This book presents a general introduction to *Mathematical Analysis and Analytical ***Modeling** that may be used as the first contact of undergraduate students with Calculus. Primarily conceived as a textbook for wind energy undergraduate students at Texas Tech University, it might be used for those science and engineering students who enjoy knowing details on the foundations of their mathematical skills. The text carefully examines the ideas behind the notion of limit, in particular sequential limit, which is at the basis of concepts like continuity, differentiation and integration; it also explores how those aforementioned concepts are applied to contextual problems and extended to analytical modeling, without affecting mathematical rigor. The book reaches a balance between logical consistency, intuition and practical applications, and may be utilized to create a bridge between the classical ways of learning Mathematics and the new way using computers to facilitate knowledge acquisition.

Chapter Zero: Elementary Set Theory

Chapter One: Sets of Numbers

Chapter Two: Sequences of Real Numbers

Chapter Three: Limit and Continuity

Chapter Four: Differentiation

Chapter Five: Integration

Chapter Six: A Short Introduction to Analytical Modeling

Chapter Seven: Series

Chapter Eight: Money Dynamics

Chapter Nine: Mathematics, Logic and Reality