Course content

Numerical methods in all themes if relevant. Complex number, eigenvalues, diagonalization with applications: Systems og differential- and differenceequations, quadratic forms. Partial differential equations: One dimentional heat- , wave- and Laplace equation. Method of least squares with applications. Powerseries, taylorseries. Taylor polynomials in 2 variables. Function of two and more variables, partial differentiation, extrema value problems.

Learning outcome

The candidate should demonstrate knowledge of the following:

• Complex numbers; polar form and Euler’s formula
• Computation of characteristic polynomials, eigenvalues and eigenvectors of a square matrix
• Convergence of series, particularly geometric series
• Power series, including Taylor’s theorem with remainder and Taylor series of well-known functions. Integration and derivation of power series.
• Functions of several variables. Partial and total derivatives. Linearization around a stationary point and its applications.
• Simple modelling, and ability to solve and interpret the resulting problems where relevant to the course content.
• Diagonalization of matrices. Computing matrix powers. Solution of differential- and difference- equations and classification of two variable quadratic forms and conic sections.
• Partial differential equations. Modelling and interpretation of results. Understanding initial and boundary conditions.
• Linear least squares problems: interpretation and solution by normal equations.

The candidate should acquire and display the following skills:

• Use of computational devices for numerical calculations and graphical representations in topics relevant to the course.
• Basic computations with complex numbers
• Calculation and manipulations of series
• Partial derivation and application in classification of local extrema of a function of two variables.
• Use of numerical and symbolic computational methods for the solution of linear algebra problems such as diagonalization of matrices and linear least squares problems.
• Solve simple partial differential equations such as 1-dimensional heat and wave equations numerically and symbolically.
• Applications of linear least squares problems to overdetermined systems and linear regression.

General competence:

• Use of mathematics to model and solve theoretical and practical problems in situations relevant to their own field, in academic and professional contexts.
• Use of computational tools to visualize and solve mathematical problems.

Learning methods and activities

Lectures and exercises. Exercises will be based on assignments and digital learning elements using Blackboard. Use of MATLAB will also be included. Exercises and learning videos for self-study will be available as a supplement to the lectures. Local digital resources will also be offered. Compulsory work: At least 4 of 6 exercises must be approved for admission to the exam.

Compulsory assignments

• Compulsory assignment

Specific conditions

Course materials

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. Notes will be released on the Blackboard page.

Credit reductions