Mathematics I

The course is divided into two sections. In the first section we have the basic concepts of the calculus of one variable. The aim is to redefine the concepts of a function and its properties. The idea of the limit and the derivative of a function is introduced along with some of their applications using the basic theorems. Finally, the concepts of the indefinite and definite integrals and their applications are discussed. The second section concerns the introduction to Linear Algebra. Basic matrices and their algebra are given with the help of which the solution of linear systems is made. Vector spaces and subspaces are defined. The base and dimension of a vector space is given. Finally we have the eigenvalues and eigenvectors of a square matrix and the method of diagonalization and its applications.

Objectives

The purpose of this course is to introduce to the student the basic concepts of Calculus I and Linear Algebra and some of their “every day” applications.

Prerequisites

There are no prerequisites.

Syllabus

Sets, real numbers and inequalities. Functions and graphs. The intuitive idea of limit is introduced. Continuous functions and basic theorems. Basic concepts and applications of differentiation are discussed. Basic concepts and applications of integration. Formulas and techniques of integration. Applications of the defined integral. Introduction to linear systems, Gauss-Jordan elimination, Cramer; Linear transformations: linear transformations and their inverses, linear transformations in geometry; Subspaces of Rn and their dimension; Linear spaces, orthogonality, Gram-Schmidt process; Inner product spaces; introduction to determinants; introduction to eigenvalues and eigenvectors; symmetric matrices and diagonalization.