### A Programmed Approach, 3th Edition

### A Programmed Approach, 3th Edition

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The programmed approach, established in the first two editions is maintained in the third and it provides a sound foundation from which the student can build a solid engineering understanding. This edition has been modified to reflect the changes in the syllabuses which students encounter before beginning undergraduate studies. The first two chapters include material that assumes the reader has little previous experience in maths. Written by CHarles Evans who lectures at the University of Portsmouth and has been teaching engineering and applied mathematics for more than 25 years. This text provides one of the essential tools for both undergraduate students and professional engineers.

Preface

Acknowledgements

To the Student

1 Basic Ideas

Arithmetic

Representation

Decimal places and significant figures

Precedence

Set notation

Deductions

Algebra

Rules of elementary algebra

Workshop

Identities and equations

Simultaneous equations

Rational expressions

Rearranging equations

Quadratic equations

Polynomials

The binomial theorem

Workshop

The general binomial theorem

Practical

Summary

Assignment

Further exercises

**Further concepts**

Indices and logarithms

Inequalities

Rules for inequalities

Partial fractions

Workshop

Set notation

Functions

Methods of proof

Practical

Summary

Exercises

Assignment

Further exercises

**Trigonometry and geometry**

Coordinate systems

Circular functions

Trigonometrical identities

The form *a* cos 0 + *b *sin 0

Solutions of equations

Workshop

Coordinate geometry

The straight line

The circle

The conic sections

Workshop

Practical

Summary

Exercises

Assignment

Further exercises

**Limits, continuity and differentiation**

Limits

The laws of limits

Workshop

Right and left limits

Continuity

Differentiability

Leibnizâ€™s theorem

Techniques of differentiation

Workshop

Logarithmic differentiation

Implicit differentiation

Parametric differentiation

Rates of change

Workshop

Practical

Summary

Exercises

Assignments

Further exercises

**Hyperbolic functions**

Definitions and identities

Differentiation of hyperbolic functions

Curve sketching

Workshop

Injective functions

Surjective functions

Bijective functions

Pseudo-inverse functions

Differentiation of inverse functions

The inverse circular functions

Workshop

The inverse hypervolic functions

Practical

Summary

Exercises

Assignment

Further exercises

**Further differentiation**

Tangents and

The programmed approach, established in the first two editions is maintained in the third and it provides a sound foundation from which the student can build a solid engineering understanding. This edition has been modified to reflect the changes in the syllabuses which students encounter before beginning undergraduate studies. The first two chapters include material that assumes the reader has little previous experience in maths. Written by CHarles Evans who lectures at the University of Portsmouth and has been teaching engineering and applied mathematics for more than 25 years. This text provides one of the essential tools for both undergraduate students and professional engineers.

