Calculus and Linear Algebra Fundamentals and Applications

This textbook offers a comprehensive coverage of the fundamentals of calculus, linear algebra and analytic geometry. Intended for bachelor’s students in science, engineering, architecture, economics, the presentation is self-contained, and supported by numerous graphs, to facilitate visualization and also to stimulate readers’ intuition. The proofs of the theorems are rigorous, yet presented in straightforward and comprehensive way. With a good balance between algebra, geometry and analysis, this book guides readers to apply the theory to solve differential equations. Many problems and solved exercises are included.

Students are expected to gain a solid background and a versatile attitude towards calculus, algebra and geometry, which can be later used to acquire new skills in more advanced scientific disciplines, such as bioinformatics, process engineering, and finance. At the same time, instructors are provided with extensive information and inspiration for the preparationof their own courses.

Aldo Ventre served as a full professor of Mathematics and Decision Theory at the Second University of Naples and at the University of Trento. Previously, he was a lecturer of Geometry and Mathematics for Economics and Social Sciences at the Universities of Salerno, and an associate professor of Geometry at the University of Naples "Federico II". His research topics included Graph Theory, Pattern Recognition, Fuzzy Sets, and Decision Theory. Author of more than 160 publications (journal and conference articles, book chapters and textbooks), he is also an active member of the editorial board of various scientific journals. In 2012, he was awarded with the Anassilaos Prize in Mathematics.