K/618/8087 Unit 8 Mathematics for Construction Assignment UK

Topics covered in this unit include trigonometry and algebraic techniques; matrices; statistical techniques; differential and integral calculus; binomial and normal distribution; dimensional analysis; arithmetic progressions; and vector analysis.

Upon successful completion of this unit, students will be able to apply mathematical methods in various contextual examples, use analytical and computational methods to evaluate and solve engineering construction problems, interpret data with statistical techniques, and apply calculus techniques. Additionally, students will develop crucial employability skills such as critical thinking, problem-solving, analysis, reasoning, and data interpretation.

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LO1 Use analytical and computational methods to solve construction-related problems

Analytical Methods

Trigonometry

• Irregular areas and volumes
• Sine rule
• Cosine rule
• Area of triangles applications
• Coordinate Systems
• Basic trigonometric ratios and their inverses
• Trigonometric ratios for the four quadrants
• Solution of triangles
• Areas and volumes of regular solids

Algebra

• Linear
• Simultaneous and quadratic equations (graphical or algebraic solving)

Matrices

• Multiplication
• Transposition
• Inversion (up to 2 × 2)
• Application to construction problems

Analysis and Design Issues

• Processes and operations
• Resource issues e.g., labour, finance
• Project planning

Levelling and Contouring

• Triangulation
• Traversing
• Cut and fill
• Setting out

LO2 Investigate applications of statistical techniques to interpret, organize, and present data using appropriate computer software packages

Statistical Methods

• Presentation of data (histograms, frequency graphs, cumulative frequency graphs)
• Central tendency and dispersion
• Dispersion (standard deviation, variance, interquartile range)
• Distribution theory: normal distribution
• Measures of dispersion (range, variance, standard deviation, quartiles, deciles, and percentiles)
• Grouped and ungrouped data
• Probability theory, binomial and normal distribution
• Applications
• Presentation of data
• Estimation
• Prediction
• Quality control

LO3 Illustrate the wide-ranging uses of calculus within different construction disciplines by solving problems of differential and integral calculus

Differential Calculus

• Basic differentiation techniques applied to algebraic, trigonometric, and logarithmic functions
• Products and quotients
• Function of a function
• Second-order derivatives
• The location of stationary values

Integral Calculus

• Indefinite and definite integration techniques applied to algebraic, trigonometric, and exponential functions
• Practical construction problems
• Solution of problems involving maxima and minima
• Growth and decay
• Centroids
• Moments of inertia
• Areas under curves and volumes of revolution
• Use in electrical theory, structural mechanics, fluid mechanics as appropriate

LO4 Use mathematical methods to solve vector analysis, arithmetic progression, and dimensional analysis problems

Trigonometrical Techniques

Vector Analysis

• Static forces
• Relative motion
• Frameworks

Arithmetic Progressions

Dimensional Analysis

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