The Introduction to Calculus series has been developed to meet the needs of students who are exploring concepts in calculus. The first book in the three book series, Introducing Differentiation provides an accessible framework for students to develop their skills in differentiation.
The topics included in this book are:
• Functions and notation
• Rates of change in linear functions
• Average and instantaneous change
• Gradient of a tangent at a point
• Differentiation by first principles
• Linear functions
• Rates of change
• Problems with curves
• Basic rules of differentiation.
The book contains real world examples and ways of introducing mathematical ideas which are fun and accessible. This book can be used with existing units of work in calculus.
The activities have a problem solving focus and are accompanied with worked examples and partially worked examples. Teacher pages set out ways of introducing each activity, teaching ideas and methods of reinforcement. Student activities are expressed in clear, unambiguous language. There is also ample space for students to carry out their own working.
Each task is related to a concept in calculus and, as students move through the task, concepts become progressively more complex. In order to increase their understanding the students can be encouraged to work co-cooperatively on problems by discussing the concepts presented in the book.
The book can be used to:
• Pre-test a class at the beginning of a unit of work
• Extend students who are working quickly
• Assess student learning at the end of a unit of work
• Provide extra material for students who require extra assistance
• Provide study material for exams
• Provide a homework resource
• Provide problem solving experience in calculus
• Enhance and improve skills in calculus
• Provide ongoing feedback as a unit of work progresses