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

Written by experienced IB workshop leaders and curriculum developers, 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 instilling confident mathematical thinking skills. Exam support is integrated, building assessment potential. *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 onl

- Front Cover
- Title Page
- 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’Hopital’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 equations and graphs of their solutions
- 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 The integral as the limit of a sum 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

- Answers
- Index
- Back Cover