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**About this book :- **
**Two and Three Dimensional Calculus with Applications in Science and Engineering ** written by
** Phil Dyke **.
Written in an approachable style and filled with numerous illustrative examples throughout, Two and Three Dimensional Calculus: with Applications in Science and Engineering assumes no prior knowledge of partial differentiation or vectors and explains difficult concepts with easy to follow examples. Rather than concentrating on mathematical structures, the book describes the development of techniques through their use in science and engineering so that students acquire skills that enable them to be used in a wide variety of practical situations. It also has enough rigor to enable those who wish to investigate the more mathematical generalizations found in most mathematics degrees to do so.

Assumes no prior knowledge of partial differentiation, multiple integration or vectors

Includes easy-to-follow examples throughout to help explain difficult concepts

Features end-of-chapter exercises with solutions to exercises in the book.

Two and Three Dimensional Calculus: with Applications in Science and Engineering is an ideal textbook for undergraduate students of engineering and applied sciences as well as those needing to use these methods for real problems in industry and commerce.

**Book Detail :- **
** Title: ** Two and Three Dimensional Calculus with Applications in Science and Engineering
** Edition: **
** Author(s): ** Phil Dyke
** Publisher: ** Wiley
** Series: **
** Year: ** 2018
** Pages: ** 382
** Type: ** PDF
** Language: ** English
** ISBN: ** 1119221781
** Country: **

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**About Author :- **
**Phil Dyke**
is Professor of Applied Mathematics at the
**University of Plymouth**. He was Head of School of Mathematics and Statistics for 18 years then Head of School of Computing, Communications and Electronics for four years but he now devotes his time to teaching and research. After graduating with a first in mathematics he gained a PhD in coastal engineering modelling. He has over 35 years� experience teaching undergraduates, most of this teaching to engineering students. He has run an international research group since 1981 applying mathematics to coastal engineering and shallow sea dynamics. Apart from contributing to these engineering mathematics books, he has written seven textbooks on mathematics and marine science, and still enjoys trying to solve environmental problems using simple mathematical models.

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**Book Contents :- **
**Two and Three Dimensional Calculus with Applications in Science and Engineering ** written by
** Phil Dyke**
cover the following topics.
'
**1. Revision of One-Dimensional Calculus **

1.1 Limits and Convergence

1.2 Differentiation

1.2.1 Rules for Differentiation

1.2.2 Mean Value Theorem

1.2.3 Taylor’s Series

1.2.4 Maxima and Minima

1.2.5 Numerical Differentiation

1.3 Integration

Exercises
**2. Partial Differentiation **

2.1 Introduction

2.2 Differentials

2.2.1 Small Errors

2.3 Total Derivative

2.4 Chain Rule

2.4.1 Leibniz Rule

2.4.2 Chain Rule in n Dimensions

2.4.3 Implicit Functions

2.5 Jacobian

2.6 Higher Derivatives

2.6.1 Higher Differentials

2.7 Taylor’sTheorem

2.8 Conjugate Functions

2.9 Case Study:Thermodynamics

Exercises
**3. Maxima and Minima **

3.1 Introduction

3.2 Maxima, Minima and Saddle Points

3.3 Lagrange Multipliers

3.3.1 Generalisations

3.4 Optimisation

3.4.1 Hill Climbing Techniques

Exercises
**4. Vector Algebra **

4.1 Introduction

4.2 Vector Addition

4.3 Components

4.4 Scalar Product

4.5 Vector Product

4.5.1 Scalar Triple Product

4.5.2 Vector Triple Product

Exercises
**5. Vector Differentiation **

5.1 Introduction

5.2 Differential Geometry

5.2.1 Space Curves

5.2.2 Surfaces

5.3 Mechanics

Exercises
**6. Gradient, Divergence, and Curl **

6.1 Introduction

6.2 Gradient

6.3 Divergence

6.4 Curl

6.5 Vector Identities

6.6 Conjugate Functions

Exercises
**7. Curvilinear Co-ordinates **

7.1 Introduction

7.2 Curved Axes and Scale Factors

7.3 Curvilinear Gradient, Divergence, and Curl

7.3.1 Gradient

7.3.2 Divergence

7.3.3 Curl

7.4 Further Results and Tensors

7.4.1 Tensor Notation

7.4.2 Covariance and Contravariance

Exercises
**8. PathIntegrals **

8.1 Introduction

8.2 Integration Along a Curve

8.3 Practical Applications

Exercises
**9. Multiple Integrals **

9.1 Introduction

9.2 The Double Integral

9.2.1 Rotation and Translation

9.2.2 Change of Order of Integration

9.2.3 Plane Polar Co-ordinates

9.2.4 Applications of Double Integration

9.3 Triple Integration

9.3.1 Cylindrical and Spherical Polar Co-ordinates

9.3.2 Applications of Triple Integration

Exercises
**10. Surface Integrals **

10.1 Introduction

10.2 Green’s Theorem in the Plane

10.3 Integration over a Curved Surface

10.4 Applications of Surface Integration

Exercises
**11. Integral Theorems **

11.1 Introduction

11.2 Stokes’ Theorem

11.3 Gauss’ DivergenceTheorem

11.3.1 Green’s Second Identity

11.4 Co-ordinate-Free Definitions

11.5 Applications of Integral Theorems

11.5.1 Electromagnetic Theory

11.5.1.1 Maxwell’s Equations

11.5.2 Fluid Mechanics

11.5.3 ElasticityTheory
**12. Solutions and Answers to Exercises **

References

Index

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