The aim of the module is to develop students' proficiency in calculus as a basis for further study in civil engineering.

Learning Outcomes

On successful completion of this module the learner should be able to:

LO1

Use various methods to find the roots of equations.

LO2

Apply differential and integral calculus and partial differential calculus to a variety of engineering applications.

LO3

Apply techniques to approximate definite integrals.

LO4

Solve simple first and second order differential equations.

Pre-requisite learning

Module Recommendations

This is prior learning (or a practical skill) that is recommended before enrolment in this module.

9890

MATH C1503

Mathematics and Statistics I

Incompatible Modules

These are modules which have learning outcomes that are too similar to the learning outcomes of this module.

No incompatible modules listed

Co-requisite Modules

No Co-requisite modules listed

Requirements

This is prior learning (or a practical skill) that is mandatory before enrolment in this module is allowed.

No requirements listed

Module Content & Assessment

Indicative Content

Roots of equations

(a) Factor theorem and remainder theorem. (b) Factorising cubic equations. (c) The discriminant and roots of quadratic equations. (d) Interpolation including Newton-Raphson method.

Further calculus

(a) Review of differentiation using product, quotient and chain rule.
(b) Review of integration by parts, substitution and partial fractions. Applications to engineering problems including centroids.
(c) Partial differentiation and application to small changes.

Approximating integrals

(a) Taylor polynomials. (b) Trapezoidal rule. (c) Simpson's rule.

Introduction to ordinary differential equations

(a) General solutions and particular solutions. (b) First order separable ODEs. (c) First order linear ODEs. (d) Second order linear ODEs with constant coefficients.

Assessment Breakdown

%

Continuous Assessment

50.00%

End of Module Formal Examination

50.00%

Continuous Assessment

Assessment Type

Assessment Description

Outcome addressed

% of total

Assessment Date

Short Answer Questions

Quiz questions

1,2,3,4

20.00

Ongoing

Examination

Class Test 1

1,2

15.00

Week 6

Examination

Class Test 2

3,4

15.00

Week 11

No Project

No Practical

End of Module Formal Examination

Assessment Type

Assessment Description

Outcome addressed

% of total

Assessment Date

Formal Exam

End of module examination

1,2,3,4

50.00

End-of-Semester

SETU Carlow Campus reserves the right to alter the nature and timings of assessment