Preface

The Taylor series about x = 𝑎 to order N may be computed using the Maple command taylor(f,x=a,N+1). For functions that possess a taylor's series the command series(f,x=a,N+1) produces the same result. For example,


taylor(sin(exp(x)), x = 0, 5)
\[ \sin (1) + \cos (1)\,x + \left( - \frac{\sin (1)}{2} + \frac{\cos (1)}{2} \right) x^2 - \frac{1}{2}\,\sin (1)\, x^2 + \left( - \frac{\sin (1)}{4} - \frac{5\,\cos (1)}{24} \right) x^4 + ) \left( x^5 \right) \]

series(sin(exp(x)), x = 0, 5)
(a*b)/c+13*d \[ {\frac {ab}{c}}+13\,d \]
Two n-by-n matrices A and B are called similar if there exists an invertible n-by-n matrix S such that