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CM111A – Calculus I Compact Lecture Notes

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 .. Solving quadratic equations .. Functions, inverse functions, and graphs .. Exponential function, logarithm, laws for logarithms .. Trigonometric functions .. 202 Proof by induction223 Complex Introduction and definition.. Elementary properties of complex 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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