A computer algebra system such as Mathematica® is able to do much more than just numerics: This text shows how to tackle real mathematical problems from basic analysis. The reader learns how Mathematica® represents domains, qualifiers and limits to implement actual proofs – a requirement to unlock the huge potential of Mathematica® for a variety of applications.

A computer algebra system such as Mathematica® is able to do much more than just numerics: This text shows how to tackle real mathematical problems from basic analysis. The reader learns how Mathematica® represents domains, qualifiers and limits to implement actual proofs – a requirement to unlock the huge potential of Mathematica® for a variety of applications.

The book deals with functions of many variables: differentiation and integration, extrema with a number of digressions to related subjects such as curves, surfaces and Morse theory. The background needed for understanding the examples and how to compute in Mathematica® will also be discussed.

The book deals with functions of many variables: differentiation and integration, extrema with a number of digressions to related subjects such as curves, surfaces and Morse theory. The background needed for understanding the examples and how to compute in Mathematica® will also be discussed.

This book is devoted to applications: differential equations, elements of special functions and differential geometry of curves and surfaces with a specific focus on visualization in Mathematica®. Discusses how Mathematica® can be used as an aid in solving mathematical problems and discovering a solution. A complete tutorial provides the background needed for understanding the examples and how to compute in Mathematica®.

This book is devoted to applications: differential equations, elements of special functions and differential geometry of curves and surfaces with a specific focus on visualization in Mathematica®. Discusses how Mathematica® can be used as an aid in solving mathematical problems and discovering a solution. A complete tutorial provides the background needed for understanding the examples and how to compute in Mathematica®.

This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics.

It will be of interest to graduate students, early-career researchers and specialists in analysis, geometry, algebra and related areas, as well as anyone interested in learning new methods and techniques.

A computer algebra system such as Mathematica® is able to do much more than just numerics: This text shows how to tackle real mathematical problems from basic analysis. The reader learns how Mathematica® represents domains, qualifiers and limits to implement actual proofs – a requirement to unlock the huge potential of Mathematica® for a variety of applications.

A computer algebra system such as Mathematica® is able to do much more than just numerics: This text shows how to tackle real mathematical problems from basic analysis. The reader learns how Mathematica® represents domains, qualifiers and limits to implement actual proofs – a requirement to unlock the huge potential of Mathematica® for a variety of applications.

The book deals with functions of many variables: differentiation and integration, extrema with a number of digressions to related subjects such as curves, surfaces and Morse theory. The background needed for understanding the examples and how to compute in Mathematica® will also be discussed.

The book deals with functions of many variables: differentiation and integration, extrema with a number of digressions to related subjects such as curves, surfaces and Morse theory. The background needed for understanding the examples and how to compute in Mathematica® will also be discussed.

This book is devoted to applications: differential equations, elements of special functions and differential geometry of curves and surfaces with a specific focus on visualization in Mathematica®. Discusses how Mathematica® can be used as an aid in solving mathematical problems and discovering a solution. A complete tutorial provides the background needed for understanding the examples and how to compute in Mathematica®.

This book is devoted to applications: differential equations, elements of special functions and differential geometry of curves and surfaces with a specific focus on visualization in Mathematica®. Discusses how Mathematica® can be used as an aid in solving mathematical problems and discovering a solution. A complete tutorial provides the background needed for understanding the examples and how to compute in Mathematica®.

This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics.

It will be of interest to graduate students, early-career researchers and specialists in analysis, geometry, algebra and related areas, as well as anyone interested in learning new methods and techniques.