Department of Mathematics
MATH132 - Mathematics
IA (Advanced)
Unit Syllabus
Basic Topics:
- The real numbers; mathematical induction.
- Complex numbers.
- Review on polynomials.
- Functions.
Calculus:
- The derivative; curve sketching, l'Hopital's
rule, rates of growth in some simple functions, optimization,
relative error, linearization.
- Limits; continuity, intermediate value
theorem; differentiability, mean value theorem; exponential and
logarithmic functions.
- Applications of the derivative in science
and finance.
- The Riemann integral, basic properties;
functions defined by integrals; improper integrals.
- Techniques of integration; application
to separable differential equations.
- Application of the integral to modelling
in science and finance.
Algebra:
- Linear equations; application to network
flow, electrical networks, economics, chemistry and mechanics.
- Matrices and matrix transformations;
application to economics and computer graphics; matrix factorization.
- Determinants; application to curves
and surfaces.
- Vectors; application to geometry in
3-space and physics.
