MAT1001 Differential Calculus: Lecture Notes

\(\newcommand{\footnotename}{footnote}\) \(\def \LWRfootnote {1}\) \(\newcommand {\footnote }[2][\LWRfootnote ]{{}^{\mathrm {#1}}}\) \(\newcommand {\footnotemark }[1][\LWRfootnote ]{{}^{\mathrm {#1}}}\) \(\let \LWRorighspace \hspace \) \(\renewcommand {\hspace }{\ifstar \LWRorighspace \LWRorighspace }\) \(\newcommand {\TextOrMath }[2]{#2}\) \(\newcommand {\mathnormal }[1]{{#1}}\) \(\newcommand \ensuremath [1]{#1}\) \(\newcommand {\LWRframebox }[2][]{\fbox {#2}} \newcommand {\framebox }[1][]{\LWRframebox } \) \(\newcommand {\setlength }[2]{}\) \(\newcommand {\addtolength }[2]{}\) \(\newcommand {\setcounter }[2]{}\) \(\newcommand {\addtocounter }[2]{}\) \(\newcommand {\arabic }[1]{}\) \(\newcommand {\number }[1]{}\) \(\newcommand {\noalign }[1]{\text {#1}\notag \\}\) \(\newcommand {\cline }[1]{}\) \(\newcommand {\directlua }[1]{\text {(directlua)}}\) \(\newcommand {\luatexdirectlua }[1]{\text {(directlua)}}\) \(\newcommand {\protect }{}\) \(\def \LWRabsorbnumber #1 {}\) \(\def \LWRabsorbquotenumber "#1 {}\) \(\newcommand {\LWRabsorboption }[1][]{}\) \(\newcommand {\LWRabsorbtwooptions }[1][]{\LWRabsorboption }\) \(\def \mathchar {\ifnextchar "\LWRabsorbquotenumber \LWRabsorbnumber }\) \(\def \mathcode #1={\mathchar }\) \(\let \delcode \mathcode \) \(\let \delimiter \mathchar \) \(\def \oe {\unicode {x0153}}\) \(\def \OE {\unicode {x0152}}\) \(\def \ae {\unicode {x00E6}}\) \(\def \AE {\unicode {x00C6}}\) \(\def \aa {\unicode {x00E5}}\) \(\def \AA {\unicode {x00C5}}\) \(\def \o {\unicode {x00F8}}\) \(\def \O {\unicode {x00D8}}\) \(\def \l {\unicode {x0142}}\) \(\def \L {\unicode {x0141}}\) \(\def \ss {\unicode {x00DF}}\) \(\def \SS {\unicode {x1E9E}}\) \(\def \dag {\unicode {x2020}}\) \(\def \ddag {\unicode {x2021}}\) \(\def \P {\unicode {x00B6}}\) \(\def \copyright {\unicode {x00A9}}\) \(\def \pounds {\unicode {x00A3}}\) \(\let \LWRref \ref \) \(\renewcommand {\ref }{\ifstar \LWRref \LWRref }\) \( \newcommand {\multicolumn }[3]{#3}\) \(\require {textcomp}\) \(\require {upgreek}\) \(\newcommand {\intertext }[1]{\text {#1}\notag \\}\) \(\let \Hat \hat \) \(\let \Check \check \) \(\let \Tilde \tilde \) \(\let \Acute \acute \) \(\let \Grave \grave \) \(\let \Dot \dot \) \(\let \Ddot \ddot \) \(\let \Breve \breve \) \(\let \Bar \bar \) \(\let \Vec \vec \) \(\require {cancel}\) \(\newcommand {\LWRsubmultirow }[2][]{#2}\) \(\newcommand {\LWRmultirow }[2][]{\LWRsubmultirow }\) \(\newcommand {\multirow }[2][]{\LWRmultirow }\) \(\newcommand {\mrowcell }{}\) \(\newcommand {\mcolrowcell }{}\) \(\newcommand {\STneed }[1]{}\) \(\def \ud {\mathrm {d}}\) \(\def \ui {\mathrm {i}}\) \(\def \uj {\mathrm {j}}\) \(\def \uh {\mathrm {h}}\) \(\newcommand {\R }{\mathbb {R}}\) \(\newcommand {\N }{\mathbb {N}}\) \(\newcommand {\C }{\mathbb {C}}\) \(\newcommand {\Z }{\mathbb {Z}}\) \(\newcommand {\CP }{\mathbb {C}P}\) \(\newcommand {\RP }{\mathbb {R}P}\) \(\def \bk {\vec {k}}\) \(\def \bm {\vec {m}}\) \(\def \bn {\vec {n}}\) \(\def \be {\vec {e}}\) \(\def \bE {\vec {E}}\) \(\def \bx {\vec {x}}\) \(\def \uL {\mathrm {L}}\) \(\def \uU {\mathrm {U}}\) \(\def \uW {\mathrm {W}}\) \(\def \uE {\mathrm {E}}\) \(\def \uT {\mathrm {T}}\) \(\def \uV {\mathrm {V}}\) \(\def \uM {\mathrm {M}}\) \(\def \uH {\mathrm {H}}\) \(\DeclareMathOperator {\sech }{sech}\) \(\DeclareMathOperator {\csch }{csch}\) \(\DeclareMathOperator {\arcsec }{arcsec}\) \(\DeclareMathOperator {\arccot }{arcCot}\) \(\DeclareMathOperator {\arccsc }{arcCsc}\) \(\DeclareMathOperator {\arccosh }{arcCosh}\) \(\DeclareMathOperator {\arcsinh }{arcsinh}\) \(\DeclareMathOperator {\arctanh }{arctanh}\) \(\DeclareMathOperator {\arcsech }{arcsech}\) \(\DeclareMathOperator {\arccsch }{arcCsch}\) \(\DeclareMathOperator {\arccoth }{arcCoth}\) \(\def \re {\textup {Re}}\) \(\def \im {\textup {Im}}\) \(\newcommand {\up }{\uppi }\) \(\newcommand {\ut }{\uptheta }\) \(\newcommand {\uw }{\upomega }\) \(\newcommand {\uph }{\upphi }\) \(\newcommand {\uvph }{\upvarphi }\) \(\polylongdiv \)