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Advanced Mathematics for Civil Engineering Aim: The purpose of this unit is to enable learners to develop knowledge and understanding of advanced mathematical techniques and be able to apply analytical skills to the solution of civil engineering problems. The knowledge and skills developed are used by other units in the qualification and they also provide a sound basis for extending the study of engineering to a higher level if desired.On completion of this unit, learners will be able to:use matrix algebra methods to describe and solve engineering problemsuse vector methods of analysis to solve engineering problemsuse calculus to model and solve engineering problemsuse numerical analysis techniques to solve engineering problemscarry out statistical tests.Learning outcome1. be able to use matrix algebra to solve civil engineering problems1.1 perform operations in matrix algebra1.2 evaluate the determinants of a matrix1.3 solve simultaneous equations using Cramer’s rule1.4 obtain the inverse of a square matrix1.5 apply Gaussian elimination to solve simultaneous equations1.6 apply matrix algebra to solve engineering problems described by sets of simultaneous equations.2. be able to use vectors methods to solve civil engineering problems2.1 perform operations with vectors2.2 solve civil engineering problems using vectors.3. be able to use differential and integral calculus to solve civil engineering problems3.1 determine first and higher order derivatives of functions3.2 use differential calculus to solve problems3.3 determine indefinite and definite integrals of algebraic and trigonometric functions and differential equations3.4 use integral calculus to solve problems.4. be able to apply numerical analysis to solve civil engineering problems.4.1 use numerical iterative methods to find the roots of a function4.2 apply numerical methods of integration to engineering variables4.3 apply numerical methods for the solution of ordinary differential equation models4.4 apply iterative numerical methods to the solution of partial differential equation models.5. understand forms of statistical distribution5.1 explain the uses of statistical distribution5.2 explain the concept of degrees of freedom.6. be able to use statistical tests6.1 perform statistical tests of difference6.2 perform statistical tests of correlation.7. be able to use linear regression techniques7.1 perform regression techniques7.2 make predictions using linear regression techniques.
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