MAT102

MAT102#

Elementary Calculus II

Objectives and Content#

Objectives#

The course contains theory of linear algebra for use in solving differential equations, data analysis, and optimization.

Content#

In this course, systems of linear equations, determinants, matrix algebra, eigenvalues, and vectors are studied. Furthermore, an introduction to differential equations, systems of homogeneous linear differential equations, population dynamic models, and functions of several variables are provided. An introduction to the programs MATLAB and NumPy will be given, which will be used in exercises. Numerical solutions of algebraic and differential equations will be a central theme.

Learning Outcomes#

On completion of the course, the student should have the following learning outcomes defined in terms of knowledge, skills, and general competence:

Knowledge#

The student:

  • Knows basic definitions regarding matrices and linear systems of equations.

  • Knows the concept of vector spaces and their dimensions.

  • Understands the use of digital tools in natural science.

  • Understands population models.

Skills#

The student:

  • Can use MATLAB or NumPy to analyze data.

  • Can use MATLAB or NumPy to numerically solve systems of differential equations.

  • Can apply the rules of matrix algebra and solve linear systems of equations.

  • Can set up simple population models.

  • Can use flow graphs to obtain a qualitative understanding of the solution curves for differential equations.

  • Can find the partial derivative of functions of several variables and use this to determine extreme points.

  • Can, by hand, calculate determinants in specific cases.

  • Can write and understand MATLAB/NumPy programs.

General Competence#

The student:

  • Has insight into the use of mathematics in natural science.

  • Has experience with using a computer to solve mathematical problems.

  • Understands how mathematical theory is useful for constructing models in natural science.

  • Knows how mathematics can be applied in data analysis.

Semester of Instruction#

Spring

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