Costas J. Papachristou – författare

This book consists of two parts. Part A (Chapters 1-3) is an introduction to the physics of conducting solids, while Part B (Chapters 4-10) is an introduction to the theory of electromagnetic fields and waves. 

The book is intended to introduce the student to classical electrodynamics and, at the same time, to explain in simple terms the quantum theory of conducting substances – in particular, the solid ones. Excessive mathematical proof is avoided as much as possible, in favor of pedagogical efficiency at an introductory level. The theory of vector fields is briefly discussed in a separate chapter, helping the student cope with the mathematical challenges of Maxwell''s theory. 

The book serves as a primary source for a sophomore-level electromagnetics course in an electronics-oriented engineering program, but it can also be used as a secondary (tutorial) source for an intermediate-level course in electrodynamics for physicists and engineers. The content isbased on the author’s lecture notes for his sophomore-level Physics course at the Hellenic Naval Academy.

This book serves as an introduction to the concept of integrability as it applies to systems of differential equations as well as to vector-valued fields.

The author focuses on specific aspects of integrability that are often encountered in a variety of problems in applied mathematics, physics and engineering. The following general cases of integrability are examined: (a) path-independence of line integrals of vector fields on the plane and in space; (b) integration of a system of ordinary differential equations by using first integrals; and (c) integrable systems of partial differential equations. Special topics include the integration of analytic functions and some elements from the geometric theory of differential systems. Certain more advanced subjects, such as Lax pairs and Bäcklund transformations, are also discussed.

The book is written at an intermediate level for educational purposes. The presentation is as simple as the topics allow, often sacrificing mathematical rigor in favor of pedagogical efficiency.

This book is based on the author’s lecture notes for his Introductory Newtonian Mechanics course at the Hellenic Naval Academy. In order to familiarize students with the use of several basic mathematical tools, such as vectors, differential operators and differential equations, it first presents the elements of vector analysis that are needed in the subsequent chapters. Further, the Mathematical Supplement at the end of the book offers a brief introduction to the concepts of differential calculus mentioned.  

The main text is divided into three parts, the first of which presents the mechanics of a single particle from both the kinetic and the dynamical perspectives. The second part then focuses on the mechanics of more complex structures, such as systems of particles, rigid bodies and ideal fluids, while the third part consists of 60 fully solved problems.  

Though chiefly intended as a primary text for freshman-level physics courses, the book can also be used as a supplemental (tutorial) resource for introductory courses on classical mechanics for physicists and engineers

This book provides a comprehensive yet informal introduction to differentiating and integrating real functions with one variable. It also covers basic first-order differential equations and introduces higher-dimensional differentiation and integration.

The focus is on significant theoretical proofs, accompanied by illustrative examples for clarity. A comprehensive bibliography aids deeper understanding. The concept of a function''s differential is a central theme, relating to the "differential" within integrals. The discussion of indefinite integrals (collections of antiderivatives) precedes definite integrals, naturally connecting the two. The Appendix offers essential math formulas, exercise properties, and an in-depth exploration of continuity and differentiability. Select exercise solutions are provided.

This book suits short introductory math courses for novice physics/engineering students. It equips them with vital differentialand integral calculus tools for real-world applications. It is also useful for first-year undergraduates, reinforcing advanced calculus foundations for better Physics comprehension.