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Classical geometry : euclidean, transformational, inversive, and projective / / Ed I. Leonard, [and three others]
| Classical geometry : euclidean, transformational, inversive, and projective / / Ed I. Leonard, [and three others] |
| Edizione | [1st edition] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2014 |
| Descrizione fisica | 1 online resource (493 p.) |
| Disciplina | 516 |
| Soggetto topico | Geometry |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-118-67914-8
1-118-83943-9 |
| Classificazione | MAT012000EDU027000MAT003000 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
CLASSICAL GEOMETRY: Euclidean, Transformational, Inversive, and Projective; Copyright; CONTENTS; Preface; PART I EUCLIDEAN GEOMETRY; 1 PART I EUCLIDEAN GEOMETRY Congruency; 1.1 Introduction; 1.2 Congruent Figures; 1.3 Parallel Lines; 1.3.1 Angles in a Triangle; 1.3.2 Thales' Theorem; 1.3.3 Quadrilaterals; 1.4 More About Congruency; 1.5 Perpendiculars and Angle Bisectors; 1.6 Construction Problems; 1.6.1 The Method of Loci; 1.7 Solutions to Selected Exercises; 1.8 Problems; 2 Concurrency; 2.1 Perpendicular Bisectors; 2.2 Angle Bisectors; 2.3 Altitudes; 2.4 Medians; 2.5 Construction Problems
2.6 Solutions to the Exercises2.7 Problems; 3 Similarity; 3.1 Similar Triangles; 3.2 Parallel Lines and Similarity; 3.3 Other Conditions Implying Similarity; 3.4 Examples; 3.5 Construction Problems; 3.6 The Power of a Point; 3.7 Solutions to the Exercises; 3.8 Problems; 4 Theorems of Ceva and Menelaus; 4.1 Directed Distances, Directed Ratios; 4.2 The Theorems; 4.3 Applications of Ceva's Theorem; 4.4 Applications of Menelaus' Theorem; 4.5 Proofs of the Theorems; 4.6 Extended Versions of the Theorems; 4.6.1 Ceva's Theorem in the Extended Plane; 4.6.2 Menelaus' Theorem in the Extended Plane 4.7 Problems5 Area; 5.1 Basic Properties; 5.1.1 Areas of Polygons; 5.1.2 Finding the Area of Polygons; 5.1.3 Areas of Other Shapes; 5.2 Applications of the Basic Properties; 5.3 Other Formulae for the Area of a Triangle; 5.4 Solutions to the Exercises; 5.5 Problems; 6 Miscellaneous Topics; 6.1 The Three Problems of Antiquity; 6.2 Constructing Segments of Specific Lengths; 6.3 Construction of Regular Polygons; 6.3.1 Construction of the Regular Pentagon; 6.3.2 Construction of Other Regular Polygons; 6.4 Miquel's Theorem; 6.5 Morley's Theorem; 6.6 The Nine-Point Circle; 6.6.1 Special Cases 6.7 The Steiner-Lehmus Theorem6.8 The Circle of Apollonius; 6.9 Solutions to the Exercises; 6.10 Problems; PART II TRANSFORMATIONAL GEOMETRY; 7 The Euclidean Transformations or lsometries; 7.1 Rotations, Reflections, and Translations; 7.2 Mappings and Transformations; 7.2.1 Isometries; 7.3 Using Rotations, Reflections, and Translations; 7.4 Problems; 8 The Algebra of lsometries; 8.1 Basic Algebraic Properties; 8.2 Groups of Isometries; 8.2.1 Direct and Opposite Isometries; 8.3 The Product of Reflections; 8.4 Problems; 9 The Product of Direct lsometries; 9.1 Angles; 9.2 Fixed Points 9.3 The Product of Two Translations9.4 The Product of a Translation and a Rotation; 9.5 The Product of Two Rotations; 9.6 Problems; 10 Symmetry and Groups; 10.1 More About Groups; 10.1.1 Cyclic and Dihedral Groups; 10.2 Leonardo's Theorem; 10.3 Problems; 11 Homotheties; 11.1 The Pantograph; 11.2 Some Basic Properties; 11.2.1 Circles; 11.3 Construction Problems; 11.4 Using Homotheties in Proofs; 11.5 Dilatation; 11.6 Problems; 12 Tessellations; 12.1 Tilings; 12.2 Monohedral Tilings; 12.3 Tiling with Regular Polygons; 12.4 Platonic and Archimedean Tilings; 12.5 Problems PART Ill INVERSIVE AND PROJECTIVE GEOMETRIES |
