Mathematical Methods in Engineering & Physics (Oct. 1970 - June 1971)

By some who have seen samples of my notes Volume 5 has been referred to as the “missing lectures” to the FLP “Red Books”. Feynman himself felt that he should have taught the mathematical methods first and then the physics since math is the “language” of physics. Feynman was apparently talked out of starting with a course in math-physics. The attendees at the lab talked him into a year-long lecture on his approach to mathematics as the language of physics. I note here also that the math lectures have been referred on the Reddit by someone as “sophomoric” since all physic students must take similar course work and presumably “master” math while learning the physics. In my own case I wanted to learn the physics and minimize the math, or better said, not confused by the physics because the math was too difficult to grasp. This is how Feynman approached physics and how he taught himself, at an early age, by developing many shortcuts through the math; “Feynman diagrams” were one clear by product of his self learning process. He did not want to get bogged down and distracted from understanding the physics. This is why and how he got involved in the Manhattan Project; he was their math wizard. One story he told of those days: Someone came running into him needing a quick answer to a nuclear decay process that was described by some expansion series like the Sum from 1 to infinity of 1/(1+n^2)[probably not the real one]. Feynman asked how accurately he wanted the answer and the person said 10% would do for now. Feynman said he took a few seconds and said the answer was 1.3 (or something like that); the person was amazed how fast he could give him that and asked how he did it. He said since you told me you only wanted the answer to 10%, it was only necessary to go to the second term in the series expansion and that was good enough for better than 10% accuracy. This story is emblematic of Feynman’s mathematical thinking which is not sophomoric. This is why he made such a contribution to the Manhattan project and ultimately QED. He did indeed “think different”. In my own experience I found in my graduate studies that the some of the professors tended to focus more on the math rigor than in teaching the real physics. In Feynman’s world he “felt” the physics and used the math to express that “feeling” and understanding. Language does not necessarily express the essence of the content contained in the idea being described. One must understand both the power and limitations of the language used when discussing a subject. Words don’t always express what one wants to say; so it is for math and physics.