Mathematics for physics/ (Record no. 151719)
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000 -LEADER | |
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fixed length control field | 00350nam a2200133Ia 4500 |
020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
International Standard Book Number | 9780199289295 |
040 ## - CATALOGING SOURCE | |
Transcribing agency | CUS |
082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER | |
Classification number | 530.15 |
Item number | WOO/M |
100 ## - MAIN ENTRY--PERSONAL NAME | |
Personal name | Woolfson, Michael M |
245 #0 - TITLE STATEMENT | |
Title | Mathematics for physics/ |
Statement of responsibility, etc. | Michael M. Woolfson, Malcolm S. Woolfson |
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
Place of publication, distribution, etc. | New York: |
Name of publisher, distributor, etc. | Oxford University Press, |
Date of publication, distribution, etc. | 2007. |
300 ## - PHYSICAL DESCRIPTION | |
Extent | xx, 783 p. : |
Other physical details | ill. ; |
Dimensions | 25 cm. |
505 ## - FORMATTED CONTENTS NOTE | |
Formatted contents note | 1. Useful formulae and relationships --<br/>1.1. Relationships for triangles --<br/>1.2. Trigonometric relationships --<br/>1.3. The binomial expansion (theorem) --<br/>1.4. The exponential e --<br/>1.5. Natural logarithms --<br/>1.6. Two-dimensional coordinate systems --<br/>Problems --<br/>2. Dimensions and dimensional analysis --<br/>2.1. Basic units and dimensions --<br/>2.2. Dimensional homogeneity --<br/>2.3. Dimensional analysis --<br/>2.4. Electrical and magnetic units --<br/>Problems --<br/>3. Sequences and series --<br/>3.1. Arithmetic series --<br/>3.2. Geometric series --<br/>3.3. Harmonic series --<br/>3.4. Tests for convergence --<br/>3.5. Power series --<br/>Problems --<br/>4. Differentiation --<br/>4.1. The basic idea of a derivative --<br/>4.2. Chain rule --<br/>4.3. Product rule --<br/>4.4. Quotient rule --<br/>4.5. Maxima, minima, and higher-order derivatives --<br/>4.6. Expressing ex as a power series in x --<br/>4.7. Taylor's theorem --<br/>Problems --<br/>5. Integration --<br/>5.1. Indefinite and definite integrals --<br/>5.2. Techniques of evaluating integrals --<br/>5.3. Substitution method --<br/>5.4. Partial fractions --<br/>5.5. Integration by parts --<br/>5.6. Integrating powers of cos x and sin x --<br/>5.7. The definite integral : area under the curve --<br/>Problems --<br/>6. Complex numbers --<br/>6.1. Definition of a complex number --<br/>6.2. Argand diagram --<br/>6.3. Ways of describing a complex number --<br/>6.4. De Moivre's theorem --<br/>6.5. Complex conjugate --<br/>6.6. Division and reduction to real-plus-imaginary form --<br/>6.7. Modulus-argument form as an aid to integration --<br/>6.8. Circuits with alternating currents and voltages --<br/>Problems. 7. Ordinary differential equations --<br/>7.1. Types of ordinary differential equation --<br/>7.2. Separation of variables --<br/>7.3. Homogeneous equations --<br/>7.4. The integrating factor --<br/>7.5. Linear constant-coefficient equations --<br/>7.6. Simple harmonic motion --<br/>7.7. Damped simple harmonic motion --<br/>7.8. Forced vibrations --<br/>7.9. An LCR circuit --<br/>Problems --<br/>8. Matrices I and determinants --<br/>8.1. Definition of a matrix --<br/>8.2. Operations of matrix algebra --<br/>8.3. Types of matrix --<br/>8.4. Applications to lens systems --<br/>8.5. Application to special relativity --<br/>8.6. Determinants --<br/>8.7. Types of determinant --<br/>8.8. Inverse matrix --<br/>8.9. Linear equations --<br/>Problems --<br/>9. Vector algebra --<br/>9.1. Scalar and vector quantities --<br/>9.2. Products of vectors --<br/>9.3. Vector representations of some rotational quantities --<br/>9.4. Linear dependence and independence --<br/>9.5. A straight line in vector form --<br/>9.6. A plane in vector form --<br/>9.7. Distance of a point from a plane --<br/>9.8. Relationships