Mathematics 1: Semester 1
FLAP units: worked through at a rate of one unit per week
i. Arithmetic and Algebra (M1.1)
ii. Solving equations (M1.4)
iii. Series expansions and approximations (M1.7)
iv. Introducing complex numbers (M3.1)
v. Polar representation of complex numbers (M3.2)
vi. Basic differentiation (M4.2)
vii. Further differentiation (M4.3)
viii. Stationary points and graph sketching (M4.4)
ix.
Taylor
series and polynomial approximations (M4.5)
x. Basic integration (M5.2)
xi. Techniques of integration (M5.3)
Mathematics 2: Semester 2
1: Introduction to hyperbolic functions and their properties, derivatives, and series forms.
2: Further examples of sequences, limits, convergence and series analysis.
3: Fourier series; EulerFourier formula on (π,π), harmonics, Dirichlet convergence conditions, odd and even functions, sine and cosine series, extension to interval (L,L)
4: Firstorder differential equations; the method of separation of variables and integrating
Factors. Exact differential equations. Simple second order equations with constant
coefficients, general and particular solutions.
Mathematics 3: Semester 2
1: Matrices and vectors and the rules of matrix algebra. Rotations expressed in matrix
form. Linear equation sets; eigenvectors.
2: Functions of two or more variables. Partial derivatives and
Taylor
’s theorem. Maxima,
minima and saddle points.
3: Line integrals, multiple integrals; double and triple integrals, changes of variables, the
Jacobian, the use of spherical and cylindrical coordinates.
