Introduction to Calculus – volume 2

Volume II is a continuation of volume I and contains chapters six through twelve. The chapter six presents an introduction to vectors, vector operations, differentiation and integration of vectors with many application. The chapter seven investigates curves and surfaces represented in a vector form and examines vector operations associated with these forms. Also investigated are methods for representing arclength, surface area and volume elements from vector representations. The directional derivative is defined along with other vector operations and their properties as these additional vectors enable one to find maximum and minimum values associated with functions of more than one variable. The chapter 8 investigates scalar and vector fields and operations involving these quantities. The Gauss divergence theorem, the Stokes theorem and Green’s theorem in the plane along with applications associated with these theorems are investigated in some detail. The chapter 9 presents applications of vectors from selected areas of science and engineering. The chapter 10 presents an introduction to the matrix calculus and the difference calculus. The chapter 11 presents an introduction to probability and statistics. The chapters 10 and 11 are presented because in todays society technology development is tending toward a digital world and students should be exposed to some of the operational calculus that is going to be needed in order to understand some of this technology. The chapter 12 is added as an after thought to introduce those interested into some more advanced areas of mathematics.

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