Module Code - Title:

MA4006 - ENGINEERING MATHEMATICS 5

Year Last Offered:

2025/6

Hours Per Week:

Lecture

3

Lab

0

Tutorial

1

Other

0

Private

6

Credits

6

Grading Type:

N

Prerequisite Modules:

MA4003

Rationale and Purpose of the Module:

To introduce the student to elementary Vector Calculus. To give the student a broad understanding of analytical and numerical techniques for solving Partial Differential Equations.

Syllabus:

Vector Calculus: Scalar and vector fields, contour maps, directional derivative and gradient vector of a scalar field, divergence and curl of a vector field (line, surface and volume integrals), Integral Theorems (Gauss', Green's and Stokes'). Partial Differential Equations: Modelling and derivation of wave, heat and Laplace's equation. Solution of such equations by separation of variables. Numerical methods for the solution of partial differential equations using finite differences.

Learning Outcomes:

Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)

1. Geometrically represent vector functions to be able to determine the tangent, arclength, curvature, velocity and acceleration. 2. Evaluate the gradient of a scalar function, the divergence of a vector function and the curl of a vector function. 3. Evaluate line and surface integrals of scalar and vector fields and volume integrals of scalar fields. In addition, use the Divergence, GreenÆs and StokesÆ Theorems. 4. Classify 2nd order partial differential equations and use the method of characteristics to solve partial differential equations. 5. Use the method of separation of variables to solve linear, homogeneous partial differential equations including the wave, heat and Laplace equations. 6. Discretise a partial differential equation using finite differences and formulate the discretised problem. Also, prove basic theoretical numerical results including the Maximum Principle, uniqueness of the numerical solution and finding an upper bound.

Affective (Attitudes and Values)

See Cognitive above.

Psychomotor (Physical Skills)

See Cognitive above.

How the Module will be Taught and what will be the Learning Experiences of the Students:

Three lectures and one tutorial per week. Two midterm tests and one final examination.

Research Findings Incorporated in to the Syllabus (If Relevant):

Prime Texts:

Kreyszig, E (1988) Advanced Engineering Mathematics (6th Edition) , Wiley

Other Relevant Texts:

James, G (2004) Advanced Modern Engineering Mathematics (3rd Edition) , Pearson Education Ltd

Programme(s) in which this Module is Offered:

Semester(s) Module is Offered:

Module Leader:

Mehakpreet.Singh@ul.ie