# Overview ​

Mathematical Analysis 2 is a 9 CFU course, part of the Engineering Sciences bachelor course. These pages contain the lecture notes and practical details related to the course.

Instructors:

Teams code: 3pddgbg (use this to join on Microsoft Teams)

Classroom: Aula 8

• Develop your intuition, it's a powerful skill – But don’t trust it completely
• Don’t aim to memorize but rather seek to understand – It is easy to remember anything when you understand it.
• Question always, be sceptical of all statements presented to you. Don’t accept them until you are sure they are believable.
• Observe, question how everything fits together, notice all the details.
• Part of the process of mathematical reasoning is creative - to be creative we must drop our inhibitions and be ready to be wrong, repeatedly.

## Schedule ​

The material of the course is divided into six parts as listed below. Each part takes two weeks and is accompanied with a set of exercises. Mathematically the parts are intimately linked.

Topic (2 weeks each)Teaching periodInstructor
Mathematical reasoning25 Sep - 6 OctButterley
Higher dimension9 - 20 OctButterley
Extrema23 Oct - 3 NovButterley
Line integrals6 - 17 NovButterley
Multiple integrals20 Nov - 1 DecGreenblatt
Surface integrals4 - 15 DecGreenblatt

See the lesson diary for full details.

The final weeks of the course are devoted to a mini-project.

ProjectTeaching periodInstructor
Project - week 18-12 JanGreenblatt
Project - week 215-19 JanButterley
• 8 Dec 2023: deadline for agreeing project topic and project team
• 29-30 Jan 2024: project presentations

## What is MA2? ​

Much of what we do in this course builds on ideas established in Mathematical Analysis 1. In particular many of the ideas are extended to the higher dimensional setting.

Mathematical Analysis 1Mathematical Analysis 2
(Functions)$f:\mathbb{R}\to \mathbb{R}$$f:{\mathbb{R}}^{n}\to \mathbb{R}$ (Scalar fields)
$\mathbf{F}:{\mathbb{R}}^{n}\to {\mathbb{R}}^{n}$ (Vector fields)
$\mathbit{\alpha }:\mathbb{R}\to {\mathbb{R}}^{n}$ (Paths)
(Derivative)${f}^{\prime }\left(x\right)=\frac{df}{dx}\left(x\right)$$\frac{\partial f}{\partial {x}_{j}}\left({x}_{1},\dots ,{x}_{n}\right)$ (Partial derivatives)
$\mathrm{\nabla }f$ (Gradient)
${D}_{v}f$ (Directional derivative)
${\mathbit{\alpha }}^{\prime }$ (Derivative of path)
$Df$ (Jacobian matrix)
$\mathrm{\nabla }\cdot \mathbf{F}$ (Divergence)
$\mathrm{\nabla }×\mathbf{F}$ (Curl)
(Extrema)$\underset{x\in \mathbb{R}}{sup}f\left(x\right)$$\underset{x\in {\mathbb{R}}^{n}}{sup}f\left(x\right)$ (Extrema)
Lagrange multiplier method
IntegralMultiple integral
Line integral
Surface integral