Defining Exponential and Trigonometric Functions Using Differential Equations

@article{Diamond2014DefiningEA,
  title={Defining Exponential and Trigonometric Functions Using Differential Equations},
  author={H. Diamond},
  journal={Mathematics Magazine},
  year={2014},
  volume={87},
  pages={37 - 42}
}
  • H. Diamond
  • Published 2014
  • Mathematics
  • 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… Expand
Defining trigonometric functions via complex sequences
In the literature we find several different ways of introducing elementary functions. For the exponential function, we mention the following ways of characterising the exponential function: (a) (b) ,Expand

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