Senior Maths Topics: Differential Calculus

Phoenix Senior Maths Topics provide thorough and detailed explanations, worked examples, summaries and practice exam questions on essential senior maths topics. Each book is a detailed treatment of a topic selected because of its importance in senior maths. They can be used at school, to supplement the textbook, providing more detail and exercises, and at home, to aid home study and exam preparation.

These books are for senior secondary students, particularly those who:

• want to study a topic in more depth
• are having difficulty with a topic

 Phoenix Senior Maths Topics books can be used:

• to learn and understand the topic: a full and detailed treatment of the topic with clear step-by-step explanations and plenty of worked examples.
• as a study and revision aid: a separate summary contains the information which has to be learned, as well as exercises and sample tests with typical examination questions. Solutions are provided.
• as a reference: all the relevant information is easy to find and easy to understand.

Contents

Using this book

Chapter 1 Limits

• Definition
• Properties of limits

Chapter 2 Continuity

Chapter 3 Gradient of a secant

Chapter 4 Gradient of a tangent

Chapter 5 The gradient function

Chapter 6 Continuity and smoothness

Chapter 7 Differentiation

• The derived function
• Differentiation from first principles
• Increment notation
• Using the delta notation

Chapter 8 Rules for differentiation

• The derivative of xn for n an integer
• The derivative of cxn
• The derivative of cx
• The derivative of a constant
• The derivative of sums and differences of functions
• The derivative of xn for negative indices
• The derivative of xn for fractional indices
• Differentiation with respect to other variables

Chapter 9 Further rules for differentiation

• The function of a function rule
• The chain rule
• The product rule
• The product rule involving the function of a function rule
• The quotient rule
• The quotient rule involving the function of a function rule

Chapter 10 Geometric applications of differentiation

• Tangents and normals
• Higher derivatives
• Stationary points
• Turning points
• Significants of the second derivative
• Maxima and minima
• Practical applications of maxima and minima

Chapter 11 Miscellaneous examples

Summary

Sample tests

Answers