Engineering Analysis (2)

Engineering Analysis

MEMT2001 Engineering Analysis (1)

4 hours One requisite

1 Chapter (1): Linear Algebra / Linear Equations, Quadratic Equations, Matrices (Algebra of matrices; types of matrices, linear system of algebraic equations, consistency of linear systems, the rank of a matrix, Gauss elimination, the inverse of a matrix, Gauss Jordon- Gauss Jacobi and Gauss-Seidel methods, Determinants and their properties, Cramer’s rule). Engineering applications such as: / Civil Engineering Applications (Calculation of the reactions and forces of some concrete structures and trusses, Determination of Beam Reactions, elastic stresses and strain, and forces factorization Using Matrix analysis, Calculation of Slope Measurement of Edge of Pavement of a Parking Area). / Electrical Engineering Applications (Calculation of the current in electrical circuits, The two-loop circuit) / Mechanical Engineering Applications (Free vibration of a two-mass system)

2 Chapter (2): Vectors Analysis / Definition of vectors, vectors multiplications, Scalar Product – the angle between two vectors, properties of scalar product, and applications of the dot product. Vector product, right-handed and left-handed systems, properties of vector product, applications of the cross product. Product of three vectors – Scalar triple product, properties of the scalar triple product, vector triple product, vector product of four vectors, scalar product of four vectors, gradient vectors and directional derivatives, divergence, curl, Laplace operators, Vector integral theorems: Greens, Stokes, and Gauss divergence theorems. Engineering applications such as: / Mechanical Engineering applications (work done, Stress, strain and tensors, momentum, circulation, tangent vector to a surface, potential function, area-surface, conservative fields, Maxwell equations) / Civil Engineering Applications (Angle between two vectors; Static forces, frameworks; Applications in geotechnical and structural analysis) / Electrical Engineering Applications (Estimation of Electric Filed, Electric Flux, Calculate the magnitude and direction of impedances, voltages, currents)

3 Chapter (3): Fourier Series / Piecewise Continuous Functions, Inner Products and Orthonormal Sets, Periodic Functions, Even and Odd Functions, Fourier Series, Half-Range Expansion, Generalized Fourier Series, Fourier Cosine Series, Fourier Sine Series, Fourier Series, Fourier Series On Other Intervals, Engineering applications such as: / The Motion of a Damped Harmonic Oscillator, Driven Mass on a Spring, / Circuit Analysis Signal Analysis, Resistor, Inductor, / String Vibrated at Some Frequency, The Natural Frequencies, / Vibrations in Building, Estimating the Strength of Buildings

4 Chapter (2): Special Functions / Gamma Function, Beta function, Properties – Relation Between Beta and Gamma Functions- Evaluation of Improper Integrals, Legendre Functions, Bessel Functions, Hermite Functions, Laguerre Functions, Hypergeometric Functions, Engineering Applications (Integration due to several engineering problems)

5 Chapter (5): Partial Differential Equations; PDEs / Important of linear PDEs, Typical boundary and initial conditions, Classification of second-order PDEs (elliptic, parabolic, hyperbolic), Wave equation (Derivation of one-dimensional wave equation - Understanding of the role of constants, parameters used in derivation - Familiarity with working with prescribed boundary conditions and initial conditions - Solution using separation of variables), Heat equation (Use of separation of variables/Fourier series for the Heat equation in one-dimensional problem - Understanding of the role of constants, parameters used in derivation - Familiarity with working with prescribed boundary conditions and initial conditions), Steady-state two dimensional heat flow (Laplace Equation), Expression of PDEs in cartesian, spherical, cylindrical, polar coordinates, Use of separation of variables in different coordinate systems. Engineering Applications (Heat Transfer, Sound Waves Transfer, Deflections of Beams and Plats)

1.1 Mapped to: KLO1, KLO4

Outline the important basic definitions and the tools of engineering mathematics and its concepts and learn how to apply them in actual engineering problems.