## INTRODUCTION TO MATHEMATICS AND STRUCTURES

 SHE Level 2 SCQF Credit Points 20.00 ECTS Credit Points 10.00 Module Code M2K224028 Module Leader Jill Sutcliffe School School of Computing, Engineering and Built Environment Subject Civil Engineering and Environmental Management Trimesters A (September start)-B (January start) A (September start)

### Summary of Content

Basic Algebra, Coordinate Geometry, Trigonometry, Calculus, Matrices, basic Statistics and Structural Mechanics.

### Syllabus

Algebra: Application of algebraic techniques to the manipulation of mathematical expressions including indices, trigonometrical, logarithmic and exponential functions; transposition of formulae and equations. Trigonometry: Radian measure, trigonometrical identities, sine and cosine rules; selected examples of solution of trigonometrical equations; resultants and determinants of force vectors. Co-ordinate Geometry: Determination of equations of straight lines and curves, equations of tangents and normals, determination of points of intersection. Matrices: Addition, subtraction, multiplication; inverse of a matrix, determinants; solution of equations. Calculus: First and second order derivatives of algebraic, trigonometrical, exponential and logarithmic functions including function of a function, product and quotient rules; applications to problems involving gradients of curves, rates of change and optimisation; standard integrals involving algebraic, trigonometrical and exponential functions; applications to indefinite and definite integrals. Statistics: Mean, variance and deviation of random variables; normal distribution. Structural Mechanics: Engineers' equation of bending; static equilibrium; deflection of beams including Macaulay's method; shear force and bending moment diagrams, Hooke's law, stress-strain diagrams and Young's Modulus; theory of bending; section properties; Euler buckling of struts.

### Learning Outcomes

On completion of this module the student should be able to:- manipulate mathematical expressions, formulae and equations by applying the basic rules of algebra- differentiate mathematical expressions by using standard rules- apply differential calculus to rates of change and maximisation/minimisation problems- integrate mathematical expressions by using standard rules-.solve problems using the Engineers'/construction' Equation of Bending- determine direct, shear and bending stresses on structural elements- solve simple beam problems to produce shear force and bending moment diagrams- use mathematical techniques to solve engineering/construction problems- apply statistical methods and equations to a data set in order to analyse and interpret results, explain variations in the data, or predict future dataNB where appropriate all examples and questions will relate to structures and structural mechanics

### Teaching / Learning Strategy

Traditional lectures will be supported by tutorials/seminars/computer laboratories with continuous assessment in the form of coursework/class tests.

Croft A and Davidson R, Mathematics for Engineers, 2nd edition, Addison Wesley. -142 Hulse R and Cain J. Structural Mechanics, 2 nd Edition, Palgrave Macmillan, 2000 Hulse R and Cain J. Structural Mechanics: Worked Examples, 1 st Edition, Palgrave Macmillan, 2009.

### Transferrable Skills

Critical thinking and problem solving (D1) Independent working (D7) Information retrieval skills (D10) Communication skills, written, oral and listening (D14)

### Module Structure

Activity Total Hours
Independent Learning (PT) 122.00
Independent Learning (FT) 110.00
Assessment (FT) 18.00
Seminars (FT) 6.00
Tutorials (PT) 12.00
Lectures (FT) 42.00
Seminars (PT) 6.00
Assessment (PT) 18.00
Tutorials (FT) 24.00
Lectures (PT) 42.00

### Assessment Methods

Component Duration Weighting Threshold Description
Coursework 2 n/a 15.00 35% Coursework 2 (problem solving based) 1000 words
Exam (School) n/a 70.00 35% Class test
Coursework 1 n/a 15.00 35% Coursework 1 (problem solving based) 1000 words