Overview

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

Instructor:

• Oliver Butterley (90 hours)

Teams code: 8dlmm2g (use this to join on Microsoft Teams)

Classroom: Aula 8

Classes:

• Monday 14:00 - 15:45 (in person)
• Wednesday 09:30 - 11:15 (in person)
• Friday 11:30 - 13:15 (online)

During October we won't have the Friday class, instead we will have the class in person on Wednesday at 11:30 - 13:15.

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 skeptical 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 five parts as listed below. Each part takes two weeks. Mathematically the parts are intimately linked.

Topic (2 weeks each)	Teaching period	Instructor
Higher dimension	29 Sep - 8 Oct	Butterley
Extrema	13 Oct - 24 Oct	Butterley
Line integrals	27 Oct - 7 Nov	Butterley
Multiple integrals	10 Nov - 21 Nov	Butterley
Surface integrals	24 Nov - 5 Dec	Butterley

See the lesson diary for full details (class topics for dates in the future are provisional and subject to change).

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

The online version of the notes and exercises is recommended, but a PDF version can also be downloaded (updated as the notes are updated).

Course material from previous years and other instructors is available.

• 2024/25 Butterley
• 2023/24 Butterley/Greenblatt
• 2022/23 Butterley
• 2021/22 Butterley
• 2020/21 Butterley
• 2019/20 Butterley / Tanimoto
• 2018/19 Tanimoto / Morsella