Oxford IB Diploma Programme: Mathematics Higher Level: Calculus Course Companion [Multiple-component retail product]

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