Bachelor of Arts (BA) - The University of Hong Kong

• Limits and continuity.• Differentiation, chain rule, implicit differentiation.• Higher order derivatives, curve sketching, maxima and minima.• Definite and indefinite integrals, change of variables.Prerequisites: HKCEE Mathematics (Additional Mathematics or AS Mathematics and Statistics orMathematics at higher level not allowed).Duration: One semester (first semester; repeated in second semester)Assessment: One 2½-hour written examination (60%) together with coursework assessment (40%).MATH0802.Basic mathematics II (6 credits)To provide students with a more solid background of calculus of one and several variables and ofmatrices that can be applied in various disciplines, aiming at students having taken an elementarycalculus course. It can be followed by MATH1803.Contents• Set and functions.• Limits and continuity.• Differentiation, application, Taylor approximation.• Integration, techniques, improper integrals.• Functions of several variables, partial differentiation.• Maxima and minima, Lagrange multipliers.• Double integrals.• Matrices, systems of linear equations, inverses, determinants.• Eigenvalues and eigenvectors.Prerequisites: HKCEE Mathematics and Additional Mathematics or AS Mathematics and Statistics orMATH0801 (AL Mathematics not allowed).Duration: One semester (first semester; repeated in second semester)Assessment: One 2½-hour written examination (60%) together with coursework assessment (40%).257MATH1101.Linear algebra I (6 credits)• Matrices and Systems of Linear Equations: Elementary row operations, row echelon form,over-determined and under-determined systems, matrix algebra, inverses of matrices, partitionedmatrices and computational considerations. • Determinant: Properties of determinant, Cramer'srule, applications of determinant and computational considerations. • Vector Spaces: Definitionand examples, subspaces, linear independence, span of a set of vectors, basis and dimension,change of basis, row space and column space of matrices. • Linear Transformations: Properties oflinear transformations, kernel of linear transformations, matrix representation, basis change andsimilarity, isomorphisms, linear functionals and dual spaces (optional).Pre-requisite: AL Pure Mathematics.Assessment: One 2½ -hour written examination (60%) together with coursework assessment (40%).MATH1102.Linear algebra II (6 credits)• Inner Product Spaces: Inner products in R n , orthogonal subspaces, projection onto subspaces,orthonormal sets and orthonormal bases, self-adjoint operators, Gram-Schmidt orthogonalizationprocess, least squares problems and computational considerations. • Eigenvalues: Eigenvalues,eigenvectors and invariant subspaces, Cayley-Hamilton theorem, systems of linear differentialequations and the exponential e At , diagonalization, hermitian and unitary matrices, normal matrices andthe Jordan form. • Positive Definite Matrices: Quadratic forms, positive definite and semi-definitematrices, Cholesky decomposition and applications.Pre-requisite: AL Pure Mathematics and having taken MATH1101.Assessment: One 2½ -hour written examination (60%) together with coursework assessment (40%).