Course Outline in PDF

Phone: +98-25-3210-3599

Fax: +98-21-000000

E-mail: moayyedi@alum.sharif.edu

            mk.moayyedi@qom.ac.ir

 

 

 

 

 

 

 

 

 

 

HW No.1

HW No.2

HW No.3

HW No.4

HW No.5

math.sharif.edu

www.Math.org

www.Math.org
Text Box: Useful Links

Homeworks

· Wylie, C. R., “Advanced Engineering Mathematics”, McGraw Hill, 1996

· Hildebrand, F.B., “Introduction to Numerical Analysis”, Dover Publication Inc.

· Kreyszig E., “Advanced Engineering Mathematics”, 10th Edition, John Wiley & Sons, Inc.

· Fong C. M., Kee, D. D., and Kaloni, P N, “Advanced Mathematics for Engineering and Science”, World Scientific Publishing Co. Ltd.

· Jackson, D, “Fourier Series and Orthogonal Polynomials”, Publication of The Mathematical Association of America.

· Riley, K.F., Hobson, M.P., and Bence, S. J., “Mathematical Methods for Physics and Engineering”, Cambridge University Press.

· Greenberg, M. D., “Advanced Engineering Mathematics”, Prentice-Hall, Inc.

· Jeffrey, A, “Advanced Engineering Mathematics”, Harcourt/Academic Press.

· HashemiNejad, M., Razani, M, “Applied Engineering Mathematics”, Ketab Daneshghahi Press.

· Shahani, A. R., “Advanced Engineering Mathematics”, KNTU Press.

 

References

Assignments: 25%

Final Examination: 65%

Individual Project or Studying: 10%

Grading Policy

Course Outline

1.  Linear Algebra, Tensors and Matrices

· Matrices and Basic Matrix Algebra

· The Determinant and Inverse of a Matrix

· Eigenvalues and Eigenvectors

· Diagonalisation of Matrices

· Symmetric, Skew-Symmetric, and Orthogonal Matrices

· System of ODEs

· Inner-product and Vector Product Spaces

· Orthogonality, Gram-Schmidt Orthogonalisation Process

· Hermitian and Normal Matrices

· Positive Definite and Negative Definite Matrices

· Tensors

2.  Advanced Theory in Complex Variables

· Complex Function

· Cauchy Riemann Equation

· Analytic and Harmonic Functions

· Line integral in the Complex plane

· Cauchy’s Integral Theorem

· Zeros and Singularities of Analytic Functions

· Laurent Series

· Residuals and Residue Theorem

· Mapping and Conformal Mapping

3.  Fourier Analysis and Partial Differential Equations

· Introduction to Fourier Series

· Convergence of Fourier Series and Their Integration and Differentiation

· Fourier Sine and Cosine Series

· Classification of PDEs (Elliptic, Hyperbolic and Parabolic PDEs)

· Perturbation Theory Applied to PDEs Solution

4.  Integral Transform

· Fourier Transform

· Laplace and Melin Transform and Application in Solution of PDEs

· Integral Equations

· Green’s Function for Sturm-Liouville Problems

· Green’s Function For Poisson’s Equation

· Wave Equation on Infinite Domains

· Heat Equation on Infinite Domains

· Green’s Function for the Wave Equation on a Cube

5.  Calculus of Variations

· Extremum of a Several Variables Function

· Extremum of a Function with Constraint

· The Euler-Lagrange Equation

· Constrained Variation

· Rayleigh-Ritz Method

Text Box: © Mohammad Kazem Moayyedi, Department of Mechanical Engineering, University of Qom, 2017

Advanced Engineering Mathematics

ME2003

Mohammad Kazem Moayyedi (PhD)

Department of Mechanical Engineering

University of Qom