 University of Guyana

Faculty of Technology

Division of Engineering Mathematics

EMT 121 – ENGINEERING MATHS

Course Description:

Course Rationale:

Course Learning Outcomes:

Form of instruction: lectures, tutorials.

Course Assessment:

 Exams-50% Coursework – 50% Tests …………………25% Quizzes ………………10% Assignments …………15%

Main Course Texts: Engineering Mathematics by K.A. Stroud (sixth edition)

Course Content:

 Week Topics Core Learning Outcomes 1-2 Indefinite integration Students should be able to: reverse the process of differentiation to obtain an indefinite integral for simple functions understand the role of the arbitrary constant use a table of indefinite integrals of simple functions understand and use the notation for indefinite integrals use the constant multiple rule and the sum rule use indefinite integration to solve practical problems such as obtaining velocity from a formula for acceleration or displacement from a formula for velocity.. 3-4 Definite integration, applications to areas and volumes Students should be able to: understand the idea of a definite integral as the limit of a sum realize the importance of the Fundamental Theorem of the Calculus obtain definite integrals of simple functions use the main properties of definite integrals calculate the area under a graph and recognize the meaning of a negative value calculate the area between two curves calculate the volume of a solid of revolution use trapezium and Simpson's rules to approximate the value of a definite integral. 5-6 Methods of integration Students should be able to: obtain definite and indefinite integrals of rational functions in partial fraction form apply the method of integration by parts to indefinite and definite integrals use the method of substitution on indefinite and definite integrals solve practical problems which require the evaluation of an integral recognise simple examples of improper integrals 7-9 Sequences and series Students should be able to: understand convergence and divergence of a sequence know what is meant by a partial sum understand the concept of a power series apply simple tests for convergence of a series understand the idea of radius of convergence of a power series recognise Maclaurin series for standard functions understand how Maclaurin series generalise to Taylor series use Taylor series to obtain approximate percentage changes in a function. 10-11 Solution of simultaneous linear equations Students should be able to: represent a system of linear equations in matrix form understand how the general solution of an inhomogeneous linear system of m equations in n unknowns is obtained from the solution of the homogeneous system and a particular solution recognise the different possibilities for the solution of a system of linear equations give a geometrical interpretation of the solution of a system of linear equations understand how and why the rank of the coefficient matrix and the augmented matrix of a linear system can be used to analyse its solution use the inverse matrix to find the solution of 3 simultaneous linear equations understand the term ‘ill-conditioned’ apply the Gauss elimination method and recognise when it fails understand the Gauss-Jordan variation use appropriate software to solve simultaneous linear equations 12-13 Matrices and determinants Students should be able to: understand what is meant by a matrix recall the basic terms associated with matrices (for example, diagonal, trace, square, triangular, identity) obtain the transpose of a matrix determine any scalar multiple of a matrix recognise when two matrices can be added and find, where possible, their sum recognise when two matrices can be multiplied and find, where possible, their product calculate the determinant of 2 x 2 and 3 x 3 matrices understand the geometric interpretation of 2 x 2 and 3 x 3 determinants use the elementary properties of determinants in their evaluation state the criterion for a square matrix to have an inverse write down the inverse of a 2 x 2 matrix when it exists determine the inverse of a matrix, when it exists, using row operations calculate the rank of a matrix use appropriate software to determine inverse matrices.

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