Mathematics for Physics

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OUP Oxford, 2007 - 783 من الصفحات
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Mathematics is the essential language of science. It enables us to describe abstract physical concepts, and to apply these concepts in practical ways. Yet mathematical skills and concepts are an aspect of physics that many students fear the most. Mathematics for Physics recognizes the challenges faced by students in equipping themselves with the maths skills necessary to gain a full understanding of physics. Working from basic yet fundamental principles, the book builds the students' confidence by leading them through the subject in a steady, progressive way. As its primary aim, Mathematics for Physics shows the relevance of mathematics to the study of physics. Its unique approach demonstrates the application of mathematical concepts alongside the development of the mathematical theory. This stimulating and motivating approach helps students to master the maths and see its application in the context of physics in one seamless learning experience. Mathematics is a subject mastered most readily through active learning. Mathematics for Physics features both print and online support, with many in-text exercises and end-of-chapter problems, and web-based computer programs, to both stimulate learning and build understanding. Mathematics for Physics is the perfect introduction to the essential mathematical concepts which all physics students should master. Online Resource Centre: For lecturers: Figures from the book available to download, to facilitate lecture preparation For students: 23 computer programs, coded in FORTRAN, C, and MATLAB, to enable students to investigate and solve a range of problems - from the behaviour of clusters of stars to the design of nuclear reactors - and hence make learning as effective and engaging as possible.
 

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المحتويات

1 Useful formulae and relationships
1
2 Dimensions and dimensional analysis
20
3 Sequences and series
29
4 Differentiation
35
5 Integration
53
6 Complex numbers
70
7 Ordinary differential equations
86
8 Matrices I and determinants
106
23 The Monte Carlo method
405
24 Matrices II
433
Angular momentum and spin
444
26 Sampling theory
466
27 Straightline relationships and the linear correlation coefficient
478
28 Interpolation
497
29 Quadrature
508
30 Linear equations
522

9 Vector algebra
128
10 Conic sections and orbits
152
11 Partial differentiation
170
12 Probability and statistics
185
13 Coordinate systems and multiple integration
201
14 Distributions
221
15 Hyperbolic functions
239
16 Vector analysis
248
17 Fourier analysis
265
18 Introduction to digital signal processing
309
19 Numerical methods for ordinary differential equations
329
20 Applications of partial differential equations
337
Schrödinger wave equation and observations
359
22 The MaxwellBoltzmann distribution
395
31 Numerical solution of equations
535
32 Signals and noise
541
33 Digital filters
571
34 Introduction to estimation theory
591
35 Linear programming and optimization
607
36 Laplace transforms
622
37 Networks
635
38 Simulation with particles
647
39 Chaos and physical calculations
672
Appendices
681
References and further reading
715
Solutions to exercises and problems
717
Index
779
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حول المؤلف (2007)

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Michael M. Woolfson is Emeritus Professor of Theoretical Physics, Department of Physics, University of York, UK.
Dr Malcolm S. Woolfson is a Lecturer in Signal Processing, School of Electrical and Electronic Engineering, University of Nottingham, UK.

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