CM111A – Calculus I Compact Lecture Notes

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CM111A Calculus ICompact Lecture NotesACC CoolenDepartment of Mathematics, King s College LondonVersion of Sept 201121 A bit of history .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Birth of modern science and of calculusStage I, 1500 1630: from speculation to science ... . . . . . . . . . . . .. Birth of modern science and of calculusStage II, 1630 1680: science is written in the language of mathematics! . Birth of modern science and of calculusStage III, around 1680: how to speak the language of mathematics! . . . Style of the course. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Revision of some elementary mathematics. . . . . . . . . . . . . . . . . . . . . Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Powers of real numbers.

•Calculus: the related areas of differentiation, integration, sequences and series, that are united in their reliance on the idea of limits. •Additional topics: complex numbers and trigonometric functions. This simplifies the discussion of the ‘classical’ functions of …

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