Module Code - Title:
MA4002
-
ENGINEERING MATHEMATICS 2
Year Last Offered:
2025/6
Hours Per Week:
Grading Type:
N
Prerequisite Modules:
MA4001
Rationale and Purpose of the Module:
To develop the student's understanding of and problem solving skills in the areas of Integral Calculus and Differential Equations. To give the student an understanding of the Matrix Algebra and its application to solving systems of linear equations. To give the student an understanding of the Matrix Algebra and its application to solving systems of linear equations. To introduce the student to Multivariate Calculus.
Syllabus:
[The Indefinite Integral]: Integration techniques including integration of standard functions, substitution, by parts and using partial fractions.
[The Definite Integral]: Riemann sums, and the Fundamental theorem of calculus.
Application of integration to finding [areas, lengths, surface areas, volumes and moments of inertia].
[Numerical Integration]:Trapezoidal rule, Simpson's rule, other Newton-Cotes formulae and Gaussian quadrature.
[Ordinary Differential Equations]: first order including variables separable and linear types. Linear second order equations with constant coefficients. Numerical solution by Runge-Kutta.
[Functions of several variables and partial differentiation.] Fitting a line or curve to a set of data points.
Matrix representation of and solution of systems of linear equations. Matrix algebra, invertibility, determinants.
Learning Outcomes:
Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)
Evaluate indefinite and definite integrals analytically using tables, partial fraction representations of rational functions, by substitution, and by parts, and numerically.
Given a Riemann sum, represent its limit as a definite integral and using this technique, represent areas, arc-lengths of curves, volumes of revolution, and moments of mass as definite integrals.
Solve initial-value problems for first-order ordinary differential equations with separable variables and second-order linear ordinary differential equations analytically, and for general first-order ordinary differential equations numerically.
Given a function of several variables, evaluate its first- and higher-order partial derivatives and Taylor series approximations.
Perform arithmetic operations with matrices and evaluate matrix inverses, transposes and determinants.
Given a general system of linear equations, solve it by the Gauss-Jordan method.
Affective (Attitudes and Values)
N/A
Psychomotor (Physical Skills)
N/A
How the Module will be Taught and what will be the Learning Experiences of the Students:
Normal mathematics lectures. Students will have weekly homework (not for credit), a mid-term exam worth 30% and a final exam worth 70%.
Research Findings Incorporated in to the Syllabus (If Relevant):
Prime Texts:
Adams, R.A. (2006)
Calculus: a complete course
, Pearson Addison Wesley
Other Relevant Texts:
Anton, H. (1988)
Calculus with Analytic Geometry
, Wiley
Anton, H. (1994)
Elementary Linear Algebra
, Wiley
Atkinson, K. (1993)
Elementary Numerical Analysis
, Wiley
Fraleigh, J.B. (1985)
Calculus of a single variable
, Addison Wesley
Jeffrey, A. (1992)
Essentials of Engineering Mathematics
, Chapman Hall
Stroud, K.A. (1995)
Engineering Mathematics
, Palgrave
Programme(s) in which this Module is Offered:
Semester(s) Module is Offered:
Module Leader:
natalia.kopteva@ul.ie