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Staffing: |
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Description: |
This is the first of two units which cover most of the basic mathematics needed for engineering degree programmes. The unit contains the well recognised elements of classical engineering mathematics which universally underpin the formation of the professional engineer. There are four main sections: Algebra (vectors, complex numbers, matrices); Calculus (differentiation and integration of functions of one or more variables); Differential Equations and Probability (basic concepts, events, random variables, empirical discrete and continuous distributions). |
| Pre-requisites: | A level common core in mathematics (modules P1, P2 & P3) |
| Aims: | The principal aim of this faculty-wide unit is to bring students entering the Faculty of Engineering up to a common standard in mathematics. The unit contains the well recognised elements of classical engineering mathematics which universally underpin the formation of the professional engineer. |
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Learning outcomes: |
Students should understand and be able to use the language and methods of mathematics in the description, analysis and design of engineering systems. Students will have a composite understanding of the modular elements: complex numbers, vectors, linear algebra, probability and statistics, functions and classical mathematical analysis, introduction to numerical methods, single variable differential and integral calculus, including the solution of ordinary differential equations, multiple variable differential calculus. |
| See http://www.enm.bris.ac.uk/admin/courses/EMa1/assessment.htm | |
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Lecture 1: Introduction to Engineering Mathematics course.
Vectors Vectors. Scalars vs vectors. Directed line segments. Direction cosines. Adding, subtracting and scalar multiplication. Magnitude of a vector. Components: i,j, and k. Scalar product and projection. Concept of work done. Cross product and applications. Scalar and vector triple products, evaluation as a determinant and applications. Vector equations of lines, planes and spheres. Differentiation of a vector with respect to a single argument.
Complex Numbers Complex Numbers. Motivation and notation. Real and imaginary parts. Argand diagram, polar form, modulus and argument. Complex conjugate. Solving quadratics. Addition, subtraction, multiplication and division of complex numbers. Euler formula, exponential form, logarithms. Hyperbolic and trig functions with complex arguments. De Moivre's formula with applications.
Matrix Algebra Definition of a matrix. Column and row vectors, scalar product. Matrix addition and multiplication. Determinant of a matrix. Row operations for solving linear equations. Rank, linear dependence. Inverse matrix. Eigenvalues and eigenvectors.
Sequences, Series and Limits Definition of a sequence, limit of a sequence. Definition of a series, convergence of series. Definition of a power series, convergence radius of a power series. Functions of a real variable, inverse functions, standard functions. Continuity of a function.
Differentiation and Integration Rate of change and interpretation of derivatives. Definition of differentiability. Techniques of differentiation. Taylor series, L'Hopital's rule. Interpretation of integral as accumulation over time, distance. Definite integral: relation between integral and derivative. Techniques of integration: substitution, integration by parts, partial fractions. Improper integrals. Partial Differentiation Differential Equations Probability Revision Lectures - In May |
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| Materials: | Lecture notes will be posted on Blackboard |
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