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Oxford IB Diploma Programme: Mathematics Higher Level: Calculus Course Companion

A truly IB approach to mathematics

Author Marlene Torres-Skoumal, Author Palmira Seiler, Author Lorraine Heinrichs, and Author Josip Harcet

Suitable for:  IB Diploma Mathematics students - HL

Price:  £20.99

ISBN: 978-0-19-830484-5
Publication date: 18/09/2014
Paperback: 192 pages
Dimensions: 255x195mm

Also available as an ebook

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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.


  • Directly linked to the Oxford Higher Level Course Book, naturally extending learning
  • Drive a truly IB approach to mathematics, helping learners connect mathematical theory with the world around them
  • The most comprehensive, accurately matched to the most recent syllabus, written by experienced workshop leaders
  • Build essential mathematical skills with extensive practice enabling confident skills-development
  • Cement assessment potential, with examiner guidance and exam questions driving confidence in every topic
  • Complete worked solutions included online

This page was last updated on 23 February 2020 at 04:30 GMT

Table of Contents

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