu	Gengzhi,	son	of	Zu	Chongzhi,	developed	a	method	[12]	[13]	which	was	later	called	the	Cavalieri	method.find	the	volume	of	the	sphere.	Medieval	Near	East	Ibn	al-Haytham,	11th-century	Near	Eastern	Arab	mathematician	and	physicist	Hassan	ibn	al-Haytham,	romanized	as	Alhazen	(ca.	965–1040	CE),	derived	the	formula.	for	the	sum	of
  the	fourth	powers.	He	used	the	results	to	perform	what	is	now	called	the	integration	of	this	function,	where	the	formula	for	the	sum	of	integral	squares	and	the	fourth	power	allowed	him	to	calculate	the	volume	of	the	paraboloid.	India	In	the	14th	century,	Indian	mathematicians	proposed	a	free	method	resembling	differentiation	applicable	to	certain
  trigonometric	functions.	Thus	Madhava	of	Sangamagram	and	the	Kerala	School	of	Astronomy	and	Mathematics	defined	the	components	of	calculus.	The	complete	theory	involving	these	components	is	now	well	known	in	the	Western	world	as	the	Taylor	series	or	infinite	series	approximation.	However,	they	failed	to	"bring	together	many	different	ideas
  under	the	two	unifying	themes	of	the	derivative	and	the	integral,	show	the	connection	between	them,	and	turn	calculus	into	the	great	problem-solving	tool	we	have	today"	[14].	The	stereometric	Doliorum	of	the	modern	Johannes	Kepler	formed	the	basis	of	the	integral	calculus.	Kepler	developed	a	method	for	calculating	the	area	of	​​an	ellipse	by	adding
  the	lengths	of	a	set	of	radii	drawn	from	the	focus	of	the	ellipse.[18]	An	important	work	was	the	treatise	that	laid	the	foundations	of	Kepler's	method	[18],	written	by	Bonaventura	Cavalieri,	who	argued	that	volumes	and	areas	should	be	calculated	as	sums	of	volumes	and	areas	of	infinitely	thin	cross-sections.	The	ideas	were	similar	to	those	of
  Archimedes	in	the	Method,	but	this	treatise	is	believed	to	have	been	lost	in	the	13th	century	and	not	rediscovered	until	the	early	20th	century,	so	Cavalieri	was	unaware	of	it.	Cavalieri's	work	was	not	respected	because	his	methods	could	lead	to	erroneous	results	and	his	infinitesimal	values	​​were	initially	frowned	upon.	FormalThe	calculus	combined
  the	infinitesimal	Cavalieri	numbers	with	finite	difference	calculus,	developed	in	Europe	at	about	the	same	time.	Pierre	de	Fermat,	who	claimed	to	be	borrowed	from	Diophantus,	introduced	the	concept	of	proportionality,	which	represented	equality	up	to	an	infinitesimal	error.[19]	The	combination	succeeded	John	Wallis,	Isaac	Barrow	and	James
  Gregory,	the	two	last	proving	predecessors	of	the	second	fundamental	theorem	of	analysis	around	1670.	Product	rule	and	chain	rule[22],	concepts	of	higher	derivatives	and	Taylor	series[23]	and	analytic	functions[24]	were	developed	by	Isaac	Newton	used	in	the	idiosyncratic	notation	he	used	to	solve	problems	in	mathematical	physics.	In	his	writings,
  Newton	reformulated	his	ideas	to	suit	the	mathematical	language	of	the	time,	replacing	calculations	with	infinitesimal	equivalent	geometric	arguments	that	were	considered	error-free.	He	used	the	methods	of	calculus	to	solve	the	problem	of	the	motion	of	the	planets,	the	shape	of	the	surface	of	a	rotating	liquid,	the	compression	of	the	earth,	the
  motion	of	a	weight	sliding	on	a	cycloid,	and	many	other	problems	discussed	in	his	became	Principia	Mathematica	(1687).	In	other	work	he	developed	series	expansions	of	functions,	including	fractional	and	irrational	powers,	and	it	was	clear	that	he	understood	the	principles	of	the	Taylor	series.	He	did	not	publish	any	of	these	discoveries,	and	at	that
  time	infinitesimal	methods	were	still	considered	dubious.[25]	Gottfried	Wilhelm	Leibniz	was	the	first	to	clearly	formulate	the	rules	of	calculation.	Isaac	Newton	developed	the	use	of	calculus	in	his	laws	of	motion	and	gravitation.	These	ideas	were	converted	into	true	infinitesimal	calculus	by	Gottfried	Wilhelm	Leibniz,	whom	Newton	initially	accused	of
