Engineering Analysis (1)

Engineering Analysis

MTH1182 Calculus for Engineering (2)

4 hours No requisites

1 Chapter (1): Complex Numbers / Real and imaginary parts, modulus and argument, complex conjugate, sum, difference, product, quotient, vector interpretation, the complex plane (Argand plane), graphical representation of complex numbers, polar form, De Moivre’s theorem and its applications, the roots of unity, the fractional roots of any complex number. Engineering applications such as: / Electrical Engineering Applications (Calculations of current, voltage or resistance in AC circuits (AC stands for Alternating Current, which is a current that changes magnitude and direction over time). A common application of complex numbers (more specifically, Euler’s formula) is to compute the potential difference across two AC power supplies concerning time.) / Mechanical Engineering Applications (Modeling of rotations of a rigid body in space, Modelling the Schr?dinger equation, in quantum mechanics mechanical vibration, and electromagnetism.)

2 Chapter (2): First Order Ordinary Differential Equations / Basic concepts and definitions of 1st order differential equations; Formation of differential equations; solution of differential equations: variable separable, homogeneous, equations reducible to homogeneous form, exact differential equation, equations reducible to the exact form, linear differential equation, equations reducible to linear form (Bernoulli’s equation); orthogonal trajectories. Engineering applications such as: / Electrical Engineering Applications (Engineering modelling of RL and RC electric circuits. Engineering modelling of Growth and Decay, Logistic Growth) / Mechanical Engineering Applications (Deformation of a Beam, Newton’s law of cooling, estimating the time of death, velocity, acceleration, Engineering modelling of Bacterial Growth, Engineering modelling of Half-Life of Plutonium and Carbon Dating, Age of a Fossil, Mixture of Two Salt Solutions, Cooling of a Cake) / Civil Engineering Applications (Deformation of a Beam, Moment-curvature relationship, Deflection of a simple beam under uniform load, Deflection of a cantilever beam, Relative deflection of a point with another point)

3 Chapter (3): Second-order Ordinary Differential Equations / Second-order linear homogeneous equations with constant coefficients; differential operators; solution of homogeneous equations; Euler-Cauchy equation; linear dependence and independence; Wronskian; Solution of nonhomogeneous equations: general solution, complementary function, particular integral; solution by variation of parameters; undetermined coefficients; higher order linear homogeneous equations. Engineering applications such as: / Electrical Engineering Applications (Engineering modelling RLC- electric circuits.) / Mechanical Engineering Applications (Modeling of small oscillations of mass-spring, Modeling of Spring/Mass Systems, Temperature of a Fluid, Bending of a Circular Plate.) / Civil Engineering Applications (Deflection of a Beam, Buckling of a thin vertical Column, Bending moments and stresses, Surveying, and slope measurements.)

4 Chapter (4): Laplace Transform / Introduction, linearity, first shift theorem, Second shift theorem, multiplication by t and division by t, inverse LT, Heaviside Expansion theorem, convolution theorem, unit step and Dirac-Delta function, applications on initial value problems. Engineering applications such as: / Electrical Engineering Applications (Integrodifferential equation of Series Circuits, Transform of a Periodic Function, A Periodic Impressed Voltage, Systems of differential equations and its engineering applications ( double circuits analysis, time responses).) / Mechanical Engineering Applications (Systems of differential equations and their engineering applications (mass-spring system, Coupled Springs).) / Civil Engineering Applications (Beam embedded at its left end and free at its right end, Beam embedded at both ends.)

5 Chapter (5): Functions of Multi-Variables / Definition of functions of multi-variables, partial derivatives, The chain rule, Critical points, Engineering applications (Tangent vector and plane to a surface, critical points, figuring surfaces)

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.