Teaching Responsibility
LJMU Schools involved in Delivery:
LJMU Partner Taught
Learning Methods
Lecture
Tutorial
Module Offerings
4500ICBTEG-APR-PAR
4500ICBTEG-JAN-PAR
4500ICBTEG-SEP_NS-PAR
Aims
This module will provide the analytical knowledge and techniques needed to carry out a range of engineering tasks and will provide a base for further study of engineering mathematics.
Learning Outcomes
1.
Apply the principles of differential equations and partial differentiation to solve
problems in Engineering.
2.
Evaluate Grad, Div, Curl, line integrals and double integrals.
3.
Evaluate simple Laplace transforms and their inverses using tables with
application to initial value problems.
4.
Demonstrate the knowledge of differential equations and mathematical modelling
of physical systems and simulation using MATLAB and Simulink.
Module Content
Outline Syllabus:Basic algebra: transposition, simplification, quadratic equations, simultaneous equations.
Basic trigonometry: functions sin, cos, tan, inverses, sec, cosec, cot; identities, Rsin (x+a).
Basic calculus: Derivative as slope and rate of change, standard derivatives; product, quotient and function of a function rules; integration as reverse of differentiation, standard integrals, area under a curve; differential equations and solution by direct integration.
Complex numbers: addition, subtraction, multiplication, complex conjugate and division in algebraic form. The Argand diagram. Polar form and exponential form, with multiplication and division. De Moivre's theorem (powers and roots). Locus problems.
Calculus: Implicit, parametric and logarithmic differentiation. Maxima and minima. McLaurin’s series. Partial differentiation, first order change, analysis of errors, method of least squares. Integration techniques (substitution, partial fractions, by parts) and simple applications of integration.
Matrices and Determinants: second and third order determinants, evaluation, properties, Cramer's Rule for solution of simultaneous equations; matrices, addition, subtraction, multiplication, transpose, inverse (via adjoint), solution of simultaneous linear equations by matrix inversion.
Vectors: sum, difference, magnitude, components, Cartesian representation in three dimensions; scalar and vector products, application to simple geometrical and physical problems.
Differential Equations: solution of first order by separation of variables and integrating factor; second order with constant coefficients, auxiliary equation, complementary function, particular integral by substitution (including snag case), application to, for example, mass-spring-damper and / or L-C-R circuits.
Assessments
Exam
Report