## INTRODUCTION TO MATHEMATICS AND STRUCTURES

 SHE Level 2 SCQF Credit Points 20.00 ECTS Credit Points 10.00 Module Code M2K225130 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. The percentage of Work Based Learning for this module, as represented by the Independent Learning "Activity Type" , is 64%. There is no Work Based Assessment, but reflective learning is encouraged.

### 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 apprentice should be able to:1. manipulate mathematical expressions, formulae and equations by applying the basic rules of algebra2. differentiate mathematical expressions by using standard rules3. apply differential calculus to rates of change and maximisation/minimisation problems4. integrate mathematical expressions by using standard rules5. solve problems using the Engineers'/construction' Equation of Bending6. determine direct, shear and bending stresses on structural elements7. solve simple beam problems to produce shear force and bending moment diagrams8. use mathematical techniques to solve engineering/construction problems9. 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[A1, A2, A6, A7, B4-B6 SDS GA: 1.2,2.2,4.2,4.4]

### Teaching / Learning Strategy

Traditional lectures will be supported by tutorials/seminars/computer laboratories with continuous assessment in the form of coursework/class tests. Work Based Education aims to maximise the direct and digitally mediated contact time with students by practicing teaching and learning strategies that use authentic work based scenarios and encourage action learning, enquiry based learning, problem based learning and peer learning. All these approaches aim to directly involve the students in the process of learning and to encourage sharing of learning between students. The module team will determine the level and accuracy of knowledge acquisition at key points in the delivery, inputting when necessary either directly or with the support of external experts who will add to the authenticity, the credibility and application of the education and learning to the workplace.

Croft A. and Davidson R. (2008) Mathematics for Engineers, 3rd edition, Addison Wesley. -142 Hulse R. and Cain J. (2000) Structural Mechanics, 2 nd Edition, Palgrave Macmillan Hulse R. and Cain J. (2009) Structural Mechanics: Worked Examples, 1 st Edition, Palgrave Macmillan

### Transferrable Skills

Critical thinking and problem solving. Independent working. Information retrieval skills. Communication skills, written, oral and listening. [C1-C3, C5, D1, D3-D6, E1, E3, E5-E7 SDS GA: 5.1 - 5.3]

### Module Structure

Activity Total Hours
Tutorials (FT) 24.00
Assessment (FT) 18.00
Lectures (FT) 24.00
Independent Learning (FT) 128.00
Seminars (FT) 6.00

### Assessment Methods

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