This first year introductory university text book provides a basic foundation in applied mathematics. The topics covered include algebra; linear, quadratic, trigonometric and logarithmic functions; vectors and matrices and various calculus techniques ( differentiation, integration and separable differential equations). The application of these topics to real world phenomena is integral to this course. The content is carefully explained in this text with examples and solutions that help provide an easy entry into the mathematical world and the space of mathematicians. Mathematics is now applied in many fields of study and has become an essential problem solving tool for the sciences more generally. Aspects of mathematics now appear in most university and TAFE courses, and in fact, mathematics and quantitative skills are highly valued in the workplace, particularly the mathematizing of phenomena and "real life" problem solving. Therefore, at the very least it is important for all students nowadays to master the basics of the applied mathematics content and skills taught in this text. The content, skills and procedures in this course are considered essential. Once mastered, the knowledge can be applied to solving real life problems posed in the various sciences. Some basic mathematical content and skills can be applied across disciplines such as in the development of an understanding of (i) numbers and systems; (ii) unknowns and variables to explore relationships; and (iii) the development of related formulas and equations. In this text students will be taught (i) how to solve various types of equations (ii) how to develop and represent relationships between quantities that change over space or time and (iii) how to represent such relationships in mathematical terns. For example, students will learn how to calculate the total number of trees that have been cut over time, or how much pollution of a particular type exists in rivers and lakes at a particular time and rate of change over time, etc. There are now lots of large data sets in the various fields of the sciences, and the mathematical tools taught in this text could help deal with large data sets of information. The knowledge, procedures and skills taught in this course will allow students to identify patterns, and to understand and explain relationships involved in data sets. For example, students will be able to use their knowledge to develop models that can be used to predict maxima and minima, and more importantly, when they may occur. Finally, models of rate of change of real life functions will be developed, and the knowledge of integration and differentiation will be used to solve the separable differential models.