Advanced Calculus Explored: With Applications in Physics, Chemistry, and Beyond

Advanced Calculus Explored provides a fundamental, easy-to-follow approach to understanding higher-level maths that are not typically encountered until advanced collegiate studies. Rather than merely providing an overview of various theorems, or writing the book with intense mathematical rigor, the author extends his scope in making such topics more accessible through copious example problems and graphics. Hence, this book only assumes only a knowledge of elementary high-school calculus to follow along. Focusing first on introductory differential calculus, the author guides math enthusiasts through example problems that build on each other. Before you know it, the problems you are solving are those that build upon the foundations that are required to understand more niche math topics (such as the Gamma Function).Furthermore, this book provides insights behind the novel, powerful techniques of integration which are not taught in a standard calculus course. Such methods of integration not only help in understanding material of later chapters, but also prove of great utility for applied mathematicians and engineers. The graph-heavy chapters involving special functions and series take what was once pages of symbols and indices, and solidifies understanding of concepts which can be applied to solve unique problems in the book. Some problems, albeit challenging, stimulate thinking and application of the mathematics robustly presented in the book. Moreover, the author includes several chapters on applications of the mathematics presented in the book, which further materializes the concepts at hand. Advanced Calculus Explored is a compelling read for engineers, applied mathematicians, and anyone interested in calculus. The seamless integration of graphics and makes it even more ideal for those who are not used to mathematical rigor developed in an analysis class and can provide new insights to those who have had prior exposure to the material presented in this book. The combination of the quality of graphics the author uses, the fluidity of his presentation, and the accessibility of his writing make Advanced Calculus Explored hard to put down.

Advanced Calculus Explored is written for anyone with a strong mathematical curiosity. Although only a basic calculus background is required, the results presented combine classical techniques with creative, non-standard methods to make traditionally difficult problems quite basic. It does not feel like a technical read, but a fluid, dynamic body of math the reader engages and interacts with.The text builds up from the fundamental basics of calculus in limits and differential operations, but quickly establishes the bridge to advanced mathematical concepts (i.e. the zeta function). This process feels gradual and natural, despite the fact that many engaging and challenging problems are presented.Advanced Calculus Explored is rigorous in terms of definitions and theorems, yet the concepts are presented in such a way to emphasize intuition and deeper understanding through example and graphical application rather than classically heavy, proof-laden language. Because of this, more insight is gleaned of the fundamental workings behind techniques employed.In terms of integration techniques, this text takes a leaf of Feynman’s book by presenting many more unorthodox and non-standard methods (including Feynman Integration itself (; ) to attack more complex problems. Any reader can take away a diverse toolkit of ideas to simplify many complex problems. At the same time, Advanced Calculus Explored also presents many classical proofs and integrals to further the diversity across which it reaches.Advanced Calculus Explored also highlights an entire section of applications in the fields of chemistry, physics, statistics, and more! These applications further diversify the intended audience of the text. Anyone interested in applied mathematics or calculus topics will greatly benefit from this book.

I got this book 2 months ago for my son who wanted a challenge after taking multivariable calculus. Ever since he's been deeply invested in the book. He was intrigued by the steady progression of concepts as well as the explorations of several surprising ideas in the book, such as fractional calculus and switching the order of a summation and an integral. Despite being advanced, this book provides a friendly and comprehensive breakdown of each of these concepts that is easy to digest with just AP Calculus BC knowledge. At the end of each chapter, this book provides several challenging problems with answers in the back. My son enjoyed working out each problem and was happy to see his growth as he began to solve more and more of these challenging problems.Not only does this book teach these advanced concepts excellently, it also has a section containing the applications of these advanced concepts in physics and chemistry. My son found this particularly helpful as he was able to use his understanding of math to expand his knowledge from his science classes.I highly recommend this book to any aspiring mathematician or scientist looking for a challenge.

nice and hope see version 2 soon