# VB6041 - Mathematics for engineering 2 C

New from the academic year 2024/2025

### Examination arrangement

Examination arrangement: Aggregate score

Evaluation Weighting Duration Grade deviation Examination aids
School exam 70/100 4 hours C
Portfolio 30/100 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. Optimization without constraints. Methods utilizing the derivative. Method of least squares - linear and non-linear. Optimization with constraints. Lagrange multipliers. Linear programming. The dual problem. Solutions by simplex method on computer. Integer programming.

### 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.
• The most important concepts and methods from optimization, such as iterative methods, constraints, Lagrange multipliers, objective function, dual problem.
• 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.
• Use computers for optimization without constraints and interpret the results.
• Solve simple optimization problems with constraints using Lagrange multipliers.
• Formulate applied problems as linear programming and solve by computer and interpret the results.
• 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.

• Exercises

### Further on evaluation

Engelsk

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:
Continuing Education, Faculty of Engineering Science and Technology (EVUIVE0)

### Course materials

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

### Credit reductions

Course code Reduction From To
IMAG2023 7.5 AUTUMN 2024
IMAA2023 7.5 AUTUMN 2024
IMAT2023 7.5 AUTUMN 2024
IMAG2011 2.0 AUTUMN 2024
IMAA2011 2.0 AUTUMN 2024
IMAT2011 1.0 AUTUMN 2024
IMAG2021 2.0 AUTUMN 2024
IMAA2021 2.0 AUTUMN 2024
IMAT2021 2.0 AUTUMN 2024
IMAG2031 4.0 AUTUMN 2024
IMAT2031 4.0 AUTUMN 2024
More on the course
Facts

Version: 1
Credits:  7.5 SP
Study level: Foundation courses, level I

Coursework

Term no.: 1
Teaching semester:  SPRING 2025

Language of instruction: Norwegian

Location: Gjøvik

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

Department of Mathematical Sciences

Section for quality in education and learning environment

# 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 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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