Defining Exponential and Trigonometric Functions Using Differential Equations

  title={Defining Exponential and Trigonometric Functions Using Differential Equations},
  author={Harvey Diamond},
  journal={Mathematics Magazine},
  pages={37 - 42}
  • H. Diamond
  • Published 1 February 2014
  • Mathematics, Philosophy
  • Mathematics Magazine
Summary This note addresses the question of how to rigorously define the functions exp(x), sin(x), and cos(x), and develop their properties directly from that definition. We take a differential equations approach, defining each function as the solution of an initial value problem. Assuming only the basic existence/uniqueness theorem for solutions of linear differential equations, we derive the standard properties and identities associated with these functions. Our target audience is… 

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Calculus and Analytic Geometry

A leaner, crisper, more accessible edition (according to the preface), for the widening range of students who need knowledge of the basic concepts. No bibliography. Annotation copyright Book News,

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