The book covers calculus in both commutative division algebras like the complex numbers and non-commutative division algebras like the quaternions. The gauge covariant derivative used in gauge theory is also covered as is the 4-dimensional space-time covariant derivative used in general relativity. The complicated Cauchy-Riemann calculus used for 200 years within the complex numbers is replaced with a simpler and much more general calculus which applies in every division algebra. This is quite revolutionary. This book is aimed at undergraduates and graduates, but it will be easily understood...