Pereyra N. Limits and Derivatives of Real Functions for Physicists 2025

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Pereyra N. Limits and Derivatives of Real Functions for Physicists 2025

Textbook in PDF format Limits and Derivatives of Real Functions for Physicists offers a comprehensive and rigorous exploration of essential calculus concepts, specifically tailored for physics majors. This book provides an in-depth introduction to the limits and derivatives of real functions, with a strong emphasis on practical applications in physics. The book demystifies the "why" behind calculus principles, making advanced mathematical concepts accessible without sacrificing rigor. This text provides precise definitions and properties of limits, continuity, and derivatives, ensuring a solid mathematical foundation. Readers will explore the limits and continuity of single-variable functions, as well as the properties and applications of derivatives. By emphasizing the connection between calculus and its applications in physics, students gain a deeper appreciation of the material and its relevance to their studies. The book covers the derivatives of exponential, logarithmic, and trigonometric functions, all of which are pivotal in various physics contexts. Designed to bridge the gap between theoretical rigor and practical application, it serves as an indispensable resource for advanced undergraduate students seeking to deepen their understanding of calculus within a physics context. Whether preparing for higher-level studies or looking to strengthen their foundational knowledge, readers will find this text to be a valuable asset in their academic journey. The book's physics-centric approach and rigorous yet accessible presentation makes it a unique and essential resource for natural science majors. Clear, methodical explanations and numerous examples throughout the book facilitate understanding and retention of complex concepts. Key Features: Delves into the precise definitions and properties of limits, continuity, and derivatives, ensuring a solid mathematical foundation. Provides the reader with a strong foundation for developing analytic and problem-solving skills aimed towards calculus problems that are found throughout Physics and natural sciences in general. Engages with a wide array of examples designed to reinforce learning and develop problem-solving skills. Preface. Acknowledgments. Author Biography. Review of Logic, Set Theory, Isomorphism, and Natural Numbers. Review of Integers, Rational Numbers, and Real Numbers. Review of Convergent Real Number Sequences and Real Exponentiation. Review of Trigonometric Functions. Additional Properties of Trigonometric Functions. Intervals and Regions in R. Additional Properties of Limits. Continuous Functions. Derivatives of Real Functions. Additional Properties of Derivatives. Derivatives of Exponential and Logarithmic Functions. Derivatives of Trigonometric Functions. Analysis of Differentiable Functions. App. A - Initial Review. App. B - Geometry & Trigonometry. App. C - Intervals and Regions in R. App. D - Limits. App. E - Derivatives. References. Index