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Oxford IB Diploma Programme
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A truly IB approach to mathematics

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'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 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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