  plagiarism.	He	is	now	considered	an	independent	inventor	and	contributor	to	the	calculus.	His	contribution	was	to	provide	a	clear	set	of	rules	for	dealing	with	infinitesimals	that	makes	this	possiblesecond	and	higher	derivatives,	as	well	as	the	product	rule	and	the	chain	rule	in	their	differential	and	integral	forms.	In	contrast	to	Newton,	Leibniz	tried	to
  choose	a	notational	system.[27]	Today,	Leibniz	and	Newton	are	generally	credited	with	independently	inventing	and	developing	numbers.	Newton	was	the	first	to	use	calculus	in	general	physics,	and	Leibniz	developed	much	of	the	calculus	used	today.	Integration,	emphasizing	that	differentiation	and	integration	are	inverse	processes,	second	and
  higher	derivatives,	and	the	concept	of	an	approximating	polynomial	series.	When	Newton	and	Leibniz	first	published	their	results,	there	was	much	controversy	over	which	mathematician	(and	therefore	which	country)	deserved	the	credit.	Newton	was	the	first	to	receive	his	results	(they	were	later	published	in	his	"Method	of	Fluxions"),	while	Leibniz
  was	the	first	to	publish	his	"New	Method	of	Maximis	and	Minimis".	Newton	claimed	that	Leibniz	stole	ideas	from	his	unpublished	notes,	which	Newton	shared	with	several	members	of	the	Royal	Society.	This	controversy	divided	English-speaking	mathematicians	and	continental	European	mathematicians	for	many	years,	to	the	detriment	of	English
  mathematics.	A	careful	study	of	the	works	of	Leibniz	and	Newton	shows	that	they	arrived	at	their	results	independently	of	each	other:	Leibniz	started	first	with	integration	and	Newton	with	differentiation.	However,	Leibniz	gave	the	new	discipline	its	own	name.	Newton	called	his	calculus	the	"science	of	fluxes,"	a	term	that	persisted	in	English	schools
  into	the	19th	century.	first	published	in	1815[31]	Since	the	time	of	Leibniz	and	Newton,	many	mathematicians	have	contributed	to	the	continuous	development	of	calculus.	One	of	the	first	and	most	complete	works	on	bothand	the	integral	calculation	was	written	in	1748	by	Marija	Gaetana	Agnesi.	Foundations	by	Mario	Gaetano	Agnesi	In	calculus,
  foundations	refer	to	the	careful	development	of	a	subject	from	axioms	and	definitions.	In	early	calculus	the	use	of	infinitesimals	was	taken	for	granted	and	was	severely	criticized	by	several	authors,	notably	Michel	Rolle	and	Bishop	Berkeley.	In	his	book	The	Analyst	in	1734,	Berkeley	famously	described	infinitesimals	as	ghosts	of	past	quantities.
  Establishing	a	firm	foundation	for	calculus	occupied	mathematicians	for	most	of	the	century	after	Newton	and	Leibniz,	and	is	still	somewhat	of	an	active	area	of	​​research.	[34]	Several	mathematicians,	including	Maclarin,	tried	to	prove	the	correct	use	of	infinitesimals,	but	it	was	not	until	150	years	later,	thanks	to	the	work	of	Cauchy	and	Weierstrass,
  that	a	way	was	finally	found	to	avoid	simple	"notions"	of	infinitesimals.	.	.	[35]	The	foundations	of	differential	calculus	and	integral	calculation	were	laid.	In	the	course	of	Cauchy	analysis,	we	find	a	wide	range	of	basic	approaches,	including	the	definition	of	continuity	in	terms	of	infinitesimals	and	the	(somewhat	imprecise)	prototype	(ε,	δ)	definition	of
  limits	in	the	definition	of	the	derivative.	[36]	In	his	work,	Weierstrass	formalized	the	concept	of	limits	and	excluded	infinitesimals	(although	his	definition	can	effectively	claim	that	infinitesimal	squares	are	zero).	After	the	work	of	Weierstrass,	it	finally	became	common	to	base	calculus	on	limits	rather	than	infinitesimal	calculus,	although	the	subject	is
