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Mathematics for physics

Author: Michael M Woolfson; Malcolm S Woolfson
Publisher: Oxford ; New York : Oxford University Press, 2007.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
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"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."
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Genre/Form: Manuels d'enseignement supérieur
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Michael M Woolfson; Malcolm S Woolfson
ISBN: 9780199289295 0199289298
OCLC Number: 70823177
Description: xx, 783 pages : illustrations ; 25 cm
Contents: 1. Useful formulae and relationships --
1.1. Relationships for triangles --
1.2. Trigonometric relationships --
1.3. The binomial expansion (theorem) --
1.4. The exponential e --
1.5. Natural logarithms --
1.6. Two-dimensional coordinate systems --
Problems --
2. Dimensions and dimensional analysis --
2.1. Basic units and dimensions --
2.2. Dimensional homogeneity --
2.3. Dimensional analysis --
2.4. Electrical and magnetic units --
Problems --
3. Sequences and series --
3.1. Arithmetic series --
3.2. Geometric series --
3.3. Harmonic series --
3.4. Tests for convergence --
3.5. Power series --
Problems --
4. Differentiation --
4.1. The basic idea of a derivative --
4.2. Chain rule --
4.3. Product rule --
4.4. Quotient rule --
4.5. Maxima, minima, and higher-order derivatives --
4.6. Expressing ex as a power series in x --
4.7. Taylor's theorem --
Problems --
5. Integration --
5.1. Indefinite and definite integrals --
5.2. Techniques of evaluating integrals --
5.3. Substitution method --
5.4. Partial fractions --
5.5. Integration by parts --
5.6. Integrating powers of cos x and sin x --
5.7. The definite integral : area under the curve --
Problems --
6. Complex numbers --
6.1. Definition of a complex number --
6.2. Argand diagram --
6.3. Ways of describing a complex number --
6.4. De Moivre's theorem --
6.5. Complex conjugate --
6.6. Division and reduction to real-plus-imaginary form --
6.7. Modulus-argument form as an aid to integration --
6.8. Circuits with alternating currents and voltages --
Problems. 7. Ordinary differential equations --
7.1. Types of ordinary differential equation --
7.2. Separation of variables --
7.3. Homogeneous equations --
7.4. The integrating factor --
7.5. Linear constant-coefficient equations --
7.6. Simple harmonic motion --
7.7. Damped simple harmonic motion --
7.8. Forced vibrations --
7.9. An LCR circuit --
Problems --
8. Matrices I and determinants --
8.1. Definition of a matrix --
8.2. Operations of matrix algebra --
8.3. Types of matrix --
8.4. Applications to lens systems --
8.5. Application to special relativity --
8.6. Determinants --
8.7. Types of determinant --
8.8. Inverse matrix --
8.9. Linear equations --
Problems --
9. Vector algebra --
9.1. Scalar and vector quantities --
9.2. Products of vectors --
9.3. Vector representations of some rotational quantities --
9.4. Linear dependence and independence --
9.5. A straight line in vector form --
9.6. A plane in vector form --
9.7. Distance of a point from a plane --
9.8. Relationships between lines and planes --
9.9. Differentiation of vectors --
9.10. Motion under a central force --
Problems --
10. Conic sections and orbits --
10.1. Kepler and Newton --
10.2. Conic sections and the cone --
10.3. The circle and the ellipse --
10.4. The parabola --
10.5. The hyperbola --
10.6. The orbits of planets and Kepler's laws --
10.7. The dynamics of orbits --
10.8. Alpha-particle scattering --
Problems --
11. Partial differentiation --
11.1. What is partial differentiation? --
11.2. Higher partial derivatives --
11.3. The total derivative --
11.4 Partial differentiation and thermodynamics --
11.5. Taylor series for a function of two variables --
11.6. Maxima and minima in a multidimensional space --
Problems. 12. Probability and statistics --
12.1. What is probability? --
12.2. Combining probabilities --
12.3. Making selections --
12.4. The birthday problem --
12.5. Bayes' theorem --
12.6. Too much information? --
12.7. Mean ; variance and standard deviation ; median --
12.8. Combining different estimates --
Problems --
13. Coordinate systems and multiple integration --
13.1. Two-dimensional coordinate systems --
13.2. Integration in a rectangular Cartesian system --
13.3. Integration with polar coordinates --
13.4. Changing coordinate systems --
13.5. Three-dimensional coordinate systems --
13.6. Integration in three dimensions --
13.7. Moments of inertia --
13.8. Parallel-axis theorem --
13.9. Perpendicular-axis theorem --
Problems --
14. Distributions --
14.1. Kinds of distribution --
14.2. Firing at a target --
14.3. Normal distribution --
14.4. Binomial distribution --
14.5. Poisson distribution --
Problems --
15. Hyperbolic functions --
15.1. Definitions --
15.2. Relationships linking hyperbolic functions --
15.3. Differentiation of hyperbolic functions --
15.4. Taylor expansions of sinh x and cosh x --
