Elements of Mathematical Analysis
Description
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.
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Dr. Costas J. Papachristou is a senior faculty member at the Hellenic Naval Academy (The Naval Academy of Greece). He received a Ph.D. in Theoretical Physics from Brigham Young University, USA, and spent another year at BYU as a research faculty in Physics. At the HNA, he teaches freshman- and sophomore-level Physics. His research interests are mainly in Theoretical and Mathematical Physics (in particular, symmetry and integrability properties of classical field equations, classical electromagnetism), but he is also active in Physics Education. He is an amateur musician and a columnist for Greek newspapers and magazines.
Content
1. Functions.- 2. Derivative and Differential.- 3. Some Applications of Derivatives.- 4. Indefinite Integral.- 5. Definite Integral.- 6. Series.- 7. An Elementary Introduction to Differential Equations.- 8. Introduction to Differentiation in Higher Dimensions.- 9. Complex Numbers.- 10. Introduction to Complex Analysis.- Appendix.- Answers to Selected Exercises.- Selected Bibliography.- Index.