The tutor shows a simple example of the integral test. The integral test for convergence of an infinite series states that, when an = f(n) both ∑an and ∫1∞f(x)dx either converge or diverge. We can therefore use the integral test …
The tutor points out a very convenient utility. I haven’t upgraded to Windows 10, so am still running Windows 7. From the Start menu (the circle with the colored window panes), if I click All Programs, then Accessories, the desktop …
Math: calculating mortgage payment on the Windows desktop calculator Read more »
The tutor shares a really neat find from the world of accounting. Although I’m an academic, the first post-secondary diploma I received, believe it or not, was in accounting and office management. While I haven’t used it much professionally, what …
Accounting and Business: Depreciation: Sum-of-years’-digits method Read more »
The tutor shows how to use a spreadsheet (Excel) to compute a recursive deduction rate using a circular reference. In yesterday’s post I brought up an example in which a deduction depends upon the income minus that same deduction. It’s …
Spreadsheets: Excel circular reference: recursive deduction calculation Read more »
Sometimes, deduction rates can be tricky. The tutor offers an example of a “circular argument.” Let’s imagine a benevolent employer offers a health plan that costs 6% of the employee’s net income. The company’s definition of net income is gross …
The tutor shows an example of naming items in a spreadsheet for use in a formula. This post focuses on Microsoft Excel; hopefully I’ll do a similar one for a generic spreadsheet soon. Let’s imagine Jones faces two tax rates: …
The tutor shows how to find the general solution to the recurrence relation from last post. In my previous post I posed the recurrence relation 2an+1 – an = 3, a0=12 then generated the first few terms: The general solution …
Math: finding the general solution to a first degree nonhomogeneous recurrence relation Read more »
The tutor introduces a first degree non-homogeneous recurrence relation. An equation that describes a list of terms by a relationship among consecutive ones is called a recurrence relation. Some people call it a difference equation. An example: 17an+1 – 5an …
Math: First degree recurrence relation aka difference equation Read more »
The tutor considers a problem from Grimaldi about max trail length on Kn. For a briefing about the complete graph Kn, check my post from yesterday. In graph theory, a trail is a route that doesn’t repeat any edges. Unlike …
Math and Comp Sci: Graph theory: Max trail length on complete graph, Kn Read more »
The tutor introduces the idea of the complete graph. The complete graph on n vertices, Kn, means the graph in which each vertex is connected to each other one. When two vertices are connected by an edge, they can be …