15.5. Integration involving hyperbolic functions --
15.6. Comments about analytical functions --
Problems --
16. Vector analysis --
16.1. Scalar and vector fields --
16.2. Gradient (grad) and del operators --
16.3. Conservative fields --
16.4. Divergence (div) --
16.5. Laplacian operator --
16.6. Curl of a vector field --
16.7. Maxwell's equations and the speed of light --
Problems. 17. Fourier analysis --
17.1. Signals --
17.2. The nature of signals --
17.3. Amplitude-frequency diagrams --
17.4. Fourier transform --
17.5. The d-function, d(x) --
17.6. Inverse Fourier transform --
17.7. Several cosine signals --
17.8. Parseval's theorem --
17.9. Fourier series --
17.10. Determination of the Fourier coefficients a₀, {an}, and {bn} --
17.11. Fourier or waveform synthesis --
17.12. Power in periodic signals --
17.13. Complex form for the Fourier series --
17.14. Amplitude and phase spectrum --
17.15. Alternative variables for Fourier analysis --
17.16. Applications in physics --
17.17. Summary --
Problems --
18. Introduction to digital signal processing --
18.1. More on sampling --
18.2. Discrete Fourier transform (DFT) --
18.3. Some concluding remarks --
Problems --
19. Numerical methods for ordinary differential equations --
19.1. The need for numerical methods --
19.2. Euler methods --
19.3. Runge-Kutta method --
19.4. Numerov method --
Problems --
20. Applications of partial differential equations --
20.1. Types of partial differential equation --
20.2. Finite differences --
20.3. Diffusion --
20.4. Explicit method --
20.5. The Crank-Nicholson method --
20.6. Poisson's and Laplace's equations --
20.7. Numerical solution of a hot-plate problem --
20.8. Boundary conditions for hot-plate problems --
20.9. Wave equation --
20.10. Finite-difference approach for a vibrating string --
20.11. Two-dimensional vibrations --
Problems. 21. Quantum mechanics I : Schrödinger wave equation and observations --
21.1. Transition from classical to modern physics : a brief history --
21.2. Intuitive derivation of the Schrödinger wave equation --
21.3. A particle in a one-dimensional box --
21.4. Observations and operators --
21.5. A square box and degeneracy --
21.6. Probabilities of measurements --
21.7. Simple harmonic oscillator --
21.8. Three-dimensional simple harmonic oscillator --
21.9. The free particle --
21.10. Compatible and incompatible measurements --
21.11. A potential barrier --
21.12. Tunnelling --
21.13. Other methods of solving the TISWE --
Problems --
22. The Maxwell-Boltzmann distribution --
22.1. Deriving the Maxwell-Boltzmann distribution --
22.2. Retention of a planetary atmosphere --
22.3. Nuclear fusion in stars --
Problems --
23. The Monte Carlo method --
23.1. Origin of the method --
23.2. Random walk --
23.3. A simple polymer model --
23.4. Uniform distribution within a sphere and random directions --
23.5. Generation of random numbers for non-uniform deviates --
23.6. Equation of state of a liquid --
23.7. Simulation of a fluid by the Monte Carlo method --
23.8. Modelling a nuclear reactor --
23.9. Description of a simple model reactor --
23.10. A cautionary tale --
Problems --
24. Matrices II --
24.1. Population studies --
24.2. Eigenvalues and eigenvectors --
24.3. Diagonalization of a matrix --
24.4. A vibrating system --
Problems. 25. Quantum mechanics II : Angular momentum and spin --
25.1. Measurement of angular momentum --
25.2. The hydrogen atom --
25.3. Electron spin --
25.4. Many-electron systems --
Problems --
26. Sampling theory --
26.1. Samples --
26.2. Sampling proportions --
26.3. The significance of differences --
Problems --
27. Straight-line relationships and the linear correlation coefficient --
27.1. General considerations --
27.2. Lines of regression --
27.3. A numerical application --
27.4. The linear correlation coefficient --
27.5. A general least-squares straight line --
27.6. Linearization of other forms of relationship --
Problems --
28. Interpolation --
28.1. Applications of interpolation --
28.2. Linear interpolation --
28.3. Parabolic interpolation --
28.4. Gauss interpolation formula --
28.5. Cubic spline interpolation --
28.6. Multidimensional interpolation --
28.7. Extrapolation --
Problems --
29. Quadrature --
29.1. Definite integrals --
29.2. Trapezium method --
29.3. Simpson's method (rule) --
29.4. Romberg method --
29.5. Gauss quadrature --
29.6. Multidimensional quadrature --
29.7. Monte Carlo integration --
Problems --
30. Linear equations --
30.1. Interpretation of linearly dependent and incompatible equations --
30.2. Gauss elimination method --
30.3. Conditioning of a set of equations --
30.4. Gauss-Seidel method --
30.5. Homogeneous equations --
30.6. Least-squares solutions --
30.7. Refinement procedures using least squares --
Problems --
31. Numerical solution of equations --
31.1. The nature of equations --
31.2. Fixed-point iteration method --
31.3. Newton-Raphson method --
Problems --
32. Signals and noise --
32.1. Introduction. