Course - Mathematical methods 2 for Computer engineering - IMAG2021
IMAG2021 - Mathematical methods 2 for Computer engineering
This course is no longer taught and is only available for examination.
Examination arrangement: School exam
Grade: Letter grades
|Evaluation||Weighting||Duration||Grade deviation||Examination aids|
|School exam||100/100||4 hours||D|
Numerical methods in all parts where applicable.
- Complex numbers,
- Eigenvalues and eigenvectors.
- Power series, geometric series, Taylor series. series for exponential and trigonometric functions.
- Function of two and more variables, partial differentiation, extreme value problems.
- Logics: Statements, arguments, basic proof theory. Mathematical induction.
- Set theory and discrete functions.
- Number theory: Divisibility and congruence, RSA as application.
- Graph theory: Important types of graphs, graph isomorphy, trees. Graph theoretical algorithms, such as Prim's and Dijkstra's algorithms.
- Combinatorics: Counting results related to quantities, functions, and graphs.
Knowledge: The candidate should demonstrate knowledge of the following
- complex numbers.
- eigenvalues and eigenvectors for square matrices.
- transformations in two dimensions.
- the concepts of series and convergence in general and geometric series in particular.
- Taylor series of important function types.
- functions of several variable and partial derivation.
- concepts in logic of statements.
- common forms of mathematical proofs, including mathematical induction.
- basic set theory.
- discrete functions.
- concepts and algorithms related to graphs, including trees and graphisomorphism.
- concepts, methods and results in number theory, modular calculus and cryptography.
Skills: The candidate can
- do calculations with complex numbers in normal and polar forms and can apply Euler's formula.
- apply characteristic polynomials in finding eigenvalues and eigenvectors of a square matrix.
- use matrix multiplication to combine transformations in the plane
- apply eigenvalues in practical applications
- use power series in approximations, knows Taylor's formula with residual term and can use the residual term to estimate the error in calculations
- derive partial derivatives and total differential and use them to linearize functions and to find stationary points of functions of two variables
- apply basic concepts, results and methods from the theory of statements and arguments, for example determine whether an argument is valid or invalid and determine whether two statements are equivalent
- construct simple mathematical proofs, including inductive proofs
- apply basic concepts and results related to set theory, discrete functions and can represent these in different ways
- apply basic concepts and results related to graphs, paths in graphs and graphisomorphism
- apply algorithms to smaller examples,
- apply basic concepts and methods from number theory related to divisibility, including Euclid's method
- apply congruences calculations and perform RSA encryption and decryption
General competence: The candidate
- can use mathematics to model and solve theoretical and practical problems in situations relevant to their own field, in academic and professional contexts.
- The candidate can use computational and analytical tools to visualize and solve mathematical problems.
Learning methods and activities
Lectures and exercises. Exercises will be based on assignments in a digital assessment system. Use of Python will also be included. Exercises and learning videos for self-study will be available as a supplement to the lectures.
Compulsory work: at least 75% of the exercises must be approved for admission to the exam. The number of obligatory assignments and weighting will be announced at the start of the semester.
Further on evaluation
- There will be a school exam (in a digital examination system) at the end of the semester.
- Retake of examination may be given as an oral examination.
Recommended previous knowledge
Mathematical methods 1 or equivalent
Required previous knowledge
You must have been admitted to a technology study this subject is related to at the NTNU.
- A specially compiled course book comprising chapters of Adams and Essex: Calculus, and Lay, Lay and McDonald: Linear Algebra and its Applications, available as the semester begins.
- Discrete Mathematics With Applications, (International Edition) Susanna S. Epp
Eventual notes will be released on the Blackboard page.
Credits: 10.0 SP
Study level: Intermediate course, level II
Language of instruction: Norwegian
Examination arrangement: School exam
- Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
- Spring ORD School exam (1) 100/100 D 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.
- 1) Siste gangs eksamen
For more information regarding registration for examination and examination procedures, see "Innsida - Exams"