Henri Bourlès is Full Professor and Chair at the Conservatoire National des Arts et Métiers, Paris, France.

"The present volume is the third one of a series which presents the fundamental elements of advanced mathematics that is at the basis of a number of contemporary scientific methods. More precisely, it deals with differential and integral calculus in their local and global components. The book is designed not only for mathematicians, but also for everyone who uses mathematics and needs to understand the control of nonlinear systems (in particular physicists and engineers). The ambitious goal is achieved also thanks to an excellent organization of the topics and the use of a very clear and understandable language. Interesting short historical notes introduce the different topics and help to frame the evolution of concept. The exposition is illustrated with some figures that help a lot in understanding the not easy topics. Very useful attachments are provided: a careful list of notation and term indeces, a reach bibliography, a list of cited authors with biographical notes." --ZBMath"The book under review is the third volume in a series that lays a solid foundation for advanced mathematics, serving as a fundamental resource for various contemporary scientific methodologies. This particular volume explores the intricate realms of both differential and integral calculus, providing a comprehensive examination of their local and global components. While primarily intended for mathematicians, the book transcends disciplinary boundaries and aims to be read by individuals from diverse fields who utilize mathematics in their work, including physicists and engineers." --MathSciNet

• 1. Differential and analytic manifolds2. Fibered bundles3. Tensor calculus on manifolds4. Differential and integral calculus on manifolds5. Connections6. Calculus of variations and optimal control

Henri Bourlès is Full Professor and Chair at the Conservatoire National des Arts et Métiers, Paris, France.

"The present volume is the third one of a series which presents the fundamental elements of advanced mathematics that is at the basis of a number of contemporary scientific methods. More precisely, it deals with differential and integral calculus in their local and global components. The book is designed not only for mathematicians, but also for everyone who uses mathematics and needs to understand the control of nonlinear systems (in particular physicists and engineers). The ambitious goal is achieved also thanks to an excellent organization of the topics and the use of a very clear and understandable language. Interesting short historical notes introduce the different topics and help to frame the evolution of concept. The exposition is illustrated with some figures that help a lot in understanding the not easy topics. Very useful attachments are provided: a careful list of notation and term indeces, a reach bibliography, a list of cited authors with biographical notes." --ZBMath"The book under review is the third volume in a series that lays a solid foundation for advanced mathematics, serving as a fundamental resource for various contemporary scientific methodologies. This particular volume explores the intricate realms of both differential and integral calculus, providing a comprehensive examination of their local and global components. While primarily intended for mathematicians, the book transcends disciplinary boundaries and aims to be read by individuals from diverse fields who utilize mathematics in their work, including physicists and engineers." --MathSciNet

• 1. Differential and analytic manifolds2. Fibered bundles3. Tensor calculus on manifolds4. Differential and integral calculus on manifolds5. Connections6. Calculus of variations and optimal control

Henri Bourlès is Full Professor and Chair at the Conservatoire National des Arts et Métiers, Paris, France.

"The present volume is the third one of a series which presents the fundamental elements of advanced mathematics that is at the basis of a number of contemporary scientific methods. More precisely, it deals with differential and integral calculus in their local and global components. The book is designed not only for mathematicians, but also for everyone who uses mathematics and needs to understand the control of nonlinear systems (in particular physicists and engineers). The ambitious goal is achieved also thanks to an excellent organization of the topics and the use of a very clear and understandable language. Interesting short historical notes introduce the different topics and help to frame the evolution of concept. The exposition is illustrated with some figures that help a lot in understanding the not easy topics. Very useful attachments are provided: a careful list of notation and term indeces, a reach bibliography, a list of cited authors with biographical notes." --ZBMath"The book under review is the third volume in a series that lays a solid foundation for advanced mathematics, serving as a fundamental resource for various contemporary scientific methodologies. This particular volume explores the intricate realms of both differential and integral calculus, providing a comprehensive examination of their local and global components. While primarily intended for mathematicians, the book transcends disciplinary boundaries and aims to be read by individuals from diverse fields who utilize mathematics in their work, including physicists and engineers." --MathSciNet

• 1. Differential and analytic manifolds2. Fibered bundles3. Tensor calculus on manifolds4. Differential and integral calculus on manifolds5. Connections6. Calculus of variations and optimal control