Bill Kinney Math Archives - Infinity is Really Big

October 29, 2019October 29, 2019

Differentiable Functions and Local Linearity

Calculus 1, Lectures 12 through 15B

An infinitely oscillating continuous and differentiable function. — *This function is both continuous and smooth at $x=0$ , in spite of oscillating infinitely often in any neighborhood of $x=0$ .*

*This function is both continuous and smooth at $x=0$ , in spite of oscillating infinitely often in any neighborhood of $x=0$ .*

In Steven Strogatz’s excellent book, Infinite Powers, there is a big emphasis on an idea he calls The Infinity Principle.

The concepts of a continuous function and of a differentiable function are … Read the rest

January 18, 2019January 28, 2019

New Video: Derivatives of Bond Prices w.r.t. Parallel Shift in Yield Curve

The series of payments that arises from a coupon bond is an example of a cashflow that can be assigned a “duration“.

A coupon bond can be purchased as an investment that pays “coupons”, which are fixed amounts of money, at certain equally-spaced times during the term of the investment, plus a redemption … Read the rest