Mathematics and physics for nanotechnology : technical tools and modelling / Paolo Di Sia.
Sia, Paolo Di| Call Number | 660.6 |
| Author | Sia, Paolo Di, author. |
| Title | Mathematics and physics for nanotechnology : technical tools and modelling / Paolo Di Sia. |
| Physical Description | 1 online resource. |
| Contents | Cover; Half Title; Title Page; Copyright Page; Table of Contents; Preface; 1: Introduction; 1.1 The Nanotechnologies World; 1.2 Classification of Nanostructures; 1.3 Applications of Nanotechnologies; 1.4 Applied Mathematics and Nanotechnology; 1.5 Spintronics, Information Technologies and Nanotechnology; 1.5.1 Spin Decoherence in Electronic Materials; 1.5.2 Transport of Polarised Spin in Hybrid Semiconductor Structures; 1.5.3 Spin-Based Solid State Quantum Computing; 1.5.4 Spin Entanglement in Solids; 1.5.5 Optical and Electronic Control of Nuclear Spin Polarisation 1.5.6 Physics of Computation1.5.7 Quantum Signal Propagation in Nanosystems; 2: Vector Analysis; 2.1 Vectors and Scalars; 2.2 Direction Angles and Direction Cosines; 2.3 Equality of Vectors; 2.4 Vector Addition and Subtraction; 2.5 Multiplication by a Scalar; 2.6 Scalar Product; 2.7 Vector Product; 2.8 Triple Scalar Product; 2.9 Triple Vector Product; 2.10 Linear Vector Space V; 3: Vector Differentiation; 3.1 Introduction; 3.2 The Gradient Operator; 3.3 Directional Derivative; 3.4 The Divergence Operator; 3.5 The Laplacian Operator; 3.6 The Curl Operator 3.7 Formulas Involving the Nabla Operator4: Coordinate Systems and Important Theorems; 4.1 Orthogonal Curvilinear Coordinates; 4.2 Special Orthogonal Coordinate Systems; 4.2.1 Cylindrical Coordinates; 4.2.2 Spherical Coordinates; 4.3 Vector Integration and Integral Theorems; 4.4 Gauss Theorem; 4.5 Stokes Theorem; 4.6 Green Theorem; 4.7 Helmholtz Theorem; 4.8 Useful Integral Relations; 5: Ordinary Differential Equations; 5.1 Introduction; 5.2 Separable Variables; 5.3 First-Order Linear Equation; 5.4 Bernoulli Equations; 5.5 Second-Order Linear Equations with Constant Coefficients 5.5.1 Homogeneous Linear Equations with Constant Coefficients5.5.2 Non-homogeneous Linear Equations with Constant Coefficients; 5.6 An Introduction to Differential Equations with Order k > 2; 6: Fourier Series and Integrals; 6.1 Periodic Functions; 6.2 Fourier Series; 6.3 Euler-Fourier Formulas; 6.4 Half-Range Fourier Series; 6.5 Change of Interval; 6.6 Parseval's Identity; 6.7 Integration and Differentiation of a Fourier Series; 6.8 Multiple Fourier Series; 6.9 Fourier Integrals and Fourier Transforms; 6.10 Fourier Transforms for Functions of Several Variables 7: Functions of One Complex Variable7.1 Complex Numbers; 7.2 Basic Operations with Complex Numbers; 7.3 Polar Form of a Complex Number; 7.4 De Moivre's Theorem and Roots of Complex Numbers; 7.5 Functions of a Complex Variable; 7.6 Limits and Continuity; 7.7 Derivatives and Analytic Functions; 7.8 Cauchy-Riemann Conditions; 7.9 Harmonic Functions; 7.10 Singular Points; 7.11 Complex Elementary Functions; 8: Complex Integration; 8.1 Line Integrals in the Complex Plane; 8.2 Cauchy's Integral Theorem; 8.3 Cauchy's Integral Formula; 8.4 Series Representations of Analytic Functions |
| Summary | Nanobiotechnology is a new interdisciplinary science with revolutionary perspectives arising from the fact that at nanosize the behaviour and characteristics of matter change with respect to ordinary macroscopic dimensions. Nanotechnology is a new way for producing and getting materials, structures and devices with greatly improved or completely new properties and functionalities. This book provides an introductory overview of the nanobiotechnology world along with a general technical framework about mathematical modelling through which we today study the phenomena of charge transport at the nanometer level. Although it is not a purely mathematics or physics book, it introduces the basic mathematical and physical notions that are important and necessary for theory and applications in nanobiotechnology. Therefore, it can be considered an extended formulary of basic and advanced concepts. It can be the starting point for discussions and insights and can be used for further developments in mathematical-physical modelling linked to the nanobiotechnology world. The book is dedicated to all those who follow their ideas in life and pursue their choices with determination and firmness, in a free and independent way. |
| Subject | Nanobiotechnology. NANOTECHNOLOGY. SCIENCE / Chemistry / Industrial & Technical. TECHNOLOGY & ENGINEERING / Chemical & Biochemical. SCIENCE / Nanostructures SCIENCE / Physics TECHNOLOGY / Electronics / Optoelectronics |
| Multimedia |
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$a 1.5.6 Physics of Computation1.5.7 Quantum Signal Propagation in Nanosystems; 2: Vector Analysis; 2.1 Vectors and Scalars; 2.2 Direction Angles and Direction Cosines; 2.3 Equality of Vectors; 2.4 Vector Addition and Subtraction; 2.5 Multiplication by a Scalar; 2.6 Scalar Product; 2.7 Vector Product; 2.8 Triple Scalar Product; 2.9 Triple Vector Product; 2.10 Linear Vector Space V; 3: Vector Differentiation; 3.1 Introduction; 3.2 The Gradient Operator; 3.3 Directional Derivative; 3.4 The Divergence Operator; 3.5 The Laplacian Operator; 3.6 The Curl Operator
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$a 3.7 Formulas Involving the Nabla Operator4: Coordinate Systems and Important Theorems; 4.1 Orthogonal Curvilinear Coordinates; 4.2 Special Orthogonal Coordinate Systems; 4.2.1 Cylindrical Coordinates; 4.2.2 Spherical Coordinates; 4.3 Vector Integration and Integral Theorems; 4.4 Gauss Theorem; 4.5 Stokes Theorem; 4.6 Green Theorem; 4.7 Helmholtz Theorem; 4.8 Useful Integral Relations; 5: Ordinary Differential Equations; 5.1 Introduction; 5.2 Separable Variables; 5.3 First-Order Linear Equation; 5.4 Bernoulli Equations; 5.5 Second-Order Linear Equations with Constant Coefficients
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$a 5.5.1 Homogeneous Linear Equations with Constant Coefficients5.5.2 Non-homogeneous Linear Equations with Constant Coefficients; 5.6 An Introduction to Differential Equations with Order k > 2; 6: Fourier Series and Integrals; 6.1 Periodic Functions; 6.2 Fourier Series; 6.3 Euler-Fourier Formulas; 6.4 Half-Range Fourier Series; 6.5 Change of Interval; 6.6 Parseval's Identity; 6.7 Integration and Differentiation of a Fourier Series; 6.8 Multiple Fourier Series; 6.9 Fourier Integrals and Fourier Transforms; 6.10 Fourier Transforms for Functions of Several Variables
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$a 7: Functions of One Complex Variable7.1 Complex Numbers; 7.2 Basic Operations with Complex Numbers; 7.3 Polar Form of a Complex Number; 7.4 De Moivre's Theorem and Roots of Complex Numbers; 7.5 Functions of a Complex Variable; 7.6 Limits and Continuity; 7.7 Derivatives and Analytic Functions; 7.8 Cauchy-Riemann Conditions; 7.9 Harmonic Functions; 7.10 Singular Points; 7.11 Complex Elementary Functions; 8: Complex Integration; 8.1 Line Integrals in the Complex Plane; 8.2 Cauchy's Integral Theorem; 8.3 Cauchy's Integral Formula; 8.4 Series Representations of Analytic Functions
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$a Nanobiotechnology is a new interdisciplinary science with revolutionary perspectives arising from the fact that at nanosize the behaviour and characteristics of matter change with respect to ordinary macroscopic dimensions. Nanotechnology is a new way for producing and getting materials, structures and devices with greatly improved or completely new properties and functionalities. This book provides an introductory overview of the nanobiotechnology world along with a general technical framework about mathematical modelling through which we today study the phenomena of charge transport at the nanometer level. Although it is not a purely mathematics or physics book, it introduces the basic mathematical and physical notions that are important and necessary for theory and applications in nanobiotechnology. Therefore, it can be considered an extended formulary of basic and advanced concepts. It can be the starting point for discussions and insights and can be used for further developments in mathematical-physical modelling linked to the nanobiotechnology world. The book is dedicated to all those who follow their ideas in life and pursue their choices with determination and firmness, in a free and independent way.
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| Summary | Nanobiotechnology is a new interdisciplinary science with revolutionary perspectives arising from the fact that at nanosize the behaviour and characteristics of matter change with respect to ordinary macroscopic dimensions. Nanotechnology is a new way for producing and getting materials, structures and devices with greatly improved or completely new properties and functionalities. This book provides an introductory overview of the nanobiotechnology world along with a general technical framework about mathematical modelling through which we today study the phenomena of charge transport at the nanometer level. Although it is not a purely mathematics or physics book, it introduces the basic mathematical and physical notions that are important and necessary for theory and applications in nanobiotechnology. Therefore, it can be considered an extended formulary of basic and advanced concepts. It can be the starting point for discussions and insights and can be used for further developments in mathematical-physical modelling linked to the nanobiotechnology world. The book is dedicated to all those who follow their ideas in life and pursue their choices with determination and firmness, in a free and independent way. |
| Contents | Cover; Half Title; Title Page; Copyright Page; Table of Contents; Preface; 1: Introduction; 1.1 The Nanotechnologies World; 1.2 Classification of Nanostructures; 1.3 Applications of Nanotechnologies; 1.4 Applied Mathematics and Nanotechnology; 1.5 Spintronics, Information Technologies and Nanotechnology; 1.5.1 Spin Decoherence in Electronic Materials; 1.5.2 Transport of Polarised Spin in Hybrid Semiconductor Structures; 1.5.3 Spin-Based Solid State Quantum Computing; 1.5.4 Spin Entanglement in Solids; 1.5.5 Optical and Electronic Control of Nuclear Spin Polarisation 1.5.6 Physics of Computation1.5.7 Quantum Signal Propagation in Nanosystems; 2: Vector Analysis; 2.1 Vectors and Scalars; 2.2 Direction Angles and Direction Cosines; 2.3 Equality of Vectors; 2.4 Vector Addition and Subtraction; 2.5 Multiplication by a Scalar; 2.6 Scalar Product; 2.7 Vector Product; 2.8 Triple Scalar Product; 2.9 Triple Vector Product; 2.10 Linear Vector Space V; 3: Vector Differentiation; 3.1 Introduction; 3.2 The Gradient Operator; 3.3 Directional Derivative; 3.4 The Divergence Operator; 3.5 The Laplacian Operator; 3.6 The Curl Operator 3.7 Formulas Involving the Nabla Operator4: Coordinate Systems and Important Theorems; 4.1 Orthogonal Curvilinear Coordinates; 4.2 Special Orthogonal Coordinate Systems; 4.2.1 Cylindrical Coordinates; 4.2.2 Spherical Coordinates; 4.3 Vector Integration and Integral Theorems; 4.4 Gauss Theorem; 4.5 Stokes Theorem; 4.6 Green Theorem; 4.7 Helmholtz Theorem; 4.8 Useful Integral Relations; 5: Ordinary Differential Equations; 5.1 Introduction; 5.2 Separable Variables; 5.3 First-Order Linear Equation; 5.4 Bernoulli Equations; 5.5 Second-Order Linear Equations with Constant Coefficients 5.5.1 Homogeneous Linear Equations with Constant Coefficients5.5.2 Non-homogeneous Linear Equations with Constant Coefficients; 5.6 An Introduction to Differential Equations with Order k > 2; 6: Fourier Series and Integrals; 6.1 Periodic Functions; 6.2 Fourier Series; 6.3 Euler-Fourier Formulas; 6.4 Half-Range Fourier Series; 6.5 Change of Interval; 6.6 Parseval's Identity; 6.7 Integration and Differentiation of a Fourier Series; 6.8 Multiple Fourier Series; 6.9 Fourier Integrals and Fourier Transforms; 6.10 Fourier Transforms for Functions of Several Variables 7: Functions of One Complex Variable7.1 Complex Numbers; 7.2 Basic Operations with Complex Numbers; 7.3 Polar Form of a Complex Number; 7.4 De Moivre's Theorem and Roots of Complex Numbers; 7.5 Functions of a Complex Variable; 7.6 Limits and Continuity; 7.7 Derivatives and Analytic Functions; 7.8 Cauchy-Riemann Conditions; 7.9 Harmonic Functions; 7.10 Singular Points; 7.11 Complex Elementary Functions; 8: Complex Integration; 8.1 Line Integrals in the Complex Plane; 8.2 Cauchy's Integral Theorem; 8.3 Cauchy's Integral Formula; 8.4 Series Representations of Analytic Functions |
| Subject | Nanobiotechnology. NANOTECHNOLOGY. SCIENCE / Chemistry / Industrial & Technical. TECHNOLOGY & ENGINEERING / Chemical & Biochemical. SCIENCE / Nanostructures SCIENCE / Physics TECHNOLOGY / Electronics / Optoelectronics |
| Multimedia |