MAT1001 Differential Calculus: Lecture Notes
\(\newcommand{\footnotename}{footnote}\)
\(\def \LWRfootnote {1}\)
\(\newcommand {\footnote }[2][\LWRfootnote ]{{}^{\mathrm {#1}}}\)
\(\newcommand {\footnotemark }[1][\LWRfootnote ]{{}^{\mathrm {#1}}}\)
\(\let \LWRorighspace \hspace \)
\(\renewcommand {\hspace }{\ifstar \LWRorighspace \LWRorighspace }\)
\(\newcommand {\TextOrMath }[2]{#2}\)
\(\newcommand {\mathnormal }[1]{{#1}}\)
\(\newcommand \ensuremath [1]{#1}\)
\(\newcommand {\LWRframebox }[2][]{\fbox {#2}} \newcommand {\framebox }[1][]{\LWRframebox } \)
\(\newcommand {\setlength }[2]{}\)
\(\newcommand {\addtolength }[2]{}\)
\(\newcommand {\setcounter }[2]{}\)
\(\newcommand {\addtocounter }[2]{}\)
\(\newcommand {\arabic }[1]{}\)
\(\newcommand {\number }[1]{}\)
\(\newcommand {\noalign }[1]{\text {#1}\notag \\}\)
\(\newcommand {\cline }[1]{}\)
\(\newcommand {\directlua }[1]{\text {(directlua)}}\)
\(\newcommand {\luatexdirectlua }[1]{\text {(directlua)}}\)
\(\newcommand {\protect }{}\)
\(\def \LWRabsorbnumber #1 {}\)
\(\def \LWRabsorbquotenumber "#1 {}\)
\(\newcommand {\LWRabsorboption }[1][]{}\)
\(\newcommand {\LWRabsorbtwooptions }[1][]{\LWRabsorboption }\)
\(\def \mathchar {\ifnextchar "\LWRabsorbquotenumber \LWRabsorbnumber }\)
\(\def \mathcode #1={\mathchar }\)
\(\let \delcode \mathcode \)
\(\let \delimiter \mathchar \)
\(\def \oe {\unicode {x0153}}\)
\(\def \OE {\unicode {x0152}}\)
\(\def \ae {\unicode {x00E6}}\)
\(\def \AE {\unicode {x00C6}}\)
\(\def \aa {\unicode {x00E5}}\)
\(\def \AA {\unicode {x00C5}}\)
\(\def \o {\unicode {x00F8}}\)
\(\def \O {\unicode {x00D8}}\)
\(\def \l {\unicode {x0142}}\)
\(\def \L {\unicode {x0141}}\)
\(\def \ss {\unicode {x00DF}}\)
\(\def \SS {\unicode {x1E9E}}\)
\(\def \dag {\unicode {x2020}}\)
\(\def \ddag {\unicode {x2021}}\)
\(\def \P {\unicode {x00B6}}\)
\(\def \copyright {\unicode {x00A9}}\)
\(\def \pounds {\unicode {x00A3}}\)
\(\let \LWRref \ref \)
\(\renewcommand {\ref }{\ifstar \LWRref \LWRref }\)
\( \newcommand {\multicolumn }[3]{#3}\)
\(\require {textcomp}\)
\(\require {upgreek}\)
\(\newcommand {\intertext }[1]{\text {#1}\notag \\}\)
\(\let \Hat \hat \)
\(\let \Check \check \)
\(\let \Tilde \tilde \)
\(\let \Acute \acute \)
\(\let \Grave \grave \)
\(\let \Dot \dot \)
\(\let \Ddot \ddot \)
\(\let \Breve \breve \)
\(\let \Bar \bar \)
\(\let \Vec \vec \)
\(\require {cancel}\)
\(\newcommand {\LWRsubmultirow }[2][]{#2}\)
\(\newcommand {\LWRmultirow }[2][]{\LWRsubmultirow }\)
\(\newcommand {\multirow }[2][]{\LWRmultirow }\)
\(\newcommand {\mrowcell }{}\)
\(\newcommand {\mcolrowcell }{}\)
\(\newcommand {\STneed }[1]{}\)
\(\def \ud {\mathrm {d}}\)
\(\def \ui {\mathrm {i}}\)
\(\def \uj {\mathrm {j}}\)
\(\def \uh {\mathrm {h}}\)
\(\newcommand {\R }{\mathbb {R}}\)
\(\newcommand {\N }{\mathbb {N}}\)
\(\newcommand {\C }{\mathbb {C}}\)
\(\newcommand {\Z }{\mathbb {Z}}\)
\(\newcommand {\CP }{\mathbb {C}P}\)
\(\newcommand {\RP }{\mathbb {R}P}\)
\(\def \bk {\vec {k}}\)
\(\def \bm {\vec {m}}\)
\(\def \bn {\vec {n}}\)
\(\def \be {\vec {e}}\)
\(\def \bE {\vec {E}}\)
\(\def \bx {\vec {x}}\)
\(\def \uL {\mathrm {L}}\)
\(\def \uU {\mathrm {U}}\)
\(\def \uW {\mathrm {W}}\)
\(\def \uE {\mathrm {E}}\)
\(\def \uT {\mathrm {T}}\)
\(\def \uV {\mathrm {V}}\)
\(\def \uM {\mathrm {M}}\)
\(\def \uH {\mathrm {H}}\)
\(\DeclareMathOperator {\sech }{sech}\)
\(\DeclareMathOperator {\csch }{csch}\)
\(\DeclareMathOperator {\arcsec }{arcsec}\)
\(\DeclareMathOperator {\arccot }{arcCot}\)
\(\DeclareMathOperator {\arccsc }{arcCsc}\)
\(\DeclareMathOperator {\arccosh }{arcCosh}\)
\(\DeclareMathOperator {\arcsinh }{arcsinh}\)
\(\DeclareMathOperator {\arctanh }{arctanh}\)
\(\DeclareMathOperator {\arcsech }{arcsech}\)
\(\DeclareMathOperator {\arccsch }{arcCsch}\)
\(\DeclareMathOperator {\arccoth }{arcCoth}\)
\(\def \re {\textup {Re}}\)
\(\def \im {\textup {Im}}\)
\(\newcommand {\up }{\uppi }\)
\(\newcommand {\ut }{\uptheta }\)
\(\newcommand {\uw }{\upomega }\)
\(\newcommand {\uph }{\upphi }\)
\(\newcommand {\uvph }{\upvarphi }\)
Chapter 5 Differential Equations
This is a non-examinable section and is not taught every year. It is included in the indicative content of the module but is not assessed by the learning outcomes. That means that this chapter can all be considered one big mathematical deviation.
At this stage in the module we have discussed both algebraic equations like \(x^{3}+4x^{2}-2x+11=0\) and how to differentiate a function. It is natural to now ask about equations which involve a derivative. These are known as differential equations.