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# Course List   ## Transformation and Numerical Analysis (Math 4)

• Course Code :
MTH 212
• Level :
• Course Hours :
3.00 Hours
• Department :
Department of Mechanical Engineering

## Area of Study :

 Demonstrate a conscious understanding of the concepts of integral transforms, Laplace and Fourier transforms.  Develop students’ mathematical skills for the methods of solution of initial and boundary values problems by using Laplace and Fourier Transforms, Fourier series, and Fourier integrals.  Acquire skills for the application of Numerical methods to the solution of Mechanical engineering problems.

## Transformation and Numerical Analysis (Math 4)

Laplace Transforms. Definitions. Properties and theorems. Inverse Laplace transforms. Calculating of Laplace transforms, Periodic functions, unit-step functions, and Dirac delta functions. Calculating of Inverse Laplace Transforms. Solution of Initial value problems and integral equations by Laplace transforms. Fourier series. Periodic and non-periodic Functions. Series of odd and even functions. Convergence Theorem.. Definitions and properties of Fourier integrals and transforms. Finite Fourier transforms and Applications. Numerical solution of nonlinear equations, Newton's method. Secant method. Numerical solution of Initial Value problems. Euler, Modified Euler, and Runge Kutta methods. Least Squares methods. Interpolation. 1- .

## a. Knowledge and Understanding:

 1- Recognize the fundamental concepts of Laplace transforms, Inverse Laplace Transforms, and Laplace transform for derivatives. 2- Define Shifted Laplace transform, unit – step functions, unit impulses, Dirac delta-function, Fourier series, Fourier integrals, and Fourier Transforms. 3- Explain Laplace transforms, Fourier series, Fourier integrals, and Fourier transforms, with convergence for the solution of initial values problems. 4- State the difference between approximate solutions, interpolate solution, numerical solutions, and exact solutions. 5- Outlines, Euler methods, and Rung -Kutta methods for the numerical solutions of Initial value problems, and Least squares method, and interpolation by Lagrange polynomials for tabulated and explicit functions.

## b. Intellectual Skills:

 1- Recognizing methods of calculating Laplace transforms of algebraic and transcendental functions, Periodic functions, derivatives, unit-step functions, unit impulses, and Dirac delta functions. 2- Use Laplace Transforms, Inverse Laplace Transforms, Fourier series, Fourier Integrals, and Fourier Transforms for the solution of initial values problems. 3- Use Fourier series, Fourier integrals, an Fourier Transform to Approximate functions. 4- Apply Laplace and Inverse Laplace transform, Fourier Transforms, and Rung -Kutta, Euler, and modified Euler, for the solution of initial value problems related to mechanical Engineering 5- Approximate and interpolate functions by using Least squares methods, and interpolation by Lagrange polynomials at the intellectual level required of this course.

## Course topics and contents:

Topic No. of hours Lecture Tutorial/Practical
Laplace Transforms. Definition. Properties and theorems. Inverse Laplace transforms. 10 6 4
Calculating of Laplace transforms of algebraic and transcendental functions, Periodic functions, derivatives, unit-step functions, unit impulses, and Dirac delta functions. 10 6 4
Calculating of Inverse Laplace Transforms. Solution of Initial value problems 10 6 4
Integral equations by Laplace transform, Fourier series. Periodic and non-periodic Functions. 10 6 4
Series of odd and even functions. Half intervals Fourrier Series Convergence Theorem. 10 6 4
Fourier Integrals and Fourier Transforms. Definitions and properties of Fourier integrals and transforms. Finite Fourier transforms. Applications 10 6 4
Numerical solution of Initial Value problems. Euler, Modified Euler, and Runge Kutta methods. Applications. 10 6 4
Least Squares methods. Interpolation. 5 3 2

## Teaching And Learning Methodologies:

Teaching and learning methods
Interactive Lecturing
Problem solving
Discussion

## Course Assessment :

Methods of assessment Relative weight % Week No. Assess What
Assignments 5.00 To assess overall understandings, concepts, Knowledge, Problem solving, and mathematical skills delivered by the course,
Final Exam 40.00 16
First Mid Exam 20.00 6 To assess the levels of math skills needed for successful completion of the course, and to improve teaching and learning for all students.
Performance 10.00
Quiz Exam 5.00
Second Mid Exam 20.00 11 To assess comprehension, Knowledge, Problem solving, and mathematical skills delivered by the course after 11 weeks of studying.

## Books:

Book Author Publisher
Advanced Engineering Mathematics Warren S. Wright, Dennis G. Zill Jones & Bartlett Learning

Handouts

## Recommended books :

Erwin Kreyszig. "Advanced Engineering Mathematics", 10 editions, John Wiley& Sons, INC, 2010. Earl W. Swokowski, "Calculus with Analytic geometry, Prindle, Weber & Schmidt Peter V. O'Neil, "Advanced Engineering Mathematics", Thomson.

## Web Sites :

o www.wolframalpha.com o www.sosmath.com, www.math.hmc.edu, o www.tutorial.math.lamar.edu, o www.web.mit.edu