Syllabus

MA200 Science (pass)

MA211 Calculus (part one)

• Methods of integration: substitution, integration by parts, partial fractions, reduction formulae
• Inverse functions
• Improper integrals (as limits of finite integrals)
• Differential equations: linear equations with constant coefficients, first order homogeneous equations.

MA212 Calculus (part two)

• Series: convergence, divergence, absolute convergence
• The Comparison, Integral and Ratio Tests
• Alternating series
• Power series, the Radius of convergence
• Functions of several variables, and vector-valued functions (in R² and R³): vectors, scalar product, cross product in R³, equations of lines and planes in parametric form
• Partial derivatives: gradients, tangent planes, maxima and minima of functions of 2 variables, Lagrange multipliers
• The Chain Rule

Texts

• G.B. Thomas & R.I. Finney, "Calculus and Analytic Geometry" (Addsison Wesley)
• S.L. Salas, E. Hille & J.T. Anderson, "Calculus, One and Several Variables" (Wiley)

MA203 Linear Algebra

• Systems of linear equations, the Gaussian (row reduction) technique
• Matrices, determinants, adjoints, inverses
• Row operations, inverse of a matrix by row reduction
• Eigenvalues and eigenvectors, diagonalisation of a matrix with distinct eigenvalues; application to Markov processes, transition matrices
• Orthogonal matrices, orthogonal reduction of 2 by 2 and 3 by 3 matrices; applications to quadratic forms

Texts

• J.B. Fraleigh & R.A. Beauregard, "Linear Algebra" (Addison Wesley)

References

• F. Ayres, "Matrices" (Schaum Outline)

MA204 Discrete Maths

• Enumeration: the Rules of Sum and Product, tree diagrams, inclusion and exclusion, combinations and permutations, distributions and selections
• Graphs: Euler trails and Hamiltonian cycles, properties of trees (including spanning trees, ordered rooted trees, and tree traversals), planar graphs, colouring problems, various algorithms, applications

Texts

• S. Lipschutz, "Discrete Mathematics" (Schaum Outline)