| Record Nr. | UNINA-9910464443603321 |
| Hoboken, New Jersey : , : Wiley, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Classical geometry : euclidean, transformational, inversive, and projective / / Ed I. Leonard, [and three others]
| Classical geometry : euclidean, transformational, inversive, and projective / / Ed I. Leonard, [and three others] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2014 |
| Descrizione fisica | 1 online resource (493 pages) |
| Disciplina | 516 |
| Soggetto topico | Geometry |
| ISBN |
1-118-83943-9
1-118-67914-8 |
| Classificazione |
414
516 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910796087403321 |
| Hoboken, New Jersey : , : Wiley, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Classical geometry : euclidean, transformational, inversive, and projective / / Ed I. Leonard, [and three others]
| Classical geometry : euclidean, transformational, inversive, and projective / / Ed I. Leonard, [and three others] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2014 |
| Descrizione fisica | 1 online resource (493 pages) |
| Disciplina | 516 |
| Soggetto topico | Geometry |
| ISBN |
1-118-83943-9
1-118-67914-8 |
| Classificazione |
414
516 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910809269503321 |
| Hoboken, New Jersey : , : Wiley, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Partial differential equations : theory and completely solved problems / / Thomas Hillen, I. Ed Leonard, Henry van Roessel
| Partial differential equations : theory and completely solved problems / / Thomas Hillen, I. Ed Leonard, Henry van Roessel |
| Autore | Hillen Thomas <1966-> |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2012 |
| Descrizione fisica | 1 online resource (694 p.) |
| Disciplina | 515/.353 |
| Soggetto topico | Differential equations, Partial |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-118-44146-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page ; Copyright; Contents ; Preface ; PART I: THEORY ; Chapter 1: Introduction ; 1.1 Partial Differential Equations ; 11.2 Classification of Second-order Linear Pdes ; 1.3 Side Conditions ; 1.3.1 Boundary Conditions on an Interval ; 1.4 Linear Pdes ; 1.4.1 Principle of Superposition ; 1.5 Steady-state and Equilibrium Solutions ; 1.6 First Example for Separation of Variables ; 1.7 Derivation of the Diffusion Equation ; 1.7.1 Boundary Conditions ; 1.8 Derivation of the Heat Equation ; 1.9 Derivation of the Wave Equation ; 1.10 Examples of Laplace''s Equation ; 1.11 Summary
