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

Information Systems Program

Objectives

1. Use the Laplace transform and the theorems (first shift theorem, transform of differentiation and integration theorems, etcâ€¦.) 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

Textbook

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

Course Content

content serial	Description
1	First order ordinary differential equations:
2	Separable equations – Initial value problems- Homogeneous equations
3	Linear equations and Bernoulli’s equation
4	Exact equations.
5	Second order ordinary differential equations with constant coefficients: Fundamental set of solutions - Linear independence of solutions: Wronskian- General solution of homogeneous equations
6	Second order ordinary differential equations with constant coefficients: Non-homogeneous equations (Method of undetermined coefficients)
7	Second order ordinary differential equations with constant coefficients: The method of variation of parameters + 7th Week Examination
8	Laplace transforms: Basic definition- First shifting theorem (s-shifting)
9	Laplace transform : Derivatives of Transforms - Transform integration
10	: Laplace transforms: Unit Step Function - Second Shifting Theorem (t-shifting)
11	Inverse Laplace transforms
12	Applications: Solution of ODEs using Laplace transforms Solution of R-L circuit using the + 12th Week Examination
13	Fourier series: Fourier series for functions of period 2P
14	Fourier series: Fourier series for even and odd functions
15	Linear programming and simplex method
16	Final Examination
1	First order ordinary differential equations:
2	Separable equations – Initial value problems- Homogeneous equations
3	Linear equations and Bernoulli’s equation
4	Exact equations.
5	Second order ordinary differential equations with constant coefficients: Fundamental set of solutions - Linear independence of solutions: Wronskian- General solution of homogeneous equations
6	Second order ordinary differential equations with constant coefficients: Non-homogeneous equations (Method of undetermined coefficients)
7	Second order ordinary differential equations with constant coefficients: The method of variation of parameters + 7th Week Examination
8	Laplace transforms: Basic definition- First shifting theorem (s-shifting)
9	Laplace transform : Derivatives of Transforms - Transform integration
10	: Laplace transforms: Unit Step Function - Second Shifting Theorem (t-shifting)
11	Inverse Laplace transforms
12	Applications: Solution of ODEs using Laplace transforms Solution of R-L circuit using the + 12th Week Examination
13	Fourier series: Fourier series for functions of period 2P
14	Fourier series: Fourier series for even and odd functions
15	Linear programming and simplex method
16	Final Examination
1	First order ordinary differential equations:
2	Separable equations – Initial value problems- Homogeneous equations
3	Linear equations and Bernoulli’s equation
4	Exact equations.
5	Second order ordinary differential equations with constant coefficients: Fundamental set of solutions - Linear independence of solutions: Wronskian- General solution of homogeneous equations
6	Second order ordinary differential equations with constant coefficients: Non-homogeneous equations (Method of undetermined coefficients)
7	Second order ordinary differential equations with constant coefficients: The method of variation of parameters + 7th Week Examination
8	Laplace transforms: Basic definition- First shifting theorem (s-shifting)
9	Laplace transform : Derivatives of Transforms - Transform integration
10	: Laplace transforms: Unit Step Function - Second Shifting Theorem (t-shifting)
11	Inverse Laplace transforms
12	Applications: Solution of ODEs using Laplace transforms Solution of R-L circuit using the + 12th Week Examination
13	Fourier series: Fourier series for functions of period 2P
14	Fourier series: Fourier series for even and odd functions
15	Linear programming and simplex method
16	Final Examination
1	First order ordinary differential equations:
2	Separable equations – Initial value problems- Homogeneous equations
3	Linear equations and Bernoulli’s equation
4	Exact equations.
5	Second order ordinary differential equations with constant coefficients: Fundamental set of solutions - Linear independence of solutions: Wronskian- General solution of homogeneous equations
6	Second order ordinary differential equations with constant coefficients: Non-homogeneous equations (Method of undetermined coefficients)
7	Second order ordinary differential equations with constant coefficients: The method of variation of parameters + 7th Week Examination
8	Laplace transforms: Basic definition- First shifting theorem (s-shifting)
9	Laplace transform : Derivatives of Transforms - Transform integration
10	: Laplace transforms: Unit Step Function - Second Shifting Theorem (t-shifting)
11	Inverse Laplace transforms
12	Applications: Solution of ODEs using Laplace transforms Solution of R-L circuit using the + 12th Week Examination
13	Fourier series: Fourier series for functions of period 2P
14	Fourier series: Fourier series for even and odd functions
15	Linear programming and simplex method
16	Final Examination

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.

Degree Bachelor
Code: BA201
Credit hrs: 3
Prequisites: BA102

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Calculus III