What the rain knows

I’m not sure yet precisely how I should try working through Apostol. The last time that I did a mathematics book, it was a probability and stats text, and I ended up solving all of the exercises for which there were solutions in the back of the book, longhand, in a couple of marble composition notebooks. In each instance where I chose to use R or MS Excel to solve a problem (sometimes, I will sheepishly admit, instead of working it through by hand), I would print out the commands used and the results and tape them onto the relevant notebook page.

I used Gunnlaugur Þór Briem’s bash script to install Steve Mayer’s LatexRender plugin and can testify that it works, but am not sure how much practical it would be to use this blog as a notebook. Probably not very.

I’m thinking of reading CaF and Apostol in parallel.

Both volumes of my set are from the 32nd printing. The books themselves are simple, but definitely exude that can’t-quite-put-your-finger-on-it 1960’s math and engineering textbook charm.

From the Excerpts from the Preface to the First Edition

It is possible to combine a strong theoretical development with sound training technique; this book represents an attempt to strike a sensible balance between the two. While treating the calculus as a deductive science, the book does not neglect applications to physical problems.

The approach of this book has been suggested by the historical and philosophical development of calculus and analytic geometry. For example, integration is treated before differentiation. Although to some this may seem unusual, it is historically correct and pedagogically sound.

When I read the above, Apostol’s approach didn’t strike me as odd. I was an engineering student at a large East-Coast American state university in the mid-1990’s and I could have sworn that they began with integrals as well. Shock: I popped open my copy of Thomas and Finney’s Calculus and Analytic Geometry (8th ed.) just now and, lo and behold, they start out with derivatives.

From the Preface to the Second Edition

Differences from the first edition:

• Linear algebra added.
• Mean-value theorems and applications of calculus show up earlier in the text.
• Smaller chapters centered on a single main idea.