|
 Academic Year:
| 2012/3 |
| Owning Department/School:
| Department of Mechanical Engineering (administered by the Learning Partnerships Office) |
| Credits:
| 12 |
| Level:
| Certificate (FHEQ level 4) |
| Period: |
Academic Year at Swindon College |
| Assessment:
| CW30EX70 |
| Supplementary Assessment: |
Like-for-like reassessment (where allowed by programme regulations) |
| Requisites:
| |
| Description:
| Aims: The aims of this unit are to investigate arithmetical and algebraic techniques including analysing linear and non-linear relationships, calculus, trigonometry and geometry. The unit also includes an introduction to vector and scalar quantities, complex numbers, principles of statistics and probability and mathematical modelling techniques. Learning Outcomes: On completion of the unit the student should be able to: * apply arithmetical and algebraic techniques to solve given problems; * establish linear and non-linear relationships for given data; * solve simple calculus problems; * use geometrical and trigonometric techniques; * use vector and scalar quantities to solve problems; * determine unknown values using complex number techniques; * investigate mathematical modelling techniques; * use higher order calculus techniques; * determine probable outcomes using statistical methods. Skills: During this unit students should gain the following skills: Intellectual: * development of the appreciation of a rigorous proof (T,A) Professional: * development of an appropriately analytic approach (T,F) Practical: * the process of acquisition of suitable mathematical tools and procedures, which are of universal application in engineering and similar fields of employment (T,A) Key: * mathematical proficiency and maturity (F) * a broad introduction to, and understanding of, basic ideas and tools of modern pure mathematics (including analysis, linear algebra and geometry) and applied mathematics (including mathematical methods, mathematical modelling and matrices) (T,A) * appreciation of the role of rigorous proof in mathematics, and an introduction to constructing and following such proofs (F). Content: This unit concentrates on: Introduction to Arithmetic and Algebra * numbers and number bases (binary, octal, denary, hexadecimal) * factors (HCF and LCF) and prime numbers * fractions and decimals * powers and logarithms * algebraic expressions * introduction to polynomials and factorisation Linear relationships * functions, composition rules (function of a function), odd and even functions * independent and dependent variables, arguments * domains and ranges * characteristics of linear equations and inequalities * graphing linear equations, y = mx + c, applications, simultaneous equations * partial fractions Non-linear relationships * polynomial functions (powers of 2 and higher) * binomial series Introduction to calculus * first-order differentiation * integration Trigonometry and Geometry * degrees and radians * sin, cos, tan and their applications * hyperbolic functions * Pythagoras' Theorem * trigonometric identities * applications, e.g. midpoint of a straight line, distance between two points Vectors * vectors and scalars * vector arithmetic Complex Numbers * polar and Cartesian co-ordinates * complex number algebra * complex number division, conjugates Mathematical modelling * matrices * adding, subtracting and multiplying matrices * determinant and inverse of a matrix Further Calculus * applications of polynomials and calculus * partial differentiation * higher-order differentiation * differentiation rules and techniques: Product Rule, Quotient Rule * integration rules and techniques: partial fractions, by parts, substitution Statistics and Probability * mean, median, mode, variance, standard deviation * probability (laws, distributions). |
| Programme availability: |
LP10505 is Compulsory on the following programmes:Programmes administered by the Learning Partnerships Office
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