| Module Title |
Engineering Mathematics III |
| Module Code |
EEG1009 (ITS: EM201) |
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Faculty |
Mechanical & Manufacturing Eng |
School |
Engineering & Computing |
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NFQ level |
8 |
Credit Rating |
5 |
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Description
This module provides students with the mathematical techniques and skills (analytic and computational) to solve engineering problems involving multivariate calculus and second order ordinary differential equations with constant coefficients.
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Learning Outcomes
1. differentiate and integrate standard functions of several variables
2. define and calculate selected quantities in vector calculus
3. formulate and solve engineering optimization problems
4. solve second order ordinary differentail equations with constant coefficients
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| Workload | Full time hours per semester | | Type | Hours | Description |
|---|
| Lecture | 36 | Class based instruction on theory, analytical solution and problem formulation using a computer algebra system (CAS). | | Tutorial | 12 | Group discussion, analytic problem solving and solution verification using CAS. | | Independent Study | 77 | Problem solving relating to tutorial material and weekly review of class materials in preparation for the final examination. Home work exercises may be assigned using a STEM online homework system. |
| Total Workload: 125 |
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| Section Breakdown | | CRN | 10191 | Part of Term | Semester 1 | | Coursework | 0% | Examination Weight | 0% | | Grade Scale | 40PASS | Pass Both Elements | Y | | Resit Category | RC3 | Best Mark | Y | | Module Co-ordinator | Donnacha Lowney | Module Teacher | Brian Corcoran, Harry Esmonde, Jeremiah Murphy |
| | Section Breakdown | | CRN | 12079 | Part of Term | Semester 1 | | Coursework | 0% | Examination Weight | 0% | | Grade Scale | 50PASS | Pass Both Elements | Y | | Resit Category | RC3 | Best Mark | N | | Module Co-ordinator | Donnacha Lowney | Module Teacher | |
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| Assessment Breakdown |
| Type | Description | % of total | Assessment Date |
|---|
| In Class Test | Individual class test to solve problems. | 10% | Week 4 | | In Class Test | Individual class test to solve problems | 10% | Week 8 | | Formal Examination | End of semester exam. | 80% | End-of-Semester |
| Reassessment Requirement Type |
Resit arrangements are explained by the following categories;
RC1: A resit is available for both* components of the module.
RC2: No resit is available for a 100% coursework module.
RC3: No resit is available for the coursework component where there is a coursework and summative examination element.
* ‘Both’ is used in the context of the module having a coursework/summative examination split; where the module is 100% coursework, there will also be a resit of the assessment
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Pre-requisite |
None
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Co-requisite |
None |
| Compatibles |
None |
| Incompatibles |
None |
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All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml
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Indicative Content and Learning Activities
Fundamentals
Vectors and matrix algebra.
Differential equations
First and second order with constant coefficients.
Partial differentiation
First, higher order and mixed partial derivatives; multi-variate Taylor series; stationary values; max/min problems; Hessian matrix; composite functions, chain rule and total derivative; material time derivative; change of independent variable; dependent and independent functions; Jacobian determinant.
Modelling data and approximating functions
Least squares; linearised models, optimisation using Lagrange multipliers; error analysis.
Coordinate systems
Cartesian; polar; spherical; transformations and Jacobian matrix.
Introduction to common partial differential equations (PDEs)
Wave, heat, Laplace and Schrodinger equations; configurations tractable to analytical solution.
Operators
Gradient of scalar field, divergence and curl of vector fields; directional derivative; Laplacian; irrotational and conservative vector fields.
Calculus of vector-valued functions
Arc-length; unit tangent and normal vectors; curvature; velocity.
Double and triple integrals: formalism
Line, area and volume integrals; applications to areas, moments and centre of mass
Vector calculus
Line, surface and volume integrals; Stokes, Greens and Divergence Theorems; applications: work, circulation and flux
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Indicative Reading List
Books:
- Croft, Davidson and Hargreaves: 0, Engineering Mathematics,
- Anthony Croft,Tony Croft,Robert Davison,James Flint,Martin Hargreaves: 2017, Engineering Mathematics, Pearson Education, 978-1-2921-4665-2
- Erwin Kreyszig: 2010, Advanced Engineering Mathematics, John Wiley & Sons, 267, 978-0-4704-5836-5
- Seán Dineen: 2014, Multivariate Calculus and Geometry, Springer, 978-1-4471-6418-0
- K. B. Vijaya Kumar,Antony P. Monteiro: 2023, Mathematica for Physicists and Engineers, John Wiley & Sons, 421, 978-3-5274-1424-6
- Pragati Gautam,Swapnil Verma,Komal Negi: 2024, Getting Started with Maxima, Techsar Pvt Ltd, 451, 978-81-971909-1-9
Articles:
None |
Other Resources
None |
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