Mathematics for engineering 3 A

General numerics

Representations of floating point numbers in the computer, calculations with floating point numbers and various sources of error. Error magnification and condition.

Numerical linear algebra

Orthogonality in vector spaces and orthogonal bases. Gram-Schmidt orthogonalization. QR factorization. Singular value decomposition (SVD). Cholesky factorization and conjugate gradients.

Optimization

Linear programming. Method of least squares. Lagrange multipliers.

Knowledge

The candidate has good knowledge of:

• Common sources of error in numerical calculations.
• Vector spaces and orthogonal bases and is familiar with orthogonalization algorithms.
• Various matrix factorizations and their applications.
• The main concepts and methods from optimization, such as iterative methods, constraints, Lagrange multipliers, objective function, dual problem.
• Digital tools for analyzing mathematical problems.

Skills

The candidate:

• Can solve linear systems numerically and estimate errors related to numerical calculations.
• Can apply eigenvalues, eigenvectors, and singular value decomposition (SVD) to solve engineering problems using digital tools.
• Can use computers to solve unconstrained optimization problems and interpret the results.
• Can solve some simple constrained optimization problems using Lagrange multipliers.
• Can formulate some applied problems such as tasks in linear programming, solve them using computers, and interpret the results.
• Should be capable of using digital tools to analyze mathematical problems.

General Competence

The candidate:

• Is well-versed in and can apply a mathematical symbol and formula apparatus relevant to communicating in the engineering field.
• Has experience applying mathematical methods and digital tools to problems from their own and adjacent fields.
• Is capable of connecting mathematical concepts and techniques to models encountered both within and outside of their studies.

Lectures, exercises, compulsory tasks.

Compulsory tasks include both analytical and numerical solution methods, and includes problems that are solved using digital tools.