Mechanical Design Engineering BEng/MEng
Engineering Mathematics 2 ENG2086
- Academic Session: 2024-25
- School: School of Engineering
- Credits: 20
- Level: Level 2 (SCQF level 8)
- Typically Offered: Semester 1
- Available to Visiting Students: No
- Collaborative Online International Learning: No
Short Description
This course provides the essential mathematics needed throughout all engineering disciplines. Topics covered include: Functions of several variables; Partial differentiation; Line integrals and multidimensional integrals; Ordinary Differential Equations; Laplace Transforms; Fourier Series.
Timetable
4 lectures per week
Excluded Courses
None
Co-requisites
None
Assessment
80% Exam, 20%Written Assignment
Main Assessment In: December
Course Aims
This course aims to ensure that students are competent in the essential mathematics required for engineering programmes.
Intended Learning Outcomes of Course
By the end of this course students will be able to:
Functions of several variables (MEM Sections 9.5 to 9.7) and Line integrals and multidimensional integrals (AMEM Section 3.4)
■ Construct contour plots and determine the stationary points, rates of change and gradients of multivariable functions using partial differentiation and the chain rule.
■ Evaluate the total differential of a function and apply it to the estimation of experimental errors for engineering-based examples.
■ Determine whether a differential is exact and solve for the parent function, for applications including the determination of work done by objects in conservative fields.
■ Construct and apply integrals relating to functions of two variables: double integrals to find the volume of objects, and path integrals to find areas and the work done by objects moving in force fields.
Ordinary Differential Equations (MEM Chapter 10)
■ Classify differential equations as to order and degree, ordinary or partial, homogeneous or inhomogeneous, linear or nonlinear;
■ Recognise different types of differential equations, including separable differential equations solved by integration of each side and first-order linear differential equations solved by the integrating factor method (with engineering examples);
■ Recognise the form of the solution of higher-order differential equations;
■ Obtain the general solution and particular solution for second-order, ordinary, differential equations (auxiliary equation, complementary function, particular integral, order reduction, and variation of parameters) exemplified by the problem of engineering system.
Fourier Series (MEM Chapter 12, AMEM Chapter 7)
■ determine the Fourier series representation of simple periodic functions using the trigonometric and complex exponential forms, using the symmetry properties of the function as appropriate;
■ apply Fourier series to solve engineering problems with a periodic input.
Laplace Transforms (MEM Chapter 11)
■ Derive the Laplace transform for standard functions, and of more general functions and derivatives using definition, known properties of the transform and tables of transforms;
■ Derive the inverse Laplace transforms of standard functions, and of more general functions using known properties of the inverse transform and tables of transforms;
■ Apply Laplace transform to solve ordinary differential equations up to second order with initial conditions.
This course follows the syllabus in Modern Engineering Mathematics (MEM) and Advanced Modern Engineering Mathematics (AMEM) by Glyn James (Pearson).
Minimum Requirement for Award of Credits
Students must attend the degree examination and submit at least 75% by weight of the other components of the course's summative assessment.
Students should attend at least 75% of the timetabled classes of the course.
Note that these are minimum requirements: good students will achieve far higher participation/submission rates. Any student who misses an assessment or a significant number of classes because of illness or other good cause should report this by completing a MyCampus absence report.