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Mouthfuls of Learning, Winning, and Aspiring

I’ve just completed my 11th math-focused blog.  That in and of itself isn’t anything interesting or remarkable, just the 11th installment of mini-proofs of my commitment to achieving a goal.  The Math study is very important to me.  Despite my…

  • Urgent Excellence
  • November 30, 2025
  • Math Notebook

Power Series, Calculus of Power Series, and Ratio Test for Interval of Convergence

Date Range: November 24 – November 28 Hours Spent:12.5 hours   Summary: Power series are infinite series in the form of  Where c is the center and are the coefficients.  The standard form is the special case centered at c…

  • Urgent Excellence
  • November 30, 2025
  • Math Notebook

Convergence of Alternating Series, Absolute Convergence, Ratio Test, and Root Test for Series

Date Range: November 16 – November 22 Hours Spent:20 hours Summary: This blog entry is a little lengthier than normal as it’ll be covering two different sections.  That’s because Professor Leonard lectured on Alternating Series first, but the textbook covered…

  • Urgent Excellence
  • November 25, 2025
  • Math Notebook

The Comparison Test and Limit Comparison Test for Series

Date Range: November 10 – November 15 Hours Spent:14 hours This unit, as the name implies, covers two comparisons that are used to determine convergence or divergence of a series.  So I’ll break it down by comparison. The Comparison Test…

  • Urgent Excellence
  • November 15, 2025
  • Math Notebook

Integral Test for Convergence of Series; P-Series

Date Range: November 5 – November 10 Hours Spent:14 hours:  Summary: Calculus 2 has basically been “here is an integration technique for integrating terms that you don’t yet know how to integrate” repeated over and over.  Now I wade into…

  • Urgent Excellence
  • November 12, 2025
  • Math Notebook

Series, Geometric Series, Harmonic Series, and Divergence Test

Date Range: November 1 – November 5 Hours Spent:14 hours –   We’re introduced to telescoping series, e.g. n=1[1/(2n+3) – 1/(2n + 1)] which result in partial sums made up of the first and last terms of the respective partial series.…

  • Urgent Excellence
  • November 8, 2025
  • Math Notebook

Convergence and Divergence of Sequences

Date Range: October 27 – October 31 Hours Spent: 15 Summary:I’ve begun a new unit on infinite sequences and series.  Herein was an introduction to what sequences are, how to write them, the terminology, etc.  I first am taught to…

  • Urgent Excellence
  • November 3, 2025
  • Math Notebook

Solving 1st Order Differential Equations by Separation of Variables

Date Range: October 20 – October 26 Hours Spent: 17 hours Summary:This was an introduction to differential equations – I’ve never dealt with them before.  These are essentially equations involving two different functions, each in terms of separate variables.  I…

  • Urgent Excellence
  • October 30, 2025
  • Math Notebook

Improper Integrals and Collateral Consequences

This is the last blog that was backlogged as a result of my website server blacklisting the Yogyakarta Special Region (and my too easily shelving the task until later).  I’m currently in beautiful Vung Tau, Vietnam, a place I have…

  • Urgent Excellence
  • October 27, 2025
  • Math Notebook

Integration by Partial Fractions

Calculus 2 thus far has been, in a nutshell, “I know how to integrate these, that, and those, but I don’t yet know how to integrate this – so let’s learn how.”  Then, through each successive unit or lesson, I…

  • Urgent Excellence
  • October 23, 2025
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