The main reason for translation of this text book system divided into 19 sections is a renewed interest in a text book on mathematics
as it was outlined some 30 years ago.
That is a rigorous presentation, where all proofs are completed.
Until 1988 Mathematics were teached on a fairly high theoretical level in Denmark.
This was possible because the students mathematical skills at that time were vastly better than today.
After 1988, the way of teaching mathematics changed, the traditional theoretical level with proofs, derivations and rigorous expanations
were dropped, and replaced by teaching how mathematics could be applied in daily life society.
By the reform in 2005, the theoretical aspect almost disappered completely, and elemmentary mathematical skills were discarded
in favor of operating mathematical computer programs. The education has turned from theoretical to lexical.
A development in the educational systems towards the ideology of social constructivism, which I sense is more or less shared
by most of the Western world.(But not in Asia)
The reason for the renewed interest for a more than 10 years old textbook is that they do simply no longer exist,
neither as textbooks or internet pages material,were you get a traditional rigorous theoretical explanation of mathematics in a level, which nowadays is placed
at university undergraduate level.
- Algebra, sets, inequalities and equations (Elementary Mathematics)
- Analytic Geometry. (Elementary Mathematics)
Distance formula. Equations for the line and circle. Distance from a point to a line. Two equations with two unknows. Determinants. intersection of lines.
- Trigonometry (Elementary Mathematics)
Sine, cosine and tanget. The right angled triangle. The sine relation and the cosine relation
- Real functions (Elementary Mathematics)
Real functions. Graphs for funtions. Inverse function. Composite functions.
- Quadratic polynomials. (Elementary Mathematics)
Quadratic polynomials. Graphs. Sign for. Roots and factorization
- Trigonometric Functions (Elementary Mathematics)
Definitions. Graphs.Trigonometric equations and inequalities.
- Geometry with dividers and ruler (Elementary Mathematics)
A classical rigorous treatment of geometry, stating with 5 axioms and ending with Herons formula
- Geometrical vectors (Elementary Mathematics)
A classical introduction vectors and operations with vectors
- Percent and interest. Compound interest formula. Exponential and power functions.
logaritmic functions(Elementary Mathematics)
A classical treatment without CAS
- Polynomials. Polynomial division. Polynoimial roots. (Elementary Mathematics)
A classical approach to the theory of polynomials
- Differential calculus (Elementary Mathematics)
A classical approach to differential calculus including continuity, differential quotients, mean value theorem and asymptotes
- Differential equations (Elementary Mathematics)
A classical approach to differential equations, including first order equations. Separation of variables. Second order equations, Wronski determinant.
- Integral calculus (Elementary Mathematics)
A classical approach to integral calculus, including intgration by parts,integral and sums, Simpsons formula, integration by substitution,
evaluation of area, volumes, curve length and surfaces
- Differential equation models(Elementary Mathematics)
The dependence of pressure with height. The propagation of a flu epidemic. The interaction between predetor and prey. Two species competing on food
- Parameter curves(Elementary Mathematics)
A study in parametric curves. Differentiability and tangents. Length of curves. Areas. Archimedes spiral, logarithmic spiral
- The Conics. The ellipse, the hyperbola and the parabola.(Elementary Mathematics)
A classical analytical and geometrical approach to the conics
- Space geometry with vectors. (Elementary Mathematics)
Vectors in 3D space. scalar product, cross product, equation for a plane, distance from a point to a plane, distance between two skewed lines,
triple vector products, determinants, three equations with 3 unknowns
- Probability Theory. An introduction and beyond
A textbook on probability theory that goes beyond the introductory level.
- Numerical methods(Elementary Mathematics)
Bisection, Regulae Falsi, Newton Raphson's method