Engineering Mathematics 1 ENG1063
- Academic Session: 2021-22
- School: School of Engineering
- Credits: 40
- Level: Level 1 (SCQF level 7)
- Typically Offered: Runs Throughout Semesters 1 and 2
- Available to Visiting Students: No
- Available to Erasmus Students: No
This course provides the fundamental mathematics needed throughout all engineering disciplines. Topics covered include: numbers, algebra and geometry; functions; complex numbers; vector algebra; matrix algebra; sequences, series and limits; differential calculus and applications; integral calculus and applications; data handling and probability theory.
4 lectures per week
1 group tutorial per week
76% Written Exam: 38% Paper 1 (Blocks 1-3) December Diet, 38% Paper 2 (Blocks 4-6) April/May Diet
24% Set Exercise: Six online End-of-Block tests
Main Assessment In: December and April/May
The aim of this course is to ensure that students are competent in the fundamental mathematics required for engineering degree programmes.
Intended Learning Outcomes of Course
By the end of this course students will be able to:
BLOCK 1 - Numbers, Algebra and Geometry (Chapter 1) and Functions (Chapter 2)
■ use reliably the basic rules of arithmetic and algebra;
■ solve quadratic equations and apply the results in engineering applications;
■ apply notation for sums, products, combinations and permutations;
■ explain the effect of rounding in arithmetic calculations and quote results to an appropriate number of significant figures;
■ estimate errors in sums, differences, products and quotients;
■ explain concept of a function, inverse function and zeros;
■ form composite functions, classify functions as odd, even and periodic;
■ decompose rational functions into partial fractions;
■ sketch and be able to explain fundamental properties of common circular, exponential, logarithmic and hyperbolic functions, giving special values;
■ use theorems to simplify trigonometric expressions.
BLOCK 2 - Complex Numbers (Chapter 3) and Vector Algebra (Chapter 4)
■ show the relationship between complex numbers and vectors;
■ plot complex numbers on an Argand diagram;
■ perform basic arithmetic operations on complex numbers and demonstrate the result on an Argand diagram;
■ find modulus, phase and real and imaginary parts; convert between rectangular and polar form;
■ use Euler's formula and de Moivre's theorem for simplifying trigonometric expressions and powers of complex numbers;
■ apply complex numbers to solving engineering problems, e.g. simple a.c. circuits;
■ distinguish between scalars and vectors;
■ perform addition and subtraction of vectors, showing triangle law and effect on components;
■ evaluate scalar and vector products, giving geometrical interpretations;
■ apply vectors to solving engineering problems.
BLOCK 3 - Matrix Algebra (Chapter 5) and Sequences, Series and Limits (Chapter 7)
■ reduce engineering problems to equations involving matrices;
■ add, subtract and multiply matrices;
■ evaluate determinant of a 3 x 3 matrix and other determinants, exploiting properties of determinant;
■ find inverse of a 3 x 3 matrix and other matrices, and state conditions under which an inverse exists;
■ solve simultaneous equations;
■ determine the eigenvalues and eigenvectors of a matrix;
■ apply matrix algebra to solving engineering problems;
■ state definition of sequence and series;
■ evaluate arithmetic, geometric and other simple series;
■ evaluate limit of a sequence and series; apply comparison, and ratio tests for convergence;
■ recognise power series of common functions;
■ apply concept of a limit of a function; distinguish between continuous and discontinuous functions.
BLOCK 4 - Differential calculus and applications (Sections 8.1 to 8.6, and 9.4)
■ understand differentiation as a rate of change, and as the slope of a tangent to a curve;
■ differentiate functions of a single variable from first principles;
■ find the derivative of powers, polynomial, exponential, logarithmic and trigonometric functions;
■ apply the rules of differentiation: chain rule, product and quotient rules, and implicit differentiation;
■ find higher-order derivatives;
■ find stationary and turning points, and solve problems on extrema;
■ apply Taylor's theorem;
■ apply L'HÃ´pital's rule to determine a limiting value of a function;
■ apply the Newton-Raphson method to determine numerically the zero of a function;
■ sketch the graphs of rational and other simple functions, with an appreciation of asymptotic behaviour;
■ apply differentiation to solving engineering problems.
BLOCK 5 - Integral calculus and applications (Sections 8.7 to 8.10, 9.2 and 9.3)
■ know the connection between definite integrals and area, and the Fundamental Theorem of Calculus;
■ understand indefinite integrals as anti-derivatives and hence solve indefinite integrals;
■ be able to write down the standard indefinite integrals of powers, polynomial, exponential and trigonometric functions;
■ apply the standard techniques of integration: variable substitution, integration by parts, partial fractions;
■ apply techniques for numerically evaluating definite integrals;
■ apply integration to solving engineering problems.
BLOCK 6 - Data Handling and Probability Theory (Chapter 13)
■ apply the concept of sampling, and graphically represent data samples;
■ interpret probabilities of random events;
■ extract location and dispersion values from data sets;
■ identify and use the properties of important practical distributions: the Binomial Distribution, the Poisson Distribution, and the Normal Distribution;
■ apply data handling and probability theory to engineering problems.
Minimum Requirement for Award of Credits
Students must attend the degree examinations and submit at least 75% by weight of the other components of the course's summative assessment.
Students must complete all 5 100% tests.