# MA270 Analysis 3

**Lecturer: **Jose Rodrigo

**Term(s):** Term 1

**Status for Mathematics students:** Core for Maths

**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 MA141 Analysis 1 and MA139 Analysis 2; knowledge of vector spaces from MA150 Algebra 2

**Useful background: **Basic results about curves, surfaces and vector fields from MA144 Methods of Mathematical Modelling 2

**Synergies:** MA250 Introduction to Partial Differential Equations

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

- MA260 Norms, Metrics and Topologies
- 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.