Course description

Mathematical Analysis

Introduction

Mathematical analysis is an advanced math course that is based on the first-year course in mathematics.

Course content

Chapter references to Sydsæter et. al:

  1. Multivariable optimization problems for functions of several variables: Ch. 13.1 - 13.6
  2. Constrained optimization (general Lagrange problems): Ch. 14.1-14.4, 14.6, 14.7
  3. Implicit differentiation: Ch. 7.1,7.2, 12.1-12.3
  4. Linear and polynomial approximations. Differentials: Ch. 7.4, 7.5, 12.8, 12.9
  5. Elasticity: Ch. 7,7, 11.8
  6. Homogeneous functions: Ch. 12.6
  7. Non-linear programming: Ch. 14.8, 14.9
  8. Systems of equations: Ch. 12.10, 15.1
  9. Gaussian elimination: Ch. 15.6
  10. Matrix and vector algebra: Ch. 15.1 - 15.5, 15.7
  11. Determinants and inverse matrices: Ch. 16.1 - 16.8
  12. Integration: Integration by parts and integration by substitution: Ch. 9.4 – 9.6
  13. Differential equations: Ch. 9.8, 9.9

Learning outcome knowledge

The course deepens and extends mathematical analysis techniques from the basic course in the first year.

During the course students shall acquire knowledge of:

  • Functional analysis of both the single and the multivariable case. In the multivariable case various techniques for constrained optimization will be examined, also for the case when the constrained condition is given by inequalities.
  • Selected topics in linear algebra, where students learn vector and matrix arithmetic, Gaussian elimination, determinants, Cramer’s rule and matrix inversion.
  • Various integration techniques such as partial integration and integration by substitution.
  • Techniques for the solution of simple first order differential equations will also be reviewed.

Exam organisation

  • Written exam: 100%