- Fourier Series and Fourier Integrals An introduction, but at university level
- Differential geometry 1. Surfaces in 3-dimensional space. Students outline Parameter curves. Differentiable surfaces. Shortest path, covariant derivative, Christoffel symbols and Gauss' theorem
- Differential geometry 2. Tensor analysis with application to General Relativity. Students outline (pdf) Linear algebra and tensors. Generalized coordinates i n-dimensions. Covariant derivative. Parallel transport. Riemanns curvature tensor. Einstein's tensor
- Taylors formula. (pdf) A derivation of Taylor's formula with application to Maclaurin series of standard functions.
- Probability Theory. An introduction and beyond A textbook on probability theory that goes beyond the introductory level.
- The Platonic solids. The five regular polyhedra Proof of Eulers polyhedron theorem. The Dihedral angles, and radii of the inscribed and circumscribed spheres of the the five regular polyhedrons.
- Spherical geometry. A classical approach The right angle spherical tringle. Cosine- and sine relations for the general spherical triangle. Area of a spherical triangle.
- Calculus of Variations. Applied to known and unknown problems Euler-Lagrange equations. The simplest problem. Largest volume for a given surface. The suspended chain. The Brachistochrone. On the shape of soap membranes. On the shape of wine barrels. On the shape of a hanging water drop
- Eigenvalue problems in linear algebra. (pdf) A general discussion of algebra of matrices, and their eigenvalues. Illustrated by an example.
- Implicit_differentiation with examples. (pdf) The equation for the tangent to an ellipse. The least bending of a beam through a prism in
- Games: Probabilities and strategies Lotto, Poker, Casino. Ruin probabilities. Theory of strategies. The optimal strategy (Snell-strategy). Examples of using strategies.
- The birthday problem and other improbable probabilities The coin in the three boxes, The card game "war",(number of permutations with no fixed elements), the Sct. Petersborg paradox
- The number of bricks in a four sided pyramid. The number of oranges in a three sided_pyramid Deriving a solution to two classical problems.
- The Brachistocrone and the Tautocrone.
- Vector Analysis
- The peculiar Fibonacci numbers. A note of the properties of the Fibonacci numbers.
- 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.
- Submarine hunting and the logarithmic spiral

Two classical problems solved by advanced calculus

The gradient, divergence, and curl. Gauss' Stokes and Green theorems. Vector analysis in curvilinar coordinates.

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