MATH 141 Chapter Notes -Winding Number, Unit Circle, Complex Differential Form
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These notes are a terse summary of what we"ll need from multivariable calculus. If, after reading these, some parts are still unclear, you should consult your notes or book from your multivariable calculus or ask about it at o ce hours. We"ve also posted a more detailed review of line integrals and green"s theorem. We"ve seen that complex exponentials make trigonometric functions easier to work with and give insight into many of the properties of trig functions. Similarly, we"ll eventually reformulate some material from 18. 02 in complex form. We"ll see that it"s easier to present and the main properties are more transparent in complex form. We"ll denote vectors in the plane by (, ) In physics and in 18. 02 we usually write vectors in the plane as + . This use of and would be confusing in 18. 04, so we will write this vector as (, ).
