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

258MATH1201.Calculus I (6 credits)• The Real Number System: supremum, infimum, completeness axiom and inequalities. • Functionsand Limits: Basic properties. • Continuous Functions: Basic properties, intermediate value theoremand uniformly continuous function. • Differentiation: Differentiable function, basic rules, localextremum, Rolle's theorem, mean value theorem, L'Hospital's rule and Taylor's formula. • InfiniteSequences and Series: Sequence of real numbers, subsequence, series of constant terms, Cauchy'scriterion, tests for convergence, absolute convergence, Taylor's and binomial series and power series.Pre-requisite: AL Pure Mathematics.Assessment: One 2½ -hour written examination (60%) together with coursework assessment (40%).MATH1202.Calculus II (6 credits)• Riemann integrals: Riemann integrability, basic properties, first and second fundamental theorem ofcalculus, exponential and hyperbolic functions and logarithm. • Differentiability: Partial derivative,differentiability and Taylor's formula. • Maxima and Minima: Local extremum, method of Lagrangemultipliers and Jacobian. • Multiple Integrals: Double and triple integrals.Pre-requisite: AL Pure Mathematics and having taken MATH1201.Assessment: One 2½ -hour written examination (60%) together with coursework assessment (40%).MATH1803.Basic mathematics III (6 credits)To provide students with a background of calculus of several variables and linear algebra that can beapplied in various disciplines.Contents:• Matrices, systems of linear equations, inverses, determinants.• Functions of several variables; partial differentiation.• Limits, continuity and differentiabilty.• Maxima and minima; Lagrange multipliers.• Double integrals, triple integrals.• Vector spaces, basis.• Linear differential equations, first order, constant coefficients.• Linear difference equations (with constant coefficients).• Eigenvalues and Eigenvectors.Prerequisites: AL Pure Mathematics or MATH0802.Duration: One semester (first semester)Assessment: One 2½-hour written examination (60%) together with coursework assessment (40%).MATH1811.Mathematics I (6 credits)To provide students with the essential knowledge of linear algebra and vector calculus for furtherstudies in the physical sciences. It is intended that the course will be followed by MATH1812.Contents:• Vectors and the geometry of R n : points and vectors, addition and scalar multiplication of vectors,vector space structure of R n , inner product and cross product (including their geometricinterpretations and applications).