Calculus III

Description

This course provides the basic definition of Laplace transform and their theorems: First shift theorem, transform of differentiation and integration, unit step , second shift theorem and convolution theorem. Inverse of Laplace transform. Fourier analysis: Definition of Fourier series, Fourier series of s of period 2P, Fourier series for even and odd s, half-Range expansions and Fourier series for harmonic s. Then the student should also study Fourier integrals, Fourier cosine and sine transforms and Fourier transform. Also this course provides an introduction to linear programming, including its basic concepts, unconstrained optimization, and solving system of linear inequalities using the simplex method. Vector spaces are studied in an abstract setting, examining the concepts of linear independence, span, bases, subspaces, and dimension. There follows a discussion of the association between linear transformations and matrices

Program

Computer Science Old

Objectives

• 1. Use the Laplace transform and the theorems (first shift theorem, transform of differentiation and integration theorems, etc….) in solving differential and integral equations.
  2. Understand the Fourier analysis which includes the Fourier series and Fourier transform.
  3. Know the concept of linear programming in order to solve system of linear inequalities using the Simplex method.
  4. Learn some useful algorithms for linear systems
  5. Realize the wide applicability of linear programming