Mathematics for PhysicsOUP Oxford, 2007 - 783 من الصفحات 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. |
المحتوى
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 |
779 | |
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عبارات ومصطلحات مألوفة
amplitude spectrum angle angular momentum applied atoms axis calculation centre CHAPTER coefficient complex number components consider constant coordinates correlation corresponding cos² cosh cosine cross-correlation defined density derivative differential equation DIGITAL FILTERS dimensions distance distribution eigenfunctions eigenvalues eigenvectors electron End loop energy estimate example Exercise filter Fourier transform function given gives Hence input integral Laplace transforms linear mass matrix maximum Maxwell-Boltzmann distribution measurement method moment of inertia MONTE CARLO METHOD noise normal normal distribution orbit output particle plane positive probability problem quantities QUANTUM MECHANICS radius random numbers relationship result right-hand side sampled signal SCHRÖDINGER WAVE EQUATION shown in Figure sin² sinh solution solve standard deviation Substituting Table temperature theorem timesteps underlying signal unit variables vector velocity wave x₁ zero ду дх