Vector and Complex Calculus A Textbook for Students of the Physical Sciences
“Vector and Complex Calculus: A Textbook for Students of the Physical Sciences” by Fabian Waleffe is a comprehensive resource published by Oxford University Press on October 15, 2024. This 416-page textbook is written in English and serves as an advanced guide for students delving into the essential mathematical concepts required for applications in electromagnetism, fluid and solid mechanics, and the differential geometry of surfaces.
Readers will find a thorough exploration of vector and complex calculus, moving beyond standard multivariable calculus courses. The book covers topics such as the geometry and algebra of vectors, differential geometry of curves and surfaces, and curvilinear coordinates, culminating in a study of functions of one complex variable. Rich illustrations enhance the learning experience, while exercises at the end of each chapter encourage practice and deeper exploration of key concepts. This textbook is designed to provide foundational knowledge crucial for upper-level engineering and physics courses.
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Vector and complex calculus are essential for applications to electromagnetism, fluid and solid mechanics, and the differential geometry of surfaces. Moving beyond the limits of standard multivariable calculus courses, this comprehensive textbook takes students from the geometry and algebra of vectors, through to the key concepts and tools of vector calculus. Topics explored include the differential geometry of curves and surfaces, curvilinear coordinates, ending with a study of the essential elements of the calculus of functions of one complex variable. Vector and Complex Calculus is richly illustrated to help students develop a solid visual understanding of the material, and the tools and concepts explored are foundational for upper-level engineering and physics courses. Each chapter includes a section of exercises which lead the student to practice key concepts and explore further interesting results.
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