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:

• Oliver Butterley (60 hours)
• Rafael Greenblatt (30 hours)

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

Classroom: Aula 8

General advice

• 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 period	Instructor
Mathematical reasoning	25 Sep - 6 Oct	Butterley
Higher dimension	9 - 20 Oct	Butterley
Extrema	23 Oct - 3 Nov	Butterley
Line integrals	6 - 17 Nov	Butterley
Multiple integrals	20 Nov - 1 Dec	Greenblatt
Surface integrals	4 - 15 Dec	Greenblatt

See the lesson diary for full details.

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

Project	Teaching period	Instructor
Project - week 1	8-12 Jan	Greenblatt
Project - week 2	15-19 Jan	Butterley

• 8 Jan 2024: 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 1	Mathematical 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)
	$\mathit{\alpha }:\mathbb{R}\to {\mathbb{R}}^n$ (Paths)
(Derivative)$f^{\prime }(x)=\frac{df}{dx}(x)$	$\frac{\partial f}{\partial x_j}(x_1,\dots ,x_n)$ (Partial derivatives)
	$\mathrm{\nabla }f$ (Gradient)
	$D_{v}f$ (Directional derivative)
	${\mathit{\alpha }}^{\prime }$ (Derivative of path)
	$Df$ (Jacobian matrix)
	$\mathrm{\nabla }\cdot \mathbf{F}$ (Divergence)
	$\mathrm{\nabla }\times \mathbf{F}$ (Curl)
(Extrema)$\underset{x\in \mathbb{R}}{sup}f(x)$	$\underset{x\in {\mathbb{R}}^n}{sup}f(x)$ (Extrema)
	Lagrange multiplier method
Integral${\int }_a^{b}f(x)dx$	Multiple integral
	Line integral
	Surface integral

Additional info

Course material from previous years and other instructors is available.

• 2022/23 Butterley
• 2021/22 Butterley
• 2020/21 Butterley
• 2019/20 Butterley / Tanimoto
• 2018/19 Tanimoto / Morsella