# Differential Equations

• College Of Computing & Information Technology |

#### Description

This course provides the basic definition of Laplace transform and their theorems First shift theorem, transform of differentiation and integration, unit step function, second shift theorem and convolution theorem. Inverse of Laplace transform. Fourier analysis Definition of Fourier series, Fourier series of functions of period 2P, Fourier series for even and odd functions, half-Range expansions and Fourier series for harmonic functions. 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

Software Engineering bachelor`s degree Program

#### Objectives

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

#### Textbook

Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons Inc.

#### Course Content

content serial Description
1First order D.E. (i) Separation of variables.
2First order D.E. (ii) Homogeneous equation
3First order D.E. (iii) Exact equation.
4First order D.E. (iv) Linear equations , (v) Bernoullis equation - Revision on First order D.E. Second order D.E. with constant coeff. ( Homogeneous equations)
5Method of undermined coefficients. Second order D.E. with constant coeff. (Non-homogeneous equations). Method of variation of parameters.
6Laplace transform.
7Laplace transform Basic definition - First shifting theorem.
8Laplace transform Transform differentiation- Transform integration.
9Unit step function- Second shifting theorem.
10Inverse Laplace transforms.
11Inverse Laplace transforms.
12Solution of D.E. and integral equations using Laplace transform
13Application Solve R-L circuit using Laplace transform.
14Linear programming and simplex method.
15General Revision
1First order D.E. (i) Separation of variables.
2First order D.E. (ii) Homogeneous equation
3First order D.E. (iii) Exact equation.
4First order D.E. (iv) Linear equations , (v) Bernoullis equation - Revision on First order D.E. Second order D.E. with constant coeff. ( Homogeneous equations)
5Method of undermined coefficients. Second order D.E. with constant coeff. (Non-homogeneous equations). Method of variation of parameters.
6Laplace transform.
7Laplace transform Basic definition - First shifting theorem.
8Laplace transform Transform differentiation- Transform integration.
9Unit step function- Second shifting theorem.
10Inverse Laplace transforms.
11Inverse Laplace transforms.
12Solution of D.E. and integral equations using Laplace transform
13Application Solve R-L circuit using Laplace transform.
14Linear programming and simplex method.
15General Revision

#### Markets and Career

• Generation, transmission, distribution and utilization of electrical power for public and private sectors to secure both continuous and emergency demands.
• Electrical power feeding for civil and military marine and aviation utilities.
• Electrical works in construction engineering.

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