Description:
| Aims: The aims of this unit are to:
* introduce vector and scalar quantities;
* investigate complex numbers;
* introduce mathematical modelling techniques;
* develop principles of calculus;
* introduce principles of statistics and probability.
Learning Outcomes: On completion of the unit the student should be able to:
* 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:
* continued development of the appreciation of a rigorous proof
Professional:
* development of an appropriately analytic approach
Practical:
* continue (from part 1) the process of acquisition of suitable mathematical tools and procedures which are of universal application in engineering, science and related fields of employment
Key:
* mathematical proficiency and maturity
* a broad introduction to, and understanding of, fundamental ideas and tools of modern pure and applied mathematics
* appreciation of the role and power of rigorous proof in mathematics, and a further study of constructing and following such proofs.
Content: This unit concentrates on:
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).
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