1.11.1 Problems and Notes Chapter 2: Fourier Series ; 2.1 Piecewise Continuous Functions ; 2.2 Even, Odd, and Periodic Functions ; 2.3 Orthogonal Functions ; 2.4 Fourier Series ; 2.4.1 Fourier Sine and Cosine Series ; 2.5 Convergence of Fourier Series ; 2.5.1 Gibbs'' Phenomenon ; 2.6 Operations on Fourier Series ; 2.7 Mean Square Error ; 2.8 Complex Fourier Series ; 2.9 Summary ; 2.9.1 Problems and Notes ; Chapter 3: Separation of Variables ; 3.1 Homogeneous Equations ; 3.1.1 General Linear Homogeneous Equations ; 3.1.2 Limitations of the Method of Separation of Variables 3.2 Nonhomogeneous Equations 3.2.1 Method of Eigenfunction Expansions ; 3.3 Summary ; 3.3.1 Problems and Notes ; Chapter 4: Sturm Liouville Theory ; 4.1 Formulation ; 4.2 Properties of Sturm-liouville Problems ; 4.3 Eigenfunction Expansions ; 4.4 Rayleigh Quotient ; 4.5 Summary ; 4.5.1 Problems and Notes ; Chapter 5: Heat, Wave, and Laplace Equations ; 5.1 One-dimensional Heat Equation ; 5.2 Two-dimensional Heat Equation ; 5.3 One-dimensional Wave Equation ; 5.3.1 d'' Alembert''s Solution ; 5.4 Laplace''s Equation ; 5.4.1 Potential in a Rectangle ; 5.5 Maximum Principle 5.6 Two-dimensional Wave Equation 5.7 Eigenfunctions in Two Dimensions ; 5.8 Summary ; 5.8.1 Problems and Notes ; Chapter 6: Polar Coordinates ; 6.1 Interior Dirichlet Problem for a Disk ; 6.1.1 Poisson Integral Formula ; 6.2 Vibrating Circular Membrane ; 6.3 Bessel''s Equation ; 6.3.1 Series Solutions of Odes ; 6.4 Bessel Functions ; 6.4.1 Properties of Bessel Functions ; 6.4.2 Integral Representation of Bessel Functions ; 6.5 Fourier-bessel Series ; 6.6 Solution to the Vibrating Membrane Problem ; 6.7 Summary ; 6.7.1 Problems and Notes ; Chapter 7: Spherical Coordinates 7.1 Spherical Coordinates 7.1.1 Derivation of the Laplacian ; 7.2 Legendre''s Equation ; 7.3 Legendre Functions ; 7.3.1 Legendre Polynomials ; 7.3.2 Fourier-legendre Series ; 7.3.3 Legendre Functions of the Second Kind ; 7.3.4 Associated Legendre Functions ; 7.4 Spherical Bessel Functions ; 7.5 Interior Dirichlet Problem for a Sphere ; 7.6 Summary ; 7.6.1 Problems and Notes ; Chapter 8: Fourier Transforms ; 8.1 Fourier Integrals ; 8.1.1 Fourier Integral Representation ; 8.1.2 Examples ; 8.1.3 Fourier Sine and Cosine Integral Representations ; 8.1.4 Proof of Fourier''s Theorem 8.2 Fourier Transforms |
| Record Nr. | UNINA-9910465463003321 |
Hillen Thomas <1966->
|
||
| Hoboken, New Jersey : , : Wiley, , 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Partial differential equations : theory and completely solved problems / / Thomas Hillen, I. Ed Leonard, Henry van Roessel
| Partial differential equations : theory and completely solved problems / / Thomas Hillen, I. Ed Leonard, Henry van Roessel |
| Autore | Hillen Thomas <1966-> |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2012 |
| Descrizione fisica | 1 online resource (694 p.) |
| Disciplina | 515/.353 |
| Soggetto topico | Differential equations, Partial |
| ISBN | 1-118-44146-X |
| Classificazione | MAT007000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page ; Copyright; Contents ; Preface ; PART I: THEORY ; Chapter 1: Introduction ; 1.1 Partial Differential Equations ; 11.2 Classification of Second-order Linear Pdes ; 1.3 Side Conditions ; 1.3.1 Boundary Conditions on an Interval ; 1.4 Linear Pdes ; 1.4.1 Principle of Superposition ; 1.5 Steady-state and Equilibrium Solutions ; 1.6 First Example for Separation of Variables ; 1.7 Derivation of the Diffusion Equation ; 1.7.1 Boundary Conditions ; 1.8 Derivation of the Heat Equation ; 1.9 Derivation of the Wave Equation ; 1.10 Examples of Laplace''s Equation ; 1.11 Summary
