Teach Yourself

Calculus: A Complete Introduction is the most comprehensive yet easy-to-use introduction to using calculus. Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge. The book covers all areas of calculus, including functions, gradients, rates of change, differentiation, exponential and logarithmic functions and integration. Everything you will need to know is here in one book. Each chapter includes not only an explanation of the knowledge and skills you need, but also worked examples and test questi.

10.4 Derivatives of the hyperbolic functions.

Cover; Book title; Contents; Introduction; 1 Functions; 1.1 What is calculus?; 1.2 Functions; 1.3 Equations of functions; 1.4 General notation for functions; 1.5 Notation for increases in functions; 1.6 Graphs of functions; 1.7 Using calculators or computers for plotting functions; 1.8 Inverse functions; 1.9 Implicit functions; 1.10 Functions of more than one variable; 2 Variations in functions; limits; 2.1 Variations in functions; 2.2 Limits; 2.3 Limit of a function of the form (omitted); 2.4 A trigonometric limit, (omitted); 2.5 A geometric illustration of a limit; 2.6 Theorems on limits.

3 Gradient3.1 Gradient of the line joining two points; 3.2 Equation of a straight line; 3.3 Approximating to gradients of curves; 3.4 Towards a definition of gradient; 3.5 Definition of the gradient of a curve; 3.6 Negative gradient; 4 Rate of change; 4.1 The average change of a function over an interval; 4.2 The average rate of change of a non-linear function; 4.3 Motion of a body with non-constant velocity; 4.4 Graphical interpretation; 4.5 A definition of rate of change; 5 Differentiation; 5.1 Algebraic approach to the rate of change of a function; 5.2 The derived function.

5.3 Notation fo…