Lecturer: Vedran Sohinger

Term(s): Term 1

THIS MODULE IS NOT AVAILABLE TO MATHS (G100/G103) STUDENTS

Commitment: 30 one-hour lectures plus assignments

Assessment: 85% by 2-hour examination, 15% coursework

Formal registration prerequisites: None

Assumed knowledge: Notions of convergence, and basic results for sequences, series, differentiation and integration from introductory analysis modules like MA140 Mathematical Analysis 1 or MA142 Calculus 1 and MA152 Mathematical Analysis 2 or MA143 Calculus 2; knowledge of vector spaces from MA149 Linear Algebra or MA148 Vectors and Matrices

Useful background: Basic results about curves, surfaces and vector fields from MA145 Mathematical Methods and Modelling 2 or MA133 Differential Equations

Synergies: MA250 Introduction to Partial Differential Equations

Leads to: The following modules have this module listed as assumed knowledge or useful background:

• MA222 Metric Spaces
• MA263 Mutivariable Analysis
• MA269 Asymptotics and Integral Transforms
• MA3K8 Variational Principles, Symmetry and Conservation Laws
• MA3H0 Numerical Analysis and PDEs
• MA3D9 Geometry of Curves and Surfaces
• MA3B8 Complex Analysis
• MA3H7 Control Theory
• MA3G1 Theory of Partial Differential Equations
• MA3K0 High Dimensional Probability
• MA3G7 Functional Analysis I
• MA359 Measure Theory
• MA4L6 Analytic Number Theory

Content:

• Continuous Vector-Valued Functions
• Some Linear Algebra
• Differentiable Functions
• Uniform convergence and applications
• Convergence of sequences and series of functions
• Introduction to complex valued functions

Objectives: By the end of the module the students should be able to:

• Understand uniform and pointwise convergence of functions together with properties of the limit function
• Study the continuity, differentiability and integral of the limit of a uniformly convergent sequence of functions
• Study complex differentiability (Cauchy-Riemann equations) and complex power series
• Study contour integrals: Cauchy's integral formulas and applications.

Books: There is no recommended textbook for the course. A complete set of lecture notes will be provided.

 

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