Module description
This Mathematics Foundation module will teach you the mathematical background and knowledge required to study natural sciences.
During your Mathematics for Natural Sciences module, you’ll follow and reinforce A-level mathematics, with a focus on the principles of algebra, geometry, vectors, trigonometry, complex numbers, differentiation and integration and their application in both pure and applied areas of mathematics to solve problems are explored.
This module will cover:
- algebra, including indices, identities and inequalities, partial fractions, quadratic equations, logarithms, logarithmic equations, remainder and factor theorems, binomial theorem and Pascal’s triangle
- Functions, including mappings, domains and ranges; exponential and logarithmic functions; inverse functions; modulus function; even, odd and periodic functions; curve sketching; translations, reflections and stretches
- coordinate geometry, including equation of a straight line; parallel and perpendicular lines, distances and midpoints; quadratic curves and intersections of curves
- trigonometry, including adians; trigonometric functions, relationships and identities; graphical representation; “special” angles; trigonometric equations; transformations of trigonometric functions; sine and cosine rules; hyperbolic functions and relationships and identities
- vectors, including two and three dimensions; components; addition, subtraction and scalar multiplication; direction ratios and cosines; unit and direction vectors; geometrical properties and scalar and vector products
- matrices, including addition, subtraction and multiplication of matrices; determinant of a matrix; inverse matrix method to solve two simultaneous equations; Cramer’s rule and transformations in two dimensions represented by 2 x 2 matrices (translations, rotations and reflections)
- complex numbers, including imaginary numbers, algebraic properties, complex roots of quadratic equations, Argand diagram, polar and exponential forms of a complex number and De Moivre's theorem
- differential calculus, including differentiation from first principles; differentiation of: powers of x, polynomials, exponential, logarithmic and trigonometric functions; product, quotient and chain rules; small increments and rates of change; gradients, tangents and normals; stationary points (maxima, minima and points of inflection); parametric differentiation and implicit differentiation
- integral calculus, including fundamental theorem of calculus; integration of: powers of x, polynomials, 1/x, exponential and trigonometric functions; integration by parts; further integration techniques; indefinite and definite integrals; boundary conditions; limit of a sum; area under/between curves; volumes of revolution; trapezium rule; Differential equations: first order; separation of variables and boundary conditions.
This Mathematics for Natural Sciences module will prepare you to study a range of subjects at undergraduate level, including Mathematics BSc, Physics BSc, General Engineering BEng, Business Management BSc and Economics & Management BSc.
Assessment details
You are assessed for this Mathematics for Natural Sciences module through a combination of coursework (50%) and final exam (50%).
Educational aims & objectives
This Mathematics for Natural Sciences module will:
- provide you with an understanding of the main functional areas of mathematics
- develop your understanding of the use of relevant mathematical techniques and how to apply them in relevant contexts.
Learning outcomes
By the end of this Mathematics for Natural Sciences module, you will be able to:
- demonstrate the mathematical background knowledge to start an undergraduate programme in a range of numerate subjects
- understand and apply the mathematical techniques and methods of of algebra, vectors, trigonometry, complex numbers, differentiation and integration
- discern which mathematical techniques are appropriate for any given simple problem
- suggest ways to model mathematically simple concepts in physical sciences.
- investigate functions using analytical techniques
- reason logically and recognise incorrect reasoning
- generalise and construct mathematical proofs.
Suggested reading list
During your Mathematics for Natural Sciences module, you will be required to do a lot of reading. It is not necessary to purchase all books, but you should try and ensure you have access to some of the following:
| Required Textbook |
Recommended Textbooks |
|
L. Bostock and S. Chandler “Core Maths for Advanced Level” 3rd Edition, Nelson Thornes (2000)
ISBN-13: 978-0748755097, ISBN-10: 0748755098
|
Neill, H & Quadling, D (2005), Cambridge Advanced Mathematics: Core 1 &2, Cambridge University Press
|
| |
Neill, H & Quadling, D (2005), Cambridge Advanced Mathematics: Core 3 & 4, Cambridge University Press
|