Comment by m31415 | Hacker News Reader

Comment by m31415 | Hacker News Reader

For mathematics, I would recommend:

1. "What Is Mathematics? An Elementary Approach to Ideas and Methods" by Courant and Robbins -- a general book on mathematics in the spirit of Feynman lectures.

2. Strogatz's "Nonlinear Dynamics and Chaos" -- it's a bit narrow in scope (mostly dynamical systems with a little bit of chaos/fractals thrown in) but very good nonetheless.

3. Tristan Needham, "Visual Complex Analysis", beautiful introduction to complex analysis.

4. Cornelius Lanczos, "The Variational Principles of Mechanics" -- this is a physics book, but one of the classics in the subject, and as Gerald Sussman once remarked, you glean new insights each time you read it.

5. Cornelius Lanczos, "Linear Differential Operators" -- an excellent treatment of differential operators, Green's functions, and other things that one encounters in infinite-dimensional vector spaces. This book has some very intuitive explanations, e.g., why d/dx is not self-adjoint (i.e., Hermitian), whereas d^2/dx^2 is.

For chemistry, I would recommend "General Chemistry" by Linus Pauling, even though it's a bit outdated.

"Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University" is available[0] on youtube as a series of 25 lectures. (From 2014.)

From the description:

"This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. It closely follows Prof. Strogatz's book, "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering."

The mathematical treatment is friendly and informal, but still careful. Analytical methods, concrete examples, and geometric intuition are stressed. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

A unique feature of the course is its emphasis on applications. These include airplane wing vibrations, biological rhythms, insect outbreaks, chemical oscillators, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with the mathematical theory. The theoretical work is enlivened by frequent use of computer graphics, simulations, and videotaped demonstrations of nonlinear phenomena.

The essential prerequisite is single-variable calculus, including curve sketching, Taylor series, and separable differential equations. In a few places, multivariable calculus (partial derivatives, Jacobian matrix, divergence theorem) and linear algebra (eigenvalues and eigenvectors) are used. Fourier analysis is not assumed, and is developed where needed. Introductory physics is used throughout. Other scientific prerequisites would depend on the applications considered, but in all cases, a first course should be adequate preparation."

[0] https://www.youtube.com/playlist?list=PLbN57C5Zdl6j_qJA-pARJ...

Just a note, "Visual Complex Analysis" is a terrible book to learn complex analysis. Proofs are very iffy, akin to sketches of proofs. With that said, it is a excellent supplement to another std. complex analysis textbook.

Is it just the normal difference between e.g. an engineer's approach to real analysis and a mathematicians (but complex analysis swapped in), or something else?

I can think of a lot of fields where a decent grasp of complex analysis concepts would be very helpful even without being able to do rigorous proofs.

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