1.11.1 Problems and Notes Chapter 2: Fourier Series ; 2.1 Piecewise Continuous Functions ; 2.2 Even, Odd, and Periodic Functions ; 2.3 Orthogonal Functions ; 2.4 Fourier Series ; 2.4.1 Fourier Sine and Cosine Series ; 2.5 Convergence of Fourier Series ; 2.5.1 Gibbs'' Phenomenon ; 2.6 Operations on Fourier Series ; 2.7 Mean Square Error ; 2.8 Complex Fourier Series ; 2.9 Summary ; 2.9.1 Problems and Notes ; Chapter 3: Separation of Variables ; 3.1 Homogeneous Equations ; 3.1.1 General Linear Homogeneous Equations ; 3.1.2 Limitations of the Method of Separation of Variables 3.2 Nonhomogeneous Equations 3.2.1 Method of Eigenfunction Expansions ; 3.3 Summary ; 3.3.1 Problems and Notes ; Chapter 4: Sturm Liouville Theory ; 4.1 Formulation ; 4.2 Properties of Sturm-liouville Problems ; 4.3 Eigenfunction Expansions ; 4.4 Rayleigh Quotient ; 4.5 Summary ; 4.5.1 Problems and Notes ; Chapter 5: Heat, Wave, and Laplace Equations ; 5.1 One-dimensional Heat Equation ; 5.2 Two-dimensional Heat Equation ; 5.3 One-dimensional Wave Equation ; 5.3.1 d'' Alembert''s Solution ; 5.4 Laplace''s Equation ; 5.4.1 Potential in a Rectangle ; 5.5 Maximum Principle 5.6 Two-dimensional Wave Equation 5.7 Eigenfunctions in Two Dimensions ; 5.8 Summary ; 5.8.1 Problems and Notes ; Chapter 6: Polar Coordinates ; 6.1 Interior Dirichlet Problem for a Disk ; 6.1.1 Poisson Integral Formula ; 6.2 Vibrating Circular Membrane ; 6.3 Bessel''s Equation ; 6.3.1 Series Solutions of Odes ; 6.4 Bessel Functions ; 6.4.1 Properties of Bessel Functions ; 6.4.2 Integral Representation of Bessel Functions ; 6.5 Fourier-bessel Series ; 6.6 Solution to the Vibrating Membrane Problem ; 6.7 Summary ; 6.7.1 Problems and Notes ; Chapter 7: Spherical Coordinates 7.1 Spherical Coordinates 7.1.1 Derivation of the Laplacian ; 7.2 Legendre''s Equation ; 7.3 Legendre Functions ; 7.3.1 Legendre Polynomials ; 7.3.2 Fourier-legendre Series ; 7.3.3 Legendre Functions of the Second Kind ; 7.3.4 Associated Legendre Functions ; 7.4 Spherical Bessel Functions ; 7.5 Interior Dirichlet Problem for a Sphere ; 7.6 Summary ; 7.6.1 Problems and Notes ; Chapter 8: Fourier Transforms ; 8.1 Fourier Integrals ; 8.1.1 Fourier Integral Representation ; 8.1.2 Examples ; 8.1.3 Fourier Sine and Cosine Integral Representations ; 8.1.4 Proof of Fourier''s Theorem 8.2 Fourier Transforms |
| Record Nr. | UNINA-9910787091703321 |
|
Hillen Thomas <1966->
|
||
| Hoboken, New Jersey : , : Wiley, , 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Partial differential equations : theory and completely solved problems / / Thomas Hillen, I. Ed Leonard, Henry van Roessel
| Partial differential equations : theory and completely solved problems / / Thomas Hillen, I. Ed Leonard, Henry van Roessel |
| Autore | Hillen Thomas <1966-> |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2012 |
| Descrizione fisica | 1 online resource (694 p.) |
| Disciplina | 515/.353 |
| Soggetto topico | Differential equations, Partial |
