Module 1 Limits and continuity
Introduction
Unit 1.1 L'Hospital's rule
Unit 1.2 Continuity
Module summary
Module checklist
Exam practice
Module 2 Differentiation
Introduction
Unit 2.1 Differentiation from first principles
Unit 2.2 Differentiation techniques
Module summary
Module checklist
Exam practice
Module 3 Application of differentiation
Introduction
Unit 3.1 Newtonâ&
Unit 3.2 Optimisation: maximum and minimum values
Unit 3.3 Related rates
Unit 3.4 Rates of change
Module summary
Module checklist
Exam practice
Module 4 Integration techniques
Introduction
Unit 4.1 Basic integration
Unit 4.2 Integration by inspection
Unit 4.3 Integration by means of algebraic substitution
Unit 4.4 Integration of trigonometric functions
Unit 4.5 Integration of algebraic fractions
Unit 4.6 Integration by parts
Module summary
Module checklist
Exam practice
Module 5 The definite integral
Introduction
Unit 5.1 Definite integrals
Unit 5.2 Laplace transformation
Module summary
Module checklist
Exam practice
Module 6 Areas and volumes
Introduction
Unit 6.1 Using integration to determine area
Unit 6.2 Using integration to determine volume
Module summary
Module checklist
Exam practice
Module 7 Second moment of area and moment of inertia
Introduction
Unit 7.1 Second moment of area
Unit 7.2 Moment of inertia
Module summary
Module checklist
Exam practice
Module 8 Differential equations
Introduction
Unit 8.1 Differential equations
Unit 8.2 Solving first-order differential equations
Unit 8.3 Solving second-order differential equations
Module summary
Module checklist
Exam practice
Mock examination
Formula sheet
Short answers
Glossary