Preface

Acknowledgements

To the Student

1 Basic Ideas

Arithmetic

Representation

Decimal places and significant figures

Precedence

Set notation

Deductions

Algebra

Rules of elementary algebra

Workshop

Identities and equations

Simultaneous equations

Rational expressions

Rearranging equations

Quadratic equations

Polynomials

The binomial theorem

Workshop

The general binomial theorem

Practical

Summary

Assignment

Further exercises

**Further concepts**

Indices and logarithms

Inequalities

Rules for inequalities

Partial fractions

Workshop

Set notation

Functions

Methods of proof

Practical

Summary

Exercises

Assignment

Further exercises

**Trigonometry and geometry**

Coordinate systems

Circular functions

Trigonometrical identities

The form *a* cos 0 + *b *sin 0

Solutions of equations

Workshop

Coordinate geometry

The straight line

The circle

The conic sections

Workshop

Practical

Summary

Exercises

Assignment

Further exercises

**Limits, continuity and differentiation**

Limits

The laws of limits

Workshop

Right and left limits

Continuity

Differentiability

Leibnizâ€™s theorem

Techniques of differentiation

Workshop

Logarithmic differentiation

Implicit differentiation

Parametric differentiation

Rates of change

Workshop

Practical

Summary

Exercises

Assignments

Further exercises

**Hyperbolic functions**

Definitions and identities

Differentiation of hyperbolic functions

Curve sketching

Workshop

Injective functions

Surjective functions

Bijective functions

Pseudo-inverse functions

Differentiation of inverse functions

The inverse circular functions

Workshop

The inverse hypervolic functions

Practical

Summary

Exercises

Assignment

Further exercises

**Further differentiation**

Tangents and

The programmed approach, established in the first two editions is maintained in the third and it provides a sound foundation from which the student can build a solid engineering understanding. This edition has been modified to reflect the changes in the syllabuses which students encounter before beginning undergraduate studies. The first two chapters include material that assumes the reader has little previous experience in maths. Written by CHarles Evans who lectures at the University of Portsmouth and has been teaching engineering and applied mathematics for more than 25 years. This text provides one of the essential tools for both undergraduate students and professional engineers.

