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DEN5-SP Engineering Mathematics II

  • Duration:
  • Investment: US$ 249
Certificate:

Must complete all lessons

Content

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Description

Mathematical models are used to understand, predict and optimize engineering systems. Many of these systems are deterministic and are modeled using differential equations. Others are random in nature and are analyzed using probability theory and statistics. This course provides an introduction to differential equations and their solutions and to probability and statistics, and relates the theory to physical systems and simple real world applications. 
This course is designed to help students to understand the basic concepts and modelling of Ordinary differential equations, Laplace transforms, Matrices, Fourier series, Complex integration and Numeric linear algebra.
After completing this course, students will have professional knowledge to derive mathematical models of physical systems and solve differential equations using appropriate methods.

WHO SHOULD COPMPLETE THIS COURSE?

  • Engineers of all disciplines
  • Team leaders
  • Subject matter experts
  • Project managers
  • Supervisors
  • Analysts

COURSE OUTLINE
FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS (ODES)

  • Basic concepts
  • Separable ODEs
  • Exact ODEs
  • Linear ODEs
  • Existence and Uniqueness of solutions

SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS (ODES)

  • Homogeneous second order ODEs
  • Modelling: Free Oscillations 
  • Euler – Cauchy Equations
  • Modelling: Forced Oscillations
  • Modelling: Electric Oscillators

HIGHER ORDER LINEAR ODES

  • Homogeneous linear ODEs
  • Superposition principle
  • Initial value problem
  • Non homogeneous linear ODEs

SYSTEM ODES

  • Systems of ODE as models
  • Conversion of Nth order ODE to a system

SERIES SOLUTIONS OF ODES

  • Power series method
  • Legendre's Equation
  • Bessel functions
  • Bessel function of the second kind
  • Sturm-Liouville Problems
  • Orthogonal Eigenvalue expansions

LAPLACE TRANSFORMS

  • Transforms of Derivatives and Integrals
  • ODEs
  • Unit step functions
  • Short Impulses
  • Convolution
  • Differentiation and Integration of Transforms

MATRICES, VECTORS AND DETERMINANTS

  • Addition and Scalar multiplication
  • Linear systems of Equations
  • Gauss elimination
  • Linear Independence and Rank of matrix
  • Solutions of Linear systems
  • Determinants 
  • Cramer's Rule
  • Inverse of matrix
  • Gauss Jordan elimination

MATRIX EIGENVALUES

  • Applications of Eigenvalue problems
  • Symmetric, skew-symmetric and orthogonal matrices
  • Eigenbases, Diagonalization and Quadratic forms

FOURIER SERIES, INTEGRALS AND TRANSFORMS

  • Even and odd series
  • Half range expansions
  • Approximation by trigonometric polynomials 
  • Fourier integrals
  • Fourier cosine and sine transformers
  • Discrete and Fast Fourier transforms

PARTIAL DIFFERENTIAL EQUATIONS PDES

  • Basic concepts and modeling
  • Solution by separating variables
  • D'Alembart's Solution of wave equation characteristics
  • Solution of heat equation
  • Laplace's Equation in Cylindrical and Polar Coordinates
  • Solution of PDEs by Laplace transforms

COMPLEX NUMBERS AND FUNCTIONS

  • Polar form of complex numbers
  • Cauchy-Riemann Equations
  • Exponential functions
  • Trigonometric and hyperbolic functions
  • Logarithm and General power

COMPLEX INTEGRATION

  • Line Integral in the complex plane
  • Cauchy's Integral theorem
  • Cauchy's Integral formula
  • Derivatives of Analytic functions

POWER SERIES AND TAYLOR SERIES

  • Sequence, series and convergence tests
  • Power series
  • Functions given by power series
  • Taylor and Maclaurin series

LAURENT SERIES AND RESIDUE INTEGRATION

  • Laurent series
  • Singularities and Zeros
  • Residue Integration method
  • Residue Integration of Real Integrals

CONFORMAL MAPPING

  • Geometry of analytic functions
  • Linear fractional transformation
  • Special linear fractional transformations
  • Conformal mapping by other functions

COMPLEX ANALYSIS AND POTENTIAL THEORY

  • Electrostatic fields
  • Modelling and use of conformal mapping
  • Heat problems
  • Fluid flow
  • Poisson's Integral formula
  • General properties of harmonic functions

NUMERICS IN GENERAL

  • Solutions of equation by iteration
  • Interpolation
  • Spline Interpolation
  • Numeric Integration and Differentiation

NUMERIC LINEAR ALGEBRA

  • Linear systems
  • Least squares method
  • Matrix eigenvalues
  • Inclusion of Matrix eigenvalues
  • Power method for Matrix eigenvalues
  • Tridiagonalization and QR-factorization 

NUMERIC FOR ODES AND PDES

  • Methods for first order ODEs
  • Multistep methods
  • Methods for systems and higher order ODEs
  • Methods for elliptic PDEs
  • Methods for parabolic PDEs
  • Methods for hyperbolic PDEs

Investment

Plan Name Investment
Unlimited Access for 2 Years: US$ 249

Instructor

Indumathi V

Dip ECC Eng; BE (Electrical & Electronic Eng);
Grad Dip Adult & Voc Ed

Indu started her career in electronics, Computer and Communication engineering after completing her Diploma studies in Singapore. She has extensive knowledge in the semiconductor industry starting out a failure analysis specialist in a German MNC.

She subsequently went on to complete her Bachelor of Electrical and Electronic Engineering from the University of Western australia. After completing her bachelors, she went on to work as a Failure analysis engineer for a MNC, specializing in both destructive and non-destructive methods of failure analysis. During her career she has also led studies on the Tin Whisker project, trained local and overseas technicians and managed a team of technical specialist. she has also had extensive experience in engineering project management, quality control, process control, operations management and audit processes.

For the past 7 years Indu has also been lecturing full time in the VET sector in Perth, Australia. Indu is passionate to bring her personal and professional experience into her delivery and adopts a variety of teaching strategies to cater to the diverse student needs. she is a qualified VET lecturer holding both TAE and Graduate Diploma in Adult and VET education.

Indu is a passionate sTeM advocate and has designed and run sTeM open days particularly targeting females into the engineering industry. she is currently pursuing an MBa and has been working on industry projects in both commercial and government agencies. 

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