| Título : | Mathematics Higher Level: Calculus course companion | | Tipo de documento: | texto impreso | | Autores: | Josip Harcet, Autor ; Lorraine Heinrichs, Autor ; Palmira Seiler, Autor ; Marlene Torres-Skoumal, Autor | | Editorial: | Oxford [United Kingdom] : Oxford University Press | | Fecha de publicación: | c2014 | | Número de páginas: | 186 p. | | ISBN/ISSN/DL: | 978-0-19-830484-5 | | Idioma : | Inglés (eng) | | Etiquetas: | POLINOMIOS DE TAYLOR SERIE TAYLOR Y MACLAURIN SERIE DE TAYLOR SECUENCIAS FUNCIONES SERIE DE POTENCIA INTEGRALES IMPROPIAS CONVERGENCIA TEOREMA DE COMPRESIÓN ÁLGEBRA SECUENCIAS CONVERGENTES SECUENCIAS DIVERGENTES FUNCIONES CONTINUAS FUNCIONES DIFERENCIALES REGLA DE L'HÔPITAL | | Clasificación: | 515 CÁLCULO | | Resumen: | Written by experienced IB workshop leaders, this book covers all the course content and essential practice needed for success in the Calculus Option for Higher Level. Enabling a truly IB approach to mathematics, real-world context is thoroughly blended with mathematical applications, supporting deep understanding and confident thinking skills. | | Nota de contenido: | 1: Patterns to infinity
1.1: From limits of sequences to limits of functions
1.2: Squeeze theorem and the algebra of limits of convergent sequences
1.3: Divergent sequences: indeterminate forms and evaluation of limits
1.4: From limits of sequences to limits of functions
2: Smoothness in mathematics
2.1: Continuity and differentiability on an interval
2.2: Theorems about continuous functions
2.3: Differentiable functions: Rolle's Theorem and Mean Value Theorem
2.4: Limits at a point, indeterminate forms, and L'Hôpital's rule
2.5: What are smooth graphs of functions?
2.6: Limits of functions and limits of sequences
3: Modeling dynamic phenomena
3.1: Classifications of differential equations and their solutions
3.2: Differential Equations with separated variables
3.3: Separable variables differential Separable variables differential
3.4: Modeling of growth and decay phenomena
3.5: First order exact equations and integrating factors
3.6: Homogeneous differential equations and substitution methods
3.7: Euler Method for first order differential equations
4: The finite in the infinite
4.1: Series and convergence
4.2: Introduction to convergence tests for series
4.3: Improper Integrals
4.4: Integral test for convergence
4.5: The p-series test
4.6: Comparison test for convergence
4.7: Limit comparison test for convergence
4.8: Ratio test for convergence
4.9: Absolute convergence of series
4.10: Conditional convergence of series
5: Everything polynomic
5.1: Representing Functions by Power Series 1
5.2: Representing Power Series as Functions
5.3: Representing Functions by Power Series 2
5.4: Taylor Polynomials
5.5: Taylor and Maclaurin Series
5.6: Using Taylor Series to approximate functions
5.7: Useful applications of power series
6: Answers |
Mathematics Higher Level: Calculus course companion [texto impreso] / Josip Harcet, Autor ; Lorraine Heinrichs, Autor ; Palmira Seiler, Autor ; Marlene Torres-Skoumal, Autor . - Oxford (United Kingdom) : Oxford University Press, c2014 . - 186 p. ISBN : 978-0-19-830484-5 Idioma : Inglés ( eng) | Etiquetas: | POLINOMIOS DE TAYLOR SERIE TAYLOR Y MACLAURIN SERIE DE TAYLOR SECUENCIAS FUNCIONES SERIE DE POTENCIA INTEGRALES IMPROPIAS CONVERGENCIA TEOREMA DE COMPRESIÓN ÁLGEBRA SECUENCIAS CONVERGENTES SECUENCIAS DIVERGENTES FUNCIONES CONTINUAS FUNCIONES DIFERENCIALES REGLA DE L'HÔPITAL | | Clasificación: | 515 CÁLCULO | | Resumen: | Written by experienced IB workshop leaders, this book covers all the course content and essential practice needed for success in the Calculus Option for Higher Level. Enabling a truly IB approach to mathematics, real-world context is thoroughly blended with mathematical applications, supporting deep understanding and confident thinking skills. | | Nota de contenido: | 1: Patterns to infinity
1.1: From limits of sequences to limits of functions
1.2: Squeeze theorem and the algebra of limits of convergent sequences
1.3: Divergent sequences: indeterminate forms and evaluation of limits
1.4: From limits of sequences to limits of functions
2: Smoothness in mathematics
2.1: Continuity and differentiability on an interval
2.2: Theorems about continuous functions
2.3: Differentiable functions: Rolle's Theorem and Mean Value Theorem
2.4: Limits at a point, indeterminate forms, and L'Hôpital's rule
2.5: What are smooth graphs of functions?
2.6: Limits of functions and limits of sequences
3: Modeling dynamic phenomena
3.1: Classifications of differential equations and their solutions
3.2: Differential Equations with separated variables
3.3: Separable variables differential Separable variables differential
3.4: Modeling of growth and decay phenomena
3.5: First order exact equations and integrating factors
3.6: Homogeneous differential equations and substitution methods
3.7: Euler Method for first order differential equations
4: The finite in the infinite
4.1: Series and convergence
4.2: Introduction to convergence tests for series
4.3: Improper Integrals
4.4: Integral test for convergence
4.5: The p-series test
4.6: Comparison test for convergence
4.7: Limit comparison test for convergence
4.8: Ratio test for convergence
4.9: Absolute convergence of series
4.10: Conditional convergence of series
5: Everything polynomic
5.1: Representing Functions by Power Series 1
5.2: Representing Power Series as Functions
5.3: Representing Functions by Power Series 2
5.4: Taylor Polynomials
5.5: Taylor and Maclaurin Series
5.6: Using Taylor Series to approximate functions
5.7: Useful applications of power series
6: Answers |
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