This module builds on the differential and integral calculus introduced in Calculus A, before moving on to introduce the basics of mathematical modelling techniques using first and second order ordinary differential equations. The module develops integration methods such as integration by parts and reduction formulae and describes applications of integration including general areas under a curve. Solution methods for first and second order differential equations are introduced and used to investigate various physical problems.
1. Integration: Definitions & Properties (1.1 Indefinite integrals: antiderivatives, 1.2 Definite integrals: area under a curve)
2. Methods of Integration (2.1 Standard integrals, 2.2 Inspection, 2.3 Completing the square, 2.4 Partial fractions, 2.5 Substitution, 2.6 Integration by parts)
3. Ordinary Differential Equations (3.1 First-order ODEs, 3.2 Second-order, linear, constant coefficient ODEs)
By the end of the course, students should be able to do the following:
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SCQF Level: 7
Credits: 15