Make your own free website on Tripod.com

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.



3