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I am also software engineer and wish to study maths as extra subject to gain knowledge (not for research for now). Can anyone suggest me any online and distance learning course available in maths .

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If you want to kill 2 birds with one stone, Kenneth Iverson's Elementary Functions builds up to the Taylor series approximation of sine by way of the polynomial and simple concepts like slope and area (slyly avoiding the dreaded buzzwords differential and integral and bizarrely, avoiding even the word calculus). The style is always to show you the concept in ...

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Another way you can use Taylor series that I've always liked -- using the definition of a derivative to show that $$\frac{d}{dx} e^x = e^x.$$ The definition is $$\lim \limits_{h \to 0} \frac{e^{x+h} - e^x}{h},$$ Which is equal to $$\lim \limits_{h \to 0} \frac{e^x(e^h - 1)}{h}.$$ If we can show that $\lim \limits_{h \to 0} \frac{e^h - 1}{h} = 1$, we'll ...

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