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University Physics and Mathematics

University Mathematics. Explained!

• Elementary Mathematics. A traditional (no CAS) text book on mathematics, from high school to university
• Fourier Series and Fourier Integrals
• The duration of and the extent of influenza epidemics (Corona)
• Vector Analysis
• Solving Partial differential equations using generalized coordinates
• Taylors formula and Maclaurin series for standard functions
• Finite and infinite series. (pdf)
• Differential Geometry 1. Parameter curves and 2-dimensional surfaces
• Differential Geometry 2. Tensor analysis and curvature with application to General Relativity
• Spherical geometry. A classical approach
• Equation of a great circle
• Probability Theory. An introduction and beyond
• Games: Probabilities and strategies
• Calculating probabilities for gain in EuroJackpot and Danish lotto
• The birthday problem and other improbable probabilities
• Eigenvalue problems in linear algebra. (pdf)
• The mathematics behind parallel and central projections
• Calculus of Variations. Solution to known and unknown problems
• The Platonic solids. The five regular polyhedra
• The formula for the sums of n integers raised to a integer power
• The number of bricks in a four sided pyramid. The number of oranges in a three sided pyramid
• Geometrical constructions of ovals and of the golden ratio
• The peculiar Fibonacci numbers.
• Achilles and the turtle paradox
• Elementary Group theory
• Advanced Group Theory
• The complex number system
• Quaternion. A mathematical monster
• Solution formula for the cubic (third degree) equation
• Analytic (holomorphic) functions
• Laurent series. Residues. Contour integrals
• The Brachistochrone and the Tautochrone.
• The exact value of the sum of the reciprocals of n-square. The value of Zeta(2), Zeta(4)and Zeta(6)
• On queues in highways and before traffic lights.
• Economic models for small enterprises.
• Elementary national economics. A mathematical approach
• The mathematics of chasing and escaping
• Linear programming by examples
• Submarine hunting and the logarithmic spiral
• Legendre and the associated polynomials (explained)
• Elementary Numerical methods
• Weierstrass approximation theorem
• Lagranges interpolation formula
• Elementary Perturbation_theory
• Markov chains examples
• Limiting distributions of Markov chains
• Olympic mathematical problems 1
• Olympic mathematical problems 2
• Olympic mathematical problems 3
• Olympic mathematical problems 4
• Olympic mathematical problems 5.
• Olympic mathematical problems 6.
• Olympic mathematical problems 7.
• Olympic mathematical problems 8.

University Physics. Explained!

• Elementary Physics 1-3. A textbook on physics.
  (University undergraduate level)
• Elementary Physics 1
• Elementary Physics 2
• Elementary Physics 3
• The Special Theory of Relativity
• General Relativity and Cosmology
• The Hydrogen atom from Rutherford to Schrödinger
• Cosmology, a survey
• Statistical Mechanics
• Quantum Statistics
• The First and Second Law of Thermodynamics
• The heat pump
• Brownian movement and the determination of Avogadro's number
• Newtonian Mechanics: Dynamics
• Simulations of stable and unstable three body motion
• Theory of Rotation.
• Geometrical optics
• Can you score on a corner kick? (A theoretical approach)
The physics of rockets. (For educational purposes)
• Non trivial examples of the differential equations of physics
• Physics of Tsunamis
• Hydrodynamics (is complex mathematics)
• The two-body problem and The laws of Kepler
• The Principle of least time and the law of refraction
• A shooting star. A theoretical approach
• Applications of the wave equation
• The physics of Air Mirroring and Mirages
• Coupled pendulums and coupled harmonic oscillations
• Chaotic motion. A dynamic analysis
• Bicycle Physics
• Gyroscopes, tops, rotating eggs and other rotating objects
• The physics of induction stoves
• The physics of curling
• Twenty questions from the engineers letterbox.
• Examples of damped periodic motion
• Finding the longest oblique throw from a given height
• The deathdrome. Riding the wall of death and related problems
• Why can a box only rotate freely about two of its three principal axes?
• Circular waves and the Bessel functions
• The Conical pendulum
• Motion on a rotating disc
• Solution of the diffusion equation in spherical and cylindrical coordinates
• The Law of Bernouilli, with applications to flying and hydrodynamics
• The physics of windmills
• Calculating the runway before take off, and the buoyancy for the DC-7
• The Tides. The contributions from the moon and the sun
• Balancing or tipping over
• Does the boat capsize
• On Mercury and Venus passages over the sun
• On power, intensity and loudness in dB of sound
• Emptying a barrel from a tap
• Motion of a projectile with and without drag
• Damped and forced harmonic oscillations
• Radioactive decay chains
• Vertical motion with turbolent resistance
• Linear motion in liquid and gasses
• The dependence of pressure on altitude
• Theory of elasticity
• Dynamics of deformable bodies
• Surface tension with applications
• The peculiar Coriolis force
• The buoyancy of a hot air balloon
• Differential equatioms for filling a tub with hot water from a heating tank

Matematik, Fysik og Datalogi
Fra gymnasium til universitet

Fysik

Elementær Fysik 1 . Lærebog for gymnasiet 1g(1978)

Elementær Fysik 2. Lærebog for gymnasiet 2g (1979)

Elementær Fysik 3. Lærebog for gymnasiet 3g (1980)

Større Temahefter i fysik

Mindre Artikler

Artikler til LMFK-bladet

Programmer til fysik.

Matematik

Elementær Matematik:Et udvidet lærebogssystem i Matematik for gymnasiet

Temahefter i Matematik

Artikler til LMFK-bladet

Matematisk Analyse et større matematik program (fra 1999)

Datalogi

Java applets (spil) til undervisningsbrug

Java scripts (spil) til undervisningsbrug

Spil skrevet i Delphi

Lærebøger i programmering