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This subject develops fundamental concepts and principles in mathematical analysis. Students should gain skills in the practical techniques of differential calculus, integral calculus and infinite series, and study selected applications of these techniques in mathematical modelling.
Topics covered include heuristic and rigorous discussion of limits of real-valued functions, continuity and differentiability; Mean Value Theorem and applications; Taylor polynomials; Riemann integration, techniques of integration and applications, improper integrals; sequences and infinite series; first order differential equations, second order linear differential equations with constant coefficients and selected applications.
Intended learning outcomes
Students completing this subject should:
- understand the significance and applications of properties of functions such as limits, continuity and differentiability;
- be able to evaluate proper and improper Riemann integrals;
- develop the ability to determine the convergence and divergence of infinite series;
- be able to solve analytically first and second order ordinary differential equations, and use these equations to model some simple physical systems;
- understand simple rigorous proofs of fundamental results in real analysis.
In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:
- problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
- analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
- collaborative skills: the ability to work in a team; and
- time management skills: the ability to meet regular deadlines while balancing competing commitments.
Last updated: 18 January 2022