Engineering Analysis (1)

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

2 The complex plane (Argand plane), graphical representation of complex numbers, polar form, De Moivre’s theorem and its applications

3 The roots of unity, the fractional roots of any complex number. / 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.)

4 Chapter (2): First Order Ordinary Differential Equations / Basic concepts and definitions of 1st order differential equations; Formation of differential equations

5 Solution of differential equations: variable separable, homogeneous, equations reducible to homogeneous form

6 Exact differential equation, equations reducible to the exact form, linear differential equation, equations reducible to linear form (Bernoulli’s equation); orthogonal trajectories

7 Revision / Mid Term Exam

8 Chapter (3): Second-order Ordinary Differential Equations / Second-order linear homogeneous equations with constant coefficients; differential operators; solution of homogeneous equations

9 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

10 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.)

11 Chapter (4): Laplace Transform / Introduction, linearity, first shift theorem, Second shift theorem, multiplication by t and division by t

12 Inverse LT, Heaviside Expansion theorem, convolution theorem, unit step and Dirac-Delta function, applications on initial value problems

13 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)

14 Chapter (5): Functions of Multi-Variables / Definition of functions of multi-variables, partial derivatives, The chain rule

15 Critical points, Engineering applications (Tangent vector and plane to a surface, critical points, figuring surfaces)

1.1 Mapped to: K1

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

Teaching Strategy Traditional classroom