between lines and planes --<br/>9.9. Differentiation of vectors --<br/>9.10. Motion under a central force --<br/>Problems --<br/>10. Conic sections and orbits --<br/>10.1. Kepler and Newton --<br/>10.2. Conic sections and the cone --<br/>10.3. The circle and the ellipse --<br/>10.4. The parabola --<br/>10.5. The hyperbola --<br/>10.6. The orbits of planets and Kepler's laws --<br/>10.7. The dynamics of orbits --<br/>10.8. Alpha-particle scattering --<br/>Problems --<br/>11. Partial differentiation --<br/>11.1. What is partial differentiation? --<br/>11.2. Higher partial derivatives --<br/>11.3. The total derivative --<br/>11.4 Partial differentiation and thermodynamics --<br/>11.5. Taylor series for a function of two variables --<br/>11.6. Maxima and minima in a multidimensional space --<br/>Problems. 12. Probability and statistics --<br/>12.1. What is probability? --<br/>12.2. Combining probabilities --<br/>12.3. Making selections --<br/>12.4. The birthday problem --<br/>12.5. Bayes' theorem --<br/>12.6. Too much information? --<br/>12.7. Mean ; variance and standard deviation ; median --<br/>12.8. Combining different estimates --<br/>Problems --<br/>13. Coordinate systems and multiple integration --<br/>13.1. Two-dimensional coordinate systems --<br/>13.2. Integration in a rectangular Cartesian system --<br/>13.3. Integration with polar coordinates --<br/>13.4. Changing coordinate systems --<br/>13.5. Three-dimensional coordinate systems --<br/>13.6. Integration in three dimensions --<br/>13.7. Moments of inertia --<br/>13.8. Parallel-axis theorem --<br/>13.9. Perpendicular-axis theorem --<br/>Problems --<br/>14. Distributions --<br/>14.1. Kinds of distribution --<br/>14.2. Firing at a target --<br/>14.3. Normal distribution --<br/>14.4. Binomial distribution --<br/>14.5. Poisson distribution --<br/>Problems --<br/>15. Hyperbolic functions --<br/>15.1. Definitions --<br/>15.2. Relationships linking hyperbolic functions --<br/>15.3. Differentiation of hyperbolic functions --<br/>15.4. Taylor expansions of sinh x and cosh x --<br/>15.5. Integration involving hyperbolic functions --<br/>15.6. Comments about analytical functions --<br/>Problems --<br/>16. Vector analysis --<br/>16.1. Scalar and vector fields --<br/>16.2. Gradient (grad) and del operators --<br/>16.3. Conservative fields --<br/>16.4. Divergence (div) --<br/>16.5. Laplacian operator --<br/>16.6. Curl of a vector field --<br/>16.7. Maxwell's equations and the speed of light --<br/>Problems. 17. Fourier analysis --<br/>17.1. Signals --<br/>17.2. The nature of signals --<br/>17.3. Amplitude-frequency diagrams --<br/>17.4. Fourier transform --<br/>17.5. The d-function, d(x) --<br/>17.6. Inverse Fourier transform --<br/>17.7. Several cosine signals --<br/>17.8. Parseval's theorem --<br/>17.9. Fourier series --<br/>17.10. Determination of the Fourier coefficients a₀, {an}, and {bn} --<br/>17.11. Fourier or waveform synthesis --<br/>17.12. Power in periodic signals --<br/>17.13. Complex form for the Fourier series --<br/>17.14. Amplitude and phase spectrum --<br/>17.15. Alternative variables for Fourier analysis --<br/>17.16. Applications in physics --<br/>17.17. Summary --<br/>Problems --<br/>18. Introduction to digital signal processing --<br/>18.1. More on sampling --<br/>18.2. Discrete Fourier transform (DFT) --<br/>18.3. Some concluding remarks --<br/>Problems --<br/>19. Numerical methods for ordinary differential equations --<br/>19.1. The need for numerical methods --<br/>19.2. Euler methods --<br/>19.3. Runge-Kutta method --<br/>19.4. Numerov method --<br/>Problems --<br/>20. Applications of partial differential equations --<br/>20.1. Types of partial differential equation --<br/>20.2. Finite differences --<br/>20.3. Diffusion --<br/>20.4. Explicit method --<br/>20.5. The Crank-Nicholson method --<br/>20.6. Poisson's and Laplace's equations --<br/>20.7. Numerical solution of a hot-plate problem --<br/>20.8. Boundary conditions for hot-plate problems --<br/>20.9. Wave equation --<br/>20.10. Finite-difference approach for a vibrating string --<br/>20.11. Two-dimensional vibrations --<br/>Problems. 