Ib course book: higher level maths calculus. Per le Scuole superiori. Con espansione online

Libro 13 di 15: Oxford IB Diploma Programme

Torres-Skoumal, Marlene; Seiler, Palmira; Heinrichs, Lorraine; Harcet, Josip

 
9780198304845: Ib course book: higher level maths calculus. Per le Scuole superiori. Con espansione online

Sinossi

A truly IB approach to mathematics

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Descrizione del libro

A truly IB approach to mathematics

Contenuti

  • 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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