Preface

Acknowledgements

To the Student

1 Basic Ideas

Arithmetic

Representation

Decimal places and significant figures

Precedence

Set notation

Deductions

Algebra

Rules of elementary algebra

Workshop

Identities and equations

Simultaneous equations

Rational expressions

Rearranging equations

Quadratic equations

Polynomials

The binomial theorem

Workshop

The general binomial theorem

Practical

Summary

Assignment

Further exercises

**Further concepts**

Indices and logarithms

Inequalities

Rules for inequalities

Partial fractions

Workshop

Set notation

Functions

Methods of proof

Practical

Summary

Exercises

Assignment

Further exercises

**Trigonometry and geometry**

Coordinate systems

Circular functions

Trigonometrical identities

The form *a* cos 0 + *b *sin 0

Solutions of equations

Workshop

Coordinate geometry

The straight line

The circle

The conic sections

Workshop

Practical

Summary

Exercises

Assignment

Further exercises

**Limits, continuity and differentiation**

Limits

The laws of limits

Workshop

Right and left limits

Continuity

Differentiability

Leibnizâ€™s theorem

Techniques of differentiation

Workshop

Logarithmic differentiation

Implicit differentiation

Parametric differentiation

Rates of change

Workshop

Practical

Summary

Exercises

Assignments

Further exercises

**Hyperbolic functions**

Definitions and identities

Differentiation of hyperbolic functions

Curve sketching

Workshop

Injective functions

Surjective functions

Bijective functions

Pseudo-inverse functions

Differentiation of inverse functions

The inverse circular functions

Workshop

The inverse hypervolic functions

Practical

Summary

Exercises

Assignment

Further exercises

**Further differentiation**

Tangents and

Preface

Acknowledgements

To the Student

1 Basic Ideas

Arithmetic

Representation

Decimal places and significant figures

Precedence

Set notation

Deductions

Algebra

Rules of elementary algebra

Workshop

Identities and equations

Simultaneous equations

Rational expressions

Rearranging equations

Quadratic equations

Polynomials

The binomial theorem

Workshop

The general binomial theorem

Practical

Summary

Assignment

Further exercises

**Further concepts**

Indices and logarithms

Inequalities

Rules for inequalities

Partial fractions

Workshop

Set notation

Functions

Methods of proof

Practical

Summary

Exercises

Assignment

Further exercises

**Trigonometry and geometry**

Coordinate systems

Circular functions

Trigonometrical identities

The form *a* cos 0 + *b *sin 0

Solutions of equations

Workshop

Coordinate geometry

The straight line

The circle

The conic sections

Workshop

Practical

Summary

Exercises

Assignment

Further exercises

**Limits, continuity and differentiation**

Limits

The laws of limits

Workshop

Right and left limits

Continuity

Differentiability

Leibnizâ€™s theorem

Techniques of differentiation

Workshop

Logarithmic differentiation

Implicit differentiation

Parametric differentiation

Rates of change

Workshop

Practical

Summary

Exercises

Assignments

Further exercises

**Hyperbolic functions**

Definitions and identities

Differentiation of hyperbolic functions

Curve sketching

Workshop

Injective functions

Surjective functions

Bijective functions

Pseudo-inverse functions

Differentiation of inverse functions

The inverse circular functions

Workshop

The inverse hypervolic functions

Practical

Summary

Exercises

Assignment

Further exercises

**Further differentiation**

Tangents and

Preface

Acknowledgements

To the Student

1 Basic Ideas

Arithmetic

Representation

Decimal places and significant figures

Precedence

Set notation

Deductions

Algebra

Rules of elementary algebra

Workshop

Identities and equations

Simultaneous equations

Rational expressions

Rearranging equations

Quadratic equations

Polynomials

The binomial theorem

Workshop

The general binomial theorem

Practical

Summary

Assignment

Further exercises

**Further concepts**

Indices and logarithms

Inequalities

Rules for inequalities

Partial fractions

Workshop

Set notation

Functions

Methods of proof

Practical

Summary

Exercises

Assignment

Further exercises

**Trigonometry and geometry**

Coordinate systems

Circular functions

Trigonometrical identities

The form *a* cos 0 + *b *sin 0

Solutions of equations

Workshop

Coordinate geometry

The straight line

The circle

The conic sections

Workshop

Practical

Summary

Exercises

Assignment

Further exercises

**Limits, continuity and differentiation**

Limits

The laws of limits

Workshop

Right and left limits

Continuity

Differentiability

Leibnizâ€™s theorem

Techniques of differentiation

Workshop

Logarithmic differentiation

Implicit differentiation

Parametric differentiation

Rates of change

Workshop

Practical

Summary

Exercises

Assignments

Further exercises

**Hyperbolic functions**

Definitions and identities

Differentiation of hyperbolic functions

Curve sketching

Workshop

Injective functions

Surjective functions

Bijective functions

Pseudo-inverse functions

Differentiation of inverse functions

The inverse circular functions

Workshop

The inverse hypervolic functions

Practical

Summary

Exercises

Assignment

Further exercises

**Further differentiation**

Tangents and

Preface

Acknowledgements

To the Student

1 Basic Ideas

Arithmetic

Representation

Decimal places and significant figures

Precedence

Set notation

Deductions

Algebra

Rules of elementary algebra

Workshop

Identities and equations

Simultaneous equations

Rational expressions

Rearranging equations

Quadratic equations

Polynomials

The binomial theorem

Workshop

The general binomial theorem

Practical

Summary

Assignment

Further exercises

**Further concepts**

Indices and logarithms

Inequalities

Rules for inequalities

Partial fractions

Workshop

Set notation

Functions

Methods of proof

Practical

Summary

Exercises

Assignment

Further exercises

**Trigonometry and geometry**

Coordinate systems

Circular functions

Trigonometrical identities

The form *a* cos 0 + *b *sin 0

Solutions of equations

Workshop

Coordinate geometry

The straight line

The circle

The conic sections

Workshop

Practical

Summary

Exercises

Assignment

Further exercises

**Limits, continuity and differentiation**

Limits

The laws of limits

Workshop

Right and left limits

Continuity

Differentiability

Leibnizâ€™s theorem

Techniques of differentiation

Workshop

Logarithmic differentiation

Implicit differentiation

Parametric differentiation

Rates of change

Workshop

Practical

Summary

Exercises

Assignments

Further exercises

**Hyperbolic functions**

Definitions and identities

Differentiation of hyperbolic functions

Curve sketching

Workshop

Injective functions

Surjective functions

Bijective functions

Pseudo-inverse functions

Differentiation of inverse functions

The inverse circular functions

Workshop

The inverse hypervolic functions

Practical

Summary

Exercises

Assignment

Further exercises

**Further differentiation**

Tangents and