21. Quantum mechanics I : Schrödinger wave equation and observations --<br/>21.1. Transition from classical to modern physics : a brief history --<br/>21.2. Intuitive derivation of the Schrödinger wave equation --<br/>21.3. A particle in a one-dimensional box --<br/>21.4. Observations and operators --<br/>21.5. A square box and degeneracy --<br/>21.6. Probabilities of measurements --<br/>21.7. Simple harmonic oscillator --<br/>21.8. Three-dimensional simple harmonic oscillator --<br/>21.9. The free particle --<br/>21.10. Compatible and incompatible measurements --<br/>21.11. A potential barrier --<br/>21.12. Tunnelling --<br/>21.13. Other methods of solving the TISWE --<br/>Problems --<br/>22. The Maxwell-Boltzmann distribution --<br/>22.1. Deriving the Maxwell-Boltzmann distribution --<br/>22.2. Retention of a planetary atmosphere --<br/>22.3. Nuclear fusion in stars --<br/>Problems --<br/>23. The Monte Carlo method --<br/>23.1. Origin of the method --<br/>23.2. Random walk --<br/>23.3. A simple polymer model --<br/>23.4. Uniform distribution within a sphere and random directions --<br/>23.5. Generation of random numbers for non-uniform deviates --<br/>23.6. Equation of state of a liquid --<br/>23.7. Simulation of a fluid by the Monte Carlo method --<br/>23.8. Modelling a nuclear reactor --<br/>23.9. Description of a simple model reactor --<br/>23.10. A cautionary tale --<br/>Problems --<br/>24. Matrices II --<br/>24.1. Population studies --<br/>24.2. Eigenvalues and eigenvectors --<br/>24.3. Diagonalization of a matrix --<br/>24.4. A vibrating system --<br/>Problems. 25. Quantum mechanics II : Angular momentum and spin --<br/>25.1. Measurement of angular momentum --<br/>25.2. The hydrogen atom --<br/>25.3. Electron spin --<br/>25.4. Many-electron systems --<br/>Problems --<br/>26. Sampling theory --<br/>26.1. Samples --<br/>26.2. Sampling proportions --<br/>26.3. The significance of differences --<br/>Problems --<br/>27. Straight-line relationships and the linear correlation coefficient --<br/>27.1. General considerations --<br/>27.2. Lines of regression --<br/>27.3. A numerical application --<br/>27.4. The linear correlation coefficient --<br/>27.5. A general least-squares straight line --<br/>27.6. Linearization of other forms of relationship --<br/>Problems --<br/>28. Interpolation --<br/>28.1. Applications of interpolation --<br/>28.2. Linear interpolation --<br/>28.3. Parabolic interpolation --<br/>28.4. Gauss interpolation formula --<br/>28.5. Cubic spline interpolation --<br/>28.6. Multidimensional interpolation --<br/>28.7. Extrapolation --<br/>Problems --<br/>29. Quadrature --<br/>29.1. Definite integrals --<br/>29.2. Trapezium method --<br/>29.3. Simpson's method (rule) --<br/>29.4. Romberg method --<br/>29.5. Gauss quadrature --<br/>29.6. Multidimensional quadrature --<br/>29.7. Monte Carlo integration --<br/>Problems --<br/>30. Linear equations --<br/>30.1. Interpretation of linearly dependent and incompatible equations --<br/>30.2. Gauss elimination method --<br/>30.3. Conditioning of a set of equations --<br/>30.4. Gauss-Seidel method --<br/>30.5. Homogeneous equations --<br/>30.6. Least-squares solutions --<br/>30.7. Refinement procedures using least squares --<br/>Problems --<br/>31. Numerical solution of equations --<br/>31.1. The nature of equations --<br/>31.2. Fixed-point iteration method --<br/>31.3. Newton-Raphson method --<br/>Problems --<br/>32. Signals and noise --<br/>32.1. Introduction. 