I am looking for recommendation of 3 different books on the following topics:
1.Differential Equations
-Ordinary diff. equations
-Vector field, transport equations
-Equation of wave and heat
-Use of Fourier series in solving differential equations.
2.Logical components and architecture of the computers
-Logic ports and synthesis of boolean functions
-Completion of operations (adders, multipliers)
-Memory completion/usage, interconnections (BUS)
-Assembly programming, data path, control transfers with wired controllers
3.Differential geometry of curves and surfaces
-Parametrized curves
*tangent, arc length, length, curvature and torsion.
*Envelope of a family of lines in $\mathbb{R}^2$, involutes, caustics.
*Properties such as:
isoperimetry: find hugging curves given maximum length area. rotation number and the integral of curve, deformation invariance, convex curves.
-Parametrized surfaces in $\mathbb{R}^3$
*Examples, a normal, elements of a surface
*Curves on the surface, principal curvatures, mean curvature.
*Practical use such as:
Can a planisphere can truthfully represent the earth?
Being able to distinguish a rugby ball, football and a saddle; seen up close, not far away!
Depending on the time available, describe the relationship with the geometry of films and
soap bubbles.
Thank you in advance!!
The book "Elementary Differential Geometry" by Barret O'Neill book is located on archive.org and is free, Link: https://archive.org/details/ElementaryDifferentialGeometry
There are older books on Differential Geometry at Archive.org also , some of the older books are excellent, although the approach doesn't generally use the exterior calculus.