Course - Mathematics for engineering 2 B - IMAG2022
IMAG2022 - Mathematics for engineering 2 B
About
Examination arrangement
Examination arrangement: Aggregate score
Grade: Letter grades
| 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 assignments 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
The course has two evaluations. A continuation exam is held for the written school exam. Retake of examination may be given as an oral examination. There is no continuation exam for the portfolio.
If one evaluation is passed, and one is failed, the evaluation that is failed can be retaken if necessary next time the course is lectured ordinary.
Students that want to improve their grade in the course, can choose to retake one of the two evaluations. If the course changes its evaluation forms, the whole course must be retaken.
Continuation exam in August.
Specific conditions
Admission to a programme of study is required:
Chemistry - Engineering (FTHINGKJ)
Materials Engineering (FTHINGMAT)
Mechanical Engineering (BIMASKIN)
Naval Architecture - Engineering (699SD)
Production and Product Development – Engineering (BIMAS-F)
Renewable Energy - Engineering (BIFOREN)
Recommended previous knowledge
Mathematics for engineering 1 or similar
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 | |
| IMAT2022 | 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 | |
| IMAG2100 | 2.0 | AUTUMN 2024 | |
| IMAT2100 | 2.0 | AUTUMN 2024 | |
| IMAA2100 | 2.0 | AUTUMN 2024 |
Version: 1
Credits:
7.5 SP
Study level: Intermediate course, level II
Term no.: 1
Teaching semester: SPRING 2025
Language of instruction: Norwegian
Location: Gjøvik
- Engineering
- Mathematics
Department with academic responsibility
Department of Mathematical Sciences
Examination
Examination arrangement: Aggregate score
- Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
- Spring ORD School exam 70/100 C INSPERA
-
Room Building Number of candidates - Spring ORD Portfolio 30/100 INSPERA
-
Room Building Number of candidates - Summer UTS School exam 70/100 C INSPERA
-
Room Building Number of candidates
- * 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.
For more information regarding registration for examination and examination procedures, see "Innsida - Exams"