Ebook Download | When Least Is Best | Mr. Nahin states in his preface that 1st year undergraduate math and physics is enough to manage "a lot of mathematics in this book." He is fairly on the mark, discounting my comments about chapter six below. As usual, the reader must keep pencils and scrap paper ready to fully appreciate this book. I hoped to find a book based on applications of math and physics, an engineer's approach. This is one such fascinating book.
I was familiar with the AM-GM inequality technique to find extremas. However, Mr. Nahin dispenses of this method early and shows the reader so much more. And in this book, there is a constant exercise of looking at problems a different way. If you like geometric solutions along with the typical lines of algebraic manipulations, you'll love this book. The first five chapters are packed with problems and solutions with excellent graphic representations. Integration requirements increase throughout.
In finding extremas in chapter six, the author goes beyond ordinary calculus with the calculus of variations including the Euler-Lagrange differential equation and Beltrami's identity. The focus problem is the minimal decent time curve. It is in section 6.4 that the author truly breaks from his stated reader requirements of "high school algebra, trigonometry, and geometry, as well as the elementary integration techniques." I think most authors of this book's scope typically underestimate reader requirements. As for my part, I did not understand the calculus of variations technique on the first reading. After reading sections 6.4 through 6.8 again, I gained an appreciation of how the method works. After one more reading of these sections, I might know just enough to be dangerous. These challenging sections are well written, but a struggle within the stated reader requirements. In various cases, Mr. Nahin works through problems with results generated by computer programs. These are not my favorite problems because I lack access to the high end (very expensive) programs that he uses.
This book is well written and engaging; and it is easier to manage than An Imaginary Tale. This is my second book by Mr. Nahin, and I view him as a favorite author of technical books. In this review, I intentionally avoided mentioning specific problems covered because I do not want to spoil the surprises. I found them all quite fascinating. The reader will see so many real world physics in a different light. I highly recommend this book.
I was familiar with the AM-GM inequality technique to find extremas. However, Mr. Nahin dispenses of this method early and shows the reader so much more. And in this book, there is a constant exercise of looking at problems a different way. If you like geometric solutions along with the typical lines of algebraic manipulations, you'll love this book. The first five chapters are packed with problems and solutions with excellent graphic representations. Integration requirements increase throughout.
In finding extremas in chapter six, the author goes beyond ordinary calculus with the calculus of variations including the Euler-Lagrange differential equation and Beltrami's identity. The focus problem is the minimal decent time curve. It is in section 6.4 that the author truly breaks from his stated reader requirements of "high school algebra, trigonometry, and geometry, as well as the elementary integration techniques." I think most authors of this book's scope typically underestimate reader requirements. As for my part, I did not understand the calculus of variations technique on the first reading. After reading sections 6.4 through 6.8 again, I gained an appreciation of how the method works. After one more reading of these sections, I might know just enough to be dangerous. These challenging sections are well written, but a struggle within the stated reader requirements. In various cases, Mr. Nahin works through problems with results generated by computer programs. These are not my favorite problems because I lack access to the high end (very expensive) programs that he uses.
This book is well written and engaging; and it is easier to manage than An Imaginary Tale. This is my second book by Mr. Nahin, and I view him as a favorite author of technical books. In this review, I intentionally avoided mentioning specific problems covered because I do not want to spoil the surprises. I found them all quite fascinating. The reader will see so many real world physics in a different light. I highly recommend this book.
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