School Of Quantitative Methods & Mathematical SciencesEngineering Mathematics 1Western Sydney University Unit Code: 14505.1
Discipline: MATHEMATICAL SCIENCES
Student Contribution Band: 2
Level: 1
Credit Points: 10
About this Unit
Students will not gain credit for this unit and 14501 Mathematics 1, 14305 Elective 6 Mathematics, 14309 Foundation Mathematics 2 and 14382 Foundation Mathematics 3.
This unit covers the following areas:
Limits, continuity and differentiation – calculation of limits, continuity, differentiation, differentiation rules, implicit functions, inverse functions; applications of differentiation to curve sketching, maxima and minima problems and related to rate problems; L’Hospital’s rule.
Integration and applications-indefinite integrals, methods of substitution, definite integrals, calculation of volumes by slice and shell methods.
Logarithmic and exponential functions-the logarithm function defined as an integral and the exponential function as its inverse, properties of the logarithmic and exponential functions derivatives and integral
Trigonometric and hyperbolic functions- inverse trigonometric functions, applications to integration, hyperbolic and inverse hyperbolic function, logarithmic form of inverse hyperbolic functions, applications to integration.
Methods of integration- integration by parts, powers of trigonometric functions, reduction formulae, trigonometric substitutions, partial fractions.
Determinants and matrices – determinants and their properties; use of row and column operations; matrices, matrix algebra and the inverse of a matrix by row reduction and cofactor methods; solution of equation using determinants and matrices, diagonalisation of matrix by a similarity transformation, Eligenvalues and eigenvectors of a matrix.
Vectors – two and three dimensional vector vector algebra, scalar and vector products, equations of lines and planes in three dimensions, angles and distances between points, lines and planes.
Sequences and series-sequences, series and their convergence, ration test, errors for convergent series, power series, radius of convergence, Taylor and Maclaurin series.
Complex numbers- complex numbers, polar form, Demoivre’s theorem and roots of complex numbers, complex series, Euler’s formula complex eigenvalues and eigenvectors of a matrix.