32. Signals, noise, and noisy signals --<br/>32.3. Mathematical and statistical description of noise --<br/>32.4. Auto- and cross-correlation functions --<br/>32.5. Detection of signals in noise --<br/>32.6. White noise --<br/>32.7. Concluding remarks --<br/>Problems --<br/>33. Digital filters --<br/>33.1. Introduction --<br/>33.2. Fourier transform methods --<br/>33.3. Constant-coefficient digital filters --<br/>33.4. Other filter design methods --<br/>33.5. Summary of main results and concluding remarks --<br/>Problems --<br/>34. Introduction to estimation theory --<br/>34.1. Introduction --<br/>34.2. Estimation of a constant --<br/>34.3. Taking into account the changes in the underlying model --<br/>34.4. Further methods --<br/>34.5. Concluding remarks --<br/>Problems --<br/>35. Linear programming and optimization --<br/>35.1. Basic ideas of linear programming --<br/>35.2. Simplex method --<br/>35.3. Non-linear optimization ; gradient methods --<br/>35.4. Gradient method for two variables --<br/>35.5. A practical gradient method for any number of variables --<br/>35.6. Optimization with constraints, the Lagrange multiplier method --<br/>Problems --<br/>36. Laplace transforms --<br/>36.1. Defining the Laplace transform --<br/>36.2. Inverse Laplace transforms --<br/>36.3. Solving differential equations with Laplace transforms --<br/>36.4. Laplace transforms and transfer functions --<br/>Problems --<br/>37. Networks --<br/>37.1. Graphs and networks --<br/>37.2. Types of network --<br/>37.3. Finding cheapest paths --<br/>37.4. Critical path analysis --<br/>Problems --<br/>38. Simulation with particles --<br/>38.1. Types of problem --<br/>38.2. Binary systems --<br/>38.3. An electron in a magnetic field --<br/>38.4. N-body problems --<br/>38.5. Molecular dynamics --<br/>38.6. Modelling plasmas --<br/>38.7. Collisionless particle-in-cell model --<br/>Problems. 39. Chaos and physical calculations --<br/>39.1. The nature of chaos --<br/>39.2. An example from population studies --<br/>39.3. Other aspects of chaos --<br/>Problem --<br/>Appendices --<br/>Appendix 1. Table of integrals --<br/>Appendix 2. Inverse Fourier transform --<br/>Appendix 3. Fourier transform of a sampled signal --<br/>Appendix 4. Derivation of the discrete and inverse discrete Fourier transforms --<br/>Appendix 5. Program OSCILLAT --<br/>Appendix 6. Program EXPLICIT --<br/>Appendix 7. Program HEATCRNI --<br/>Appendix 8. Program SIMPLATE --<br/>Appendix 9. Program STRING1 --<br/>Appendix 10. Program DRUM --<br/>Appendix 11. Program SHOOT --<br/>Appendix 12. Program DRUNKARD --<br/>Appendix 13. Program POLYMER --<br/>Appendix 14. Program METROPOLIS --<br/>Appendix 15. Program REACTOR --<br/>Appendix 16. Program LESLIE --<br/>Appendix 17. Eigenvalues and eigenvectors of Hermitian matrices --<br/>Appendix 18. Distance of a point from a line --<br/>Appendix 19. Program MULGAUSS --<br/>Appendix 20. Program MCINT --<br/>Appendix 21. Program GS --<br/>Appendix 22. Second moments for uniform and Gaussian noise --<br/>Appendix 23. Convolution theorem --<br/>Appendix 24. Output from a filter when the input is a cosine --<br/>Appendix 25. Program GRADMAX --<br/>Appendix 26. Program NETWORK --<br/>Appendix 27. Program GRAVBODY --<br/>Appendix 28. Program ELECLENS --<br/>Appendix 29. Program CLUSTER --<br/>Appendix 30. Program FLUIDYN --<br/>Appendix 31. Condition for collisionless PIC --<br/>Appendix 32. Program PLASMA1 --<br/>References and further reading --<br/>Solutions to exercises and problems --<br/>Index. |
650 ## - SUBJECT | |
Keyword | Mathematical physics |
700 ## - ADDED ENTRY--PERSONAL NAME | |
Personal name | Woolfson, Malcolm S |
942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
Koha item type | General Books Science Library |
Withdrawn status | Lost status | Damaged status | Not for loan | Home library | Current library | Shelving location | Date acquired | Full call number | Accession number | Date last seen | Koha item type | Public note |
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Science Library, Sikkim University | Science Library, Sikkim University | Science Library General Section | 28/08/2016 | 530.15 WOO/M | P06405 | 16/01/2020 | General Books Science Library | Books For SU Science Library |