# IMAT2022 - Mathematics for engineering 2 B

### Examination arrangement

Examination arrangement: Aggregate score

Evaluation Weighting Duration Grade deviation Examination aids
School exam 70/100 4 hours C
Portfolio 30/100

### Course content

Basis module. Functions of several variables. Partial differentiation, gradient. Critical points and optimization. Taylor’s theorem with remainder. Introduction to partial differential equations: examples and solutions.

Partial differential equations. Different types required different approaches, focus on physical/modeling intuition. Overview of the field. Steady state equations. Examples: Laplace’s and Poisson’s equation. Solution by computer using linear algebra. Iterative numerical solutions converging to a steady state. Time-dependent systems. Examples: Heat equation, advection equation, wave equation. Solution by computer.

Programme module. Trigonometric series and Fourier series. Applications to 1D wave equation with separation of variables. Fourier transform. Computation by hand and computer. Applications of Fourier transforms. Spectral analysis (e.g. sound and light waves). Applications to solution of differential equations, including harmonic motion with external periodic forcing.

### Learning outcome

Knowledge

The candidate has good knowledge of:

• Functions of several variables, including partial derivatives and their application to classification of stationary points and optimization.
• Taylor’s theorem and approximation by Taylor series.
• Partial differential equations, their properties and applications.
• Series representations and approximations to functions, particularly Taylor and Fourier series.
• Fourier transforms and applications to spectral analysis
• Digital tools for analysis of mathematical problems

Abilities

The candidate can:

• Find and interpret the partial derivatives of a function of several variables
• Approximate functions by Taylor’s theorem and estimate the error with a remainder term.
• Solve simple optimization problems with several variables.
• Verify that a given function solves a partial differential equation
• Solve certain partial differential equations by computer, verify and interpret the results.
• Compute Fourier coefficients of functions
• Fourier transform certain functions with applications to solution of differential equations and spectral analysis
• Apply digital tools to analyse mathematical problems.

General competence

The candidate:

• Has good knowledge of, and can apply a symbolic and formulaic mathematical apparatus that is relevant for communication in engineering sciences
• Has experience of evaluation of their own and other students scientific work, and with giving precise and technically correct oral feedback.
• Has experience with applications of mathematical methods and digital tools to problems with their own and related specializations.
• Can connect mathematical concepts and techniques to models the candidate meets within and outside of their studies.

### Learning methods and activities

Lectures, exercises and group work.

Compulsory assignments

The compulsory assignments consist of two parts:

• Compulsory exercises that are based on both analytical and numerical solution of problems and interpretation of the results. The assignments include tasks to be solved with the help of digital tools.
• Compulsory group work

Special conditions

Obligatory activities from previous semesters can be accepted by the institute.

### Compulsory assignments

• Compulsory assignments (exercises and group work)

### Further on evaluation

Emnet har to delvurderinger med bokstavkarakter; prosjektarbeid (i grupper) og individuell eksamen. Begge delvurderingene må bestås for å bestå emnet.

Vurderingsgrunnlaget til prosjektarbeidet er en prosjektrapport som leveres ved semesterslutt. Innleveringen er gruppevis. Veiledning består av forelesninger, videoer og notater som dekker tema for prosjektet. I tillegg er det gruppevis veiledning i forbindelse med fagets øvingstimer.

### Course materials

Recommended course material will be announced at the start of the semester.

### Credit reductions

Course code Reduction From To
IMAA2022 7.5 AUTUMN 2023
IMAG2022 7.5 AUTUMN 2023
IMAG2011 5.5 AUTUMN 2023
IMAA2011 5.5 AUTUMN 2023
IMAT2011 5.5 AUTUMN 2023
IMAG2021 2.0 AUTUMN 2023
IMAA2021 2.0 AUTUMN 2023
IMAT2021 2.0 AUTUMN 2023
IMAG2031 4.0 AUTUMN 2023
IMAA2031 4.0 AUTUMN 2023
IMAT2031 4.0 AUTUMN 2023
IMAG2150 1.5 AUTUMN 2024
IMAT2150 1.5 AUTUMN 2024
IMAA2150 1.5 AUTUMN 2024
More on the course
Facts

Version: 1
Credits:  7.5 SP
Study level: Intermediate course, level II

Coursework

Term no.: 1
Teaching semester:  SPRING 2025

Language of instruction: Norwegian

Location: Trondheim

Subject area(s)
• Engineering
• Mathematics
Contact information
Course coordinator: Lecturer(s):

Department of Mathematical Sciences

# Examination

#### Examination arrangement: Aggregate score

Term Status code Evaluation Weighting Examination aids Date Time Examination system
Spring ORD School exam 70/100
Spring ORD Portfolio 30/100
Summer UTS School exam 70/100
• * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
Examination

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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