  still	sometimes	referred	to	as	"infinitesimal	calculus".	Bernhard	Riemann	used	these	ideas	to	precisely	define	the	integral.[37]	Also	during	this	period,	calculus	ideas	were	generalized	into	a	comprehensive	plan,	developing	complex	analysis.[38]	In	modern	mathematics,	the	fundamentals	of	calculus	are	included	in	the	domain	of	real	analysis,	which
  includes	completeand	proofs	of	calculus	theorems.	The	range	of	infinitesimal	calculations	was	also	greatly	extended.	Henri	Loebig	invented	measure	theory	based	on	earlier	developments	by	Émile	Borel	and	used	it	to	define	the	integrals	of	all	but	the	most	pathological	functions.[39]	Laurent	Schwarz	introduced	distributions	with	which	arbitrary
  functions	can	be	obtained.[40]	Bounds	are	not	the	only	rigorous	approach	to	the	fundamentals	of	calculus.	Another	option	is	to	use	Abraham	Robinson's	non-standard	analysis.	Robinson's	approach,	developed	in	the	1960s,	uses	the	technical	mechanisms	of	mathematical	logic	to	extend	the	real	number	system	with	infinitesimals	and	infinitesimals,	as
  in	the	original	Newton–Leibnitz	concept.	The	resulting	numbers	are	called	hyperreal	numbers	and	can	be	used	to	construct	a	Leibniz	extension	of	the	ordinary	rules	of	calculus.[41]	There	is	also	smooth	infinitesimal	analysis,	which	differs	from	nonstandard	analysis	in	that	it	specifies	that	infinitesimals	of	higher	power	are	ignored	during	the
  derivation.[34]	Based	on	the	ideas	of	F.	W.	Lawver	and	using	the	methods	of	category	theory,	smooth	infinitesimal	analysis	assumes	that	all	functions	are	continuous	and	cannot	be	expressed	in	discrete	units.	One	aspect	of	this	formulation	is	that	the	law	of	the	excluded	middle	does	not	apply.[34]	The	excluded	middle	rule	is	also	rejected	in
  constructivist	mathematics,	a	branch	of	mathematics	that	insists	that	a	proof	of	the	existence	of	a	number,	function,	or	other	mathematical	object	must	provide	a	construction	of	the	object.	Reformulating	calculations	into	a	constructive	framework	is	usually	part	of	the	subject	of	constructive	analysis[34].	Significance	Although	many	of	the	ideas	of
  computing	were	developed	earlier	in	Greece,	China,	India,	Iraq,	Persia,	and	Japan,	the	use	of	computing	in	Europe	began	in	the	17th	century,	when	Newton	and	Leibniz	built	on	the	work	of	earlier	mathematicians	and	introduced.	its	basic	principles.[11][25[42]The	Hungarian	polymath	John	von	Neumann	wrote	of	this	work:	Calculus	was	the	first
  achievement	of	modern	mathematics,	and	it	is	difficult	to	overestimate	its	importance.	This,	I	believe,	more	than	anything	else	marks	the	beginning	of	modern	mathematics,	and	the	system	of	mathematical	analysis	which	is	its	logical	development	remains	the	greatest	technical	achievement	of	exact	thought.[43]	Differential	calculus	applications
  include	calculations	involving	velocity	and	acceleration,	curve	slope,	and	optimization.[44]:	"341"	-	453"	Integral	calculus	applications	include	calculations	involving	area,	volume,	arc	length,	and	centroid	pressure.[44]:	â685â700â	Advanced	applications	include	Power	Series	and	Fourier	Series	Numbers	are	also	used	to	better	understand	the	nature	of
  space,	time,	and	motion	For	centuries,	mathematicians	and	philosophers	have	grappled	with	the	paradoxes	of	dividing	by	zero,	or	the	sum	of	infinitely	many	numbers.These	questions	arise	as	you	study	them	of	motion	and	area.The	ancient	Greek	philosopher	Zeno	of	Elea	provided	several	famous	examples	of	such	paradoxes.Calculus	provides	tools,
  notably	limits	and	infinite	series,	that	solve	paradoxes	[45]	Principles	Limits	and	infinitesimals	Main	article:	Calculations	Limits	of	functions	and	infinitesimal	numbers	become	no	Traditionally	developed	by	working	with	very	small	sets.	Historically,	the	first	way	this	was	achieved	was	to	use	infinitesimally	small.	These	are	objects	that	can	be	thought	of