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Senior Maths Topics: Differential Calculus


Stock: Available

Product Code: 978-1-875695-49-2

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:

o       want to study a topic in more depth

o       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.


Using this book

Chapter 1 Limits


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


Sample tests