Mukhi, Lectures on Advanced Mathematical Methods for Physicists
This book surveys Topology and Differential Geometry and also, Lie Groups and Algebras, and their Representations. The former topic is indispensable to students of gravitation and related areas of modern physics, including string theory. The latter has applications in gauge theory and particle physics, integrable systems and nuclear physics, among many others. The style of presentation is such that the mathematical statements are succinct and precise, but skip involved proofs that are not of primary importance to the physics reader.
Intended as a companion for textbooks in mathematical methods for science and engineering, this book presents a large number of numerical topics and exercises together with discussions of methods for solving such problems using Mathematica. The accompanying CD contains Mathematica Notebooks for illustrating most of the topics in the text and for solving problems in mathematical physics.
TTC Video - Understanding Calculus: Problems, Solutions, and Tips
Calculus is the greatest mathematical breakthrough since the pioneering discoveries of the ancient Greeks. Without it, we wouldn't have spaceflight, skyscrapers, jet planes, economic modeling, accurate weather forecasting, modern medical technologies, or any of the countless other achievements we take for granted in today's world. Accomplish Mathematical Wonders Calculus is one of the most powerful and astonishing tools ever invented, yet it is a skill that can be learned by anyone with an understanding of high school mathematics.
Mathematical Analysis of Problems in the Natural Sciences
Based on a two-semester course aimed at illustrating various interactions of "pure mathematics" with other sciences, such as hydrodynamics, thermodynamics, statistical physics and information theory, this text unifies three general topics of analysis and physics, which are as follows: the dimensional analysis of physical quantities, which contains various applications including Kolmogorov's model for turbulence; functions of very large number of variables and the principle of concentration along with the non-linear law of large numbers, the geometric meaning of the Gauss and Maxwell distributions, and the Kotelnikov-Shannon theorem;
Do you think "math = awesome" is a true statement? After reading this book, you might change your answer to a yes. With "jargon avoidance" in mind, this recreational math book gives you the lowdown on why math is fun, interesting and relevant in today's society. Intended for anyone who is curious about math and where it is circa 2010. This book is less concerned with exploring the mathematical details than it is with exploring the overall impact of various discoveries and insights, and aims to be insightful, cutting edge-y and mathematically rigorous.
