Department of Mathematics
MATH135 - Mathematics
IA
Unit Syllabus
Calculus:
- Real numbers, induction.
- Polynomials, degree, polynomial equations,
graphs, behaviour near infinity, roots and coefficients; iterative methods.
- Functions, inverse functions.
- The derivative; curve sketching, l'Hopital's
rule, rates of growth in some simple functions, optimization,
relative error, linearization, Newton's method.
- Applications of the derivative in science
and finance.
- Techniques of integration; application
to separable differential equations.
- Application of the integral to modelling
in science and finance.
Algebra:
- Review of trigonometric functions and
identities.
- Polynomials, degree, polynomial equations,
division and factorization, rational functions, partial fractions.
- Binomial theorem.
- Permutations, combinations and probability.
- Complex numbers.
- 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.
