Info
- Utilizzare la checkbox di selezione a fianco di ciascun documento per attivare le funzionalità di stampa, invio email, download nei formati disponibili del (i) record.
Calculus off the beaten path : a journey through its fundamental ideas / / Ignacio Zalduendo
| Calculus off the beaten path : a journey through its fundamental ideas / / Ignacio Zalduendo |
| Autore | Zalduendo Ignacio |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (225 pages) |
| Disciplina | 515 |
| Collana | Springer undergraduate mathematics series |
| Soggetto topico |
Calculus
Càlcul |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031157653
9783031157646 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Introduction -- 2400 Years of Calculus -- Calculus and Education -- 1 The Real Numbers -- The Rational Line -- Density of Q -- Some Basic Notions -- Irrationality of Q -- From Eudoxus to Dedekind -- The Real Line -- Dyadic Series-A Construction of R -- The Scarcity of Q -- The Completeness of R -- Cardinality -- Exercises -- 2 Sequences and Series -- Sequences -- Limits of Sequences -- Cantor's Nested Intervals Theorem -- Subsequences -- Series -- The Harmonic Series -- Series of Positive Terms -- Series with Positive and Negative Terms -- The Riemann Series Theorem -- Absolute and Unconditional Convergence -- Exercises -- 3 Functions -- The Elementary Functions -- Polynomials -- Circular Functions -- The Exponential Function: Bernoulli's Inequality -- Irrationality of e -- Convergence of k=1∞(1+ak) and of k=1∞ak -- Hyperbolic Functions -- Injectivity and Inverse Functions -- Curves in the Plane: Parametrized Curves -- The Cycloid -- Pythagorean Triples -- Continuity -- Bolzano and Weierstrass -- Limits -- Limits in Ancient Greece: The Area of a Circle -- Three Important Limits -- Exercises -- 4 The Derivative -- Derivative -- Tangents -- Newton-Raphson -- Derivatives of the Elementary Functions -- The Chain Rule -- Derivative of the Inverse Function -- The Derivative of a Parametrized Curve -- First Derivative, Tangent Line, and Growth -- The Mean Value Theorems -- L'Hôpital's Rule -- Snell's Law -- The Brachistochrone -- Exercises -- 5 The Integral -- Measure and Integral -- The Fundamental Theorem of Calculus -- A Pause for Comments -- Buffon's Needle -- Irrationality of π -- Improper Integrals -- Integration and Sums: Linearity of the Integral -- Uniform Convergence-The Weierstrass M-Test -- Gregory's Series -- Integration and Products: Integration by Parts -- Stirling's Formula.
Integration and Composition: Integration by Substitution -- A Note on Notation -- Length of Curves. The Catenary -- Area Enclosed by a Simple Closed Curve -- Exercises -- 6 More Derivatives -- Second Derivative, Best-Fitting Parabola, and Curvature -- The Taylor Polynomial of Order Two -- Curvature -- Random Walk and the Gauss Curve -- The Taylor Series -- Exercises -- 7 Convexity and the Isoperimetric Inequality -- The Arithmetic-Geometric Inequality -- Convexity -- Young, Hölder, Jensen, Cauchy-Schwarz… -- The Isoperimetric Inequality -- Exercises -- 8 More Integrals -- Volume -- Double Integrals -- The Basel Problem -- Solids of Revolution -- Integration of e -- Density Functions, Barycenter, and Expectation -- Center of Mass or Barycenter -- Pappus' Theorem -- The Method -- Surface Area -- Normal Distribution. Gauss, Laplace, and Stirling -- Exercises -- 9 The Gamma Function -- The Gamma Function -- Weierstrass' Formula -- Growth of the Harmonic Series, Again -- Exercises -- Bibliography -- Index. |
| Record Nr. | UNINA-9910624321703321 |
Zalduendo Ignacio
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Calculus off the beaten path : a journey through its fundamental ideas / / Ignacio Zalduendo
| Calculus off the beaten path : a journey through its fundamental ideas / / Ignacio Zalduendo |
| Autore | Zalduendo Ignacio |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (225 pages) |
| Disciplina | 515 |
| Collana | Springer undergraduate mathematics series |
| Soggetto topico |
Calculus
Càlcul |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031157653
9783031157646 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Introduction -- 2400 Years of Calculus -- Calculus and Education -- 1 The Real Numbers -- The Rational Line -- Density of Q -- Some Basic Notions -- Irrationality of Q -- From Eudoxus to Dedekind -- The Real Line -- Dyadic Series-A Construction of R -- The Scarcity of Q -- The Completeness of R -- Cardinality -- Exercises -- 2 Sequences and Series -- Sequences -- Limits of Sequences -- Cantor's Nested Intervals Theorem -- Subsequences -- Series -- The Harmonic Series -- Series of Positive Terms -- Series with Positive and Negative Terms -- The Riemann Series Theorem -- Absolute and Unconditional Convergence -- Exercises -- 3 Functions -- The Elementary Functions -- Polynomials -- Circular Functions -- The Exponential Function: Bernoulli's Inequality -- Irrationality of e -- Convergence of k=1∞(1+ak) and of k=1∞ak -- Hyperbolic Functions -- Injectivity and Inverse Functions -- Curves in the Plane: Parametrized Curves -- The Cycloid -- Pythagorean Triples -- Continuity -- Bolzano and Weierstrass -- Limits -- Limits in Ancient Greece: The Area of a Circle -- Three Important Limits -- Exercises -- 4 The Derivative -- Derivative -- Tangents -- Newton-Raphson -- Derivatives of the Elementary Functions -- The Chain Rule -- Derivative of the Inverse Function -- The Derivative of a Parametrized Curve -- First Derivative, Tangent Line, and Growth -- The Mean Value Theorems -- L'Hôpital's Rule -- Snell's Law -- The Brachistochrone -- Exercises -- 5 The Integral -- Measure and Integral -- The Fundamental Theorem of Calculus -- A Pause for Comments -- Buffon's Needle -- Irrationality of π -- Improper Integrals -- Integration and Sums: Linearity of the Integral -- Uniform Convergence-The Weierstrass M-Test -- Gregory's Series -- Integration and Products: Integration by Parts -- Stirling's Formula.
Integration and Composition: Integration by Substitution -- A Note on Notation -- Length of Curves. The Catenary -- Area Enclosed by a Simple Closed Curve -- Exercises -- 6 More Derivatives -- Second Derivative, Best-Fitting Parabola, and Curvature -- The Taylor Polynomial of Order Two -- Curvature -- Random Walk and the Gauss Curve -- The Taylor Series -- Exercises -- 7 Convexity and the Isoperimetric Inequality -- The Arithmetic-Geometric Inequality -- Convexity -- Young, Hölder, Jensen, Cauchy-Schwarz… -- The Isoperimetric Inequality -- Exercises -- 8 More Integrals -- Volume -- Double Integrals -- The Basel Problem -- Solids of Revolution -- Integration of e -- Density Functions, Barycenter, and Expectation -- Center of Mass or Barycenter -- Pappus' Theorem -- The Method -- Surface Area -- Normal Distribution. Gauss, Laplace, and Stirling -- Exercises -- 9 The Gamma Function -- The Gamma Function -- Weierstrass' Formula -- Growth of the Harmonic Series, Again -- Exercises -- Bibliography -- Index. |
| Record Nr. | UNISA-996499870903316 |
|
Zalduendo Ignacio
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||