{"id":2263,"date":"2017-06-15T21:58:42","date_gmt":"2017-06-15T21:58:42","guid":{"rendered":"http:\/\/10.10.10.4:9191\/softlect\/?p=2263"},"modified":"2019-06-22T13:25:30","modified_gmt":"2019-06-22T13:25:30","slug":"calculus-symbols","status":"publish","type":"post","link":"http:\/\/softlect.com\/index.php\/calculus-symbols\/","title":{"rendered":"Calculus Symbols"},"content":{"rendered":"
\n
\n
Symbol<\/strong><\/div>\n
Symbol Name<\/strong><\/div>\n
Meaning \/ definition<\/strong><\/div>\n
Example<\/strong><\/div>\n<\/div>\n
\n
\"\\lim_{x\\to<\/div>\n
limit<\/div>\n
limit value of a function<\/div>\n
<\/div>\n<\/div>\n
\n
\u03b5<\/em><\/div>\n
epsilon<\/div>\n
represents a very small number, near zero<\/div>\n
\u03b5 <\/em>\u21920<\/div>\n<\/div>\n
\n
e<\/em><\/div>\n
e constant \/ Euler’s number<\/div>\n
e<\/em> = 2.718281828…<\/div>\n
e<\/em> = lim (1+1\/x<\/em>)x<\/sup><\/em> ,x<\/em>\u2192\u221e<\/div>\n<\/div>\n
\n
y <\/em>‘<\/div>\n
derivative<\/div>\n
derivative – Leibniz’s notation<\/div>\n
(3x<\/em>3<\/sup>)’ = 9x<\/em>2<\/sup><\/div>\n<\/div>\n
\n
y <\/em>”<\/div>\n
second derivative<\/div>\n
derivative of derivative<\/div>\n
(3x<\/em>3<\/sup>)” = 18x<\/em><\/div>\n<\/div>\n
\n
y<\/em>(n<\/em>)<\/sup><\/div>\n
nth derivative<\/div>\n
n times derivation<\/div>\n
(3x<\/em>3<\/sup>)(3)<\/sup> = 18<\/div>\n<\/div>\n
\n
\"\\frac{dy}{dx}\"<\/div>\n
derivative<\/div>\n
derivative – Lagrange’s notation<\/div>\n
d<\/em>(3x<\/em>3<\/sup>)\/dx<\/em> = 9x<\/em>2<\/sup><\/div>\n<\/div>\n
\n
\"\\frac{d^2y}{dx^2}\"<\/div>\n
second derivative<\/div>\n
derivative of derivative<\/div>\n
d<\/em>2<\/sup>(3x<\/em>3<\/sup>)\/dx<\/em>2<\/sup> = 18x<\/em><\/div>\n<\/div>\n
\n
\"\\frac{d^ny}{dx^n}\"<\/div>\n
nth derivative<\/div>\n
n times derivation<\/div>\n
<\/div>\n<\/div>\n
\n
\"\\dot{y}\"<\/div>\n
time derivative<\/div>\n
derivative by time – Newton notation<\/div>\n
<\/div>\n<\/div>\n
\n
\"\"<\/div>\n
time second derivative<\/div>\n
derivative of derivative<\/div>\n
<\/div>\n<\/div>\n
\n
\"\\frac{\\partial<\/div>\n
partial derivative<\/div>\n
<\/div>\n
\u2202(x<\/em>2<\/sup>+y<\/em>2<\/sup>)\/\u2202x<\/em> = 2x<\/em><\/div>\n<\/div>\n
\n
\u222b<\/div>\n
integral<\/div>\n
opposite to derivation<\/div>\n
<\/div>\n<\/div>\n
\n
\u222c<\/div>\n
double integral<\/div>\n
integration of function of 2 variables<\/div>\n
<\/div>\n<\/div>\n
\n
\u222d<\/div>\n
triple integral<\/div>\n
integration of function of 3 variables<\/div>\n
<\/div>\n<\/div>\n
\n
\u222e<\/div>\n
closed contour \/ line integral<\/div>\n
<\/div>\n
<\/div>\n<\/div>\n
\n
\u222f<\/div>\n
closed surface integral<\/div>\n
<\/div>\n
<\/div>\n<\/div>\n
\n
\u2230<\/div>\n
closed volume integral<\/div>\n
<\/div>\n
<\/div>\n<\/div>\n
\n
[a<\/em>,b<\/em>]<\/div>\n
closed interval<\/div>\n
[a<\/em>,b<\/em>] = {x <\/em>| a <\/em>\u2264 x <\/em>\u2264 b<\/em>}<\/div>\n
<\/div>\n<\/div>\n
\n
(a<\/em>,b<\/em>)<\/div>\n
open interval<\/div>\n
(a<\/em>,b<\/em>) = {x <\/em>| a <\/em>< x <\/em>< b<\/em>}<\/div>\n
<\/div>\n<\/div>\n
\n
i<\/em><\/div>\n
imaginary unit<\/div>\n
i<\/em> \u2261 \u221a-1<\/div>\n
z<\/em> = 3 + 2i<\/em><\/div>\n<\/div>\n
\n
z<\/em>*<\/div>\n
complex conjugate<\/div>\n
z <\/em>= a<\/em>+bi<\/em> \u2192 z<\/em>*=a<\/em>–bi<\/em><\/div>\n
z*<\/em> = 3 + 2i<\/em><\/div>\n<\/div>\n
\n
z<\/em><\/div>\n
complex conjugate<\/div>\n
z <\/em>= a<\/em>+bi<\/em> \u2192 z <\/em>= a<\/em>–bi<\/em><\/div>\n
z<\/em> = 3 + 2i<\/em><\/div>\n<\/div>\n
\n
\u2207<\/div>\n
nabla \/ del<\/div>\n
gradient \/ divergence operator<\/div>\n
\u2207f <\/em>(x<\/em>,y<\/em>,z<\/em>)<\/div>\n<\/div>\n
\n
\"\"<\/div>\n
vector<\/div>\n
<\/div>\n
<\/div>\n<\/div>\n
\n
\"\"<\/div>\n
unit vector<\/div>\n
<\/div>\n
<\/div>\n<\/div>\n
\n
x <\/em>* y<\/em><\/div>\n
convolution<\/div>\n
y<\/em>(t<\/em>) = x<\/em>(t<\/em>) * h<\/em>(t<\/em>)<\/div>\n
<\/div>\n<\/div>\n
\n
\"\"<\/div>\n
Laplace transform<\/div>\n
F<\/em>(s<\/em>) = \"\"{f <\/em>(t<\/em>)}<\/div>\n
<\/div>\n<\/div>\n
\n
\"\"<\/div>\n
Fourier transform<\/div>\n
X<\/em>(\u03c9<\/em>) = \"\"{f <\/em>(t<\/em>)}<\/div>\n
<\/div>\n<\/div>\n
\n
\u03b4<\/em><\/div>\n
delta function<\/div>\n
<\/div>\n
<\/div>\n<\/div>\n
\n
\u221e<\/div>\n
lemniscate<\/div>\n
infinity symbol<\/div>\n
<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Symbol Symbol Name Meaning \/ definition Example limit limit value of a function \u03b5 epsilon represents a very small number, near zero \u03b5 \u21920 e e constant \/ Euler’s number… <\/p>\n","protected":false},"author":1,"featured_media":3127,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[34],"tags":[],"aioseo_notices":[],"amp_enabled":true,"_links":{"self":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts\/2263"}],"collection":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/comments?post=2263"}],"version-history":[{"count":3,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts\/2263\/revisions"}],"predecessor-version":[{"id":3535,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts\/2263\/revisions\/3535"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/media\/3127"}],"wp:attachment":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/media?parent=2263"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/categories?post=2263"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/tags?post=2263"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}