Two and Three Dimensional Calculus with Applications in Science and Engineering by Phil Dyke
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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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