| ISBN | 1-118-44146-X |
| Classificazione | MAT007000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page ; Copyright; Contents ; Preface ; PART I: THEORY ; Chapter 1: Introduction ; 1.1 Partial Differential Equations ; 11.2 Classification of Second-order Linear Pdes ; 1.3 Side Conditions ; 1.3.1 Boundary Conditions on an Interval ; 1.4 Linear Pdes ; 1.4.1 Principle of Superposition ; 1.5 Steady-state and Equilibrium Solutions ; 1.6 First Example for Separation of Variables ; 1.7 Derivation of the Diffusion Equation ; 1.7.1 Boundary Conditions ; 1.8 Derivation of the Heat Equation ; 1.9 Derivation of the Wave Equation ; 1.10 Examples of Laplace''s Equation ; 1.11 Summary
1.11.1 Problems and Notes Chapter 2: Fourier Series ; 2.1 Piecewise Continuous Functions ; 2.2 Even, Odd, and Periodic Functions ; 2.3 Orthogonal Functions ; 2.4 Fourier Series ; 2.4.1 Fourier Sine and Cosine Series ; 2.5 Convergence of Fourier Series ; 2.5.1 Gibbs'' Phenomenon ; 2.6 Operations on Fourier Series ; 2.7 Mean Square Error ; 2.8 Complex Fourier Series ; 2.9 Summary ; 2.9.1 Problems and Notes ; Chapter 3: Separation of Variables ; 3.1 Homogeneous Equations ; 3.1.1 General Linear Homogeneous Equations ; 3.1.2 Limitations of the Method of Separation of Variables 3.2 Nonhomogeneous Equations 3.2.1 Method of Eigenfunction Expansions ; 3.3 Summary ; 3.3.1 Problems and Notes ; Chapter 4: Sturm Liouville Theory ; 4.1 Formulation ; 4.2 Properties of Sturm-liouville Problems ; 4.3 Eigenfunction Expansions ; 4.4 Rayleigh Quotient ; 4.5 Summary ; 4.5.1 Problems and Notes ; Chapter 5: Heat, Wave, and Laplace Equations ; 5.1 One-dimensional Heat Equation ; 5.2 Two-dimensional Heat Equation ; 5.3 One-dimensional Wave Equation ; 5.3.1 d'' Alembert''s Solution ; 5.4 Laplace''s Equation ; 5.4.1 Potential in a Rectangle ; 5.5 Maximum Principle 5.6 Two-dimensional Wave Equation 5.7 Eigenfunctions in Two Dimensions ; 5.8 Summary ; 5.8.1 Problems and Notes ; Chapter 6: Polar Coordinates ; 6.1 Interior Dirichlet Problem for a Disk ; 6.1.1 Poisson Integral Formula ; 6.2 Vibrating Circular Membrane ; 6.3 Bessel''s Equation ; 6.3.1 Series Solutions of Odes ; 6.4 Bessel Functions ; 6.4.1 Properties of Bessel Functions ; 6.4.2 Integral Representation of Bessel Functions ; 6.5 Fourier-bessel Series ; 6.6 Solution to the Vibrating Membrane Problem ; 6.7 Summary ; 6.7.1 Problems and Notes ; Chapter 7: Spherical Coordinates 7.1 Spherical Coordinates 7.1.1 Derivation of the Laplacian ; 7.2 Legendre''s Equation ; 7.3 Legendre Functions ; 7.3.1 Legendre Polynomials ; 7.3.2 Fourier-legendre Series ; 7.3.3 Legendre Functions of the Second Kind ; 7.3.4 Associated Legendre Functions ; 7.4 Spherical Bessel Functions ; 7.5 Interior Dirichlet Problem for a Sphere ; 7.6 Summary ; 7.6.1 Problems and Notes ; Chapter 8: Fourier Transforms ; 8.1 Fourier Integrals ; 8.1.1 Fourier Integral Representation ; 8.1.2 Examples ; 8.1.3 Fourier Sine and Cosine Integral Representations ; 8.1.4 Proof of Fourier''s Theorem 8.2 Fourier Transforms |
| Record Nr. | UNINA-9910819250603321 |
|
Hillen Thomas <1966->
|
||
| Hoboken, New Jersey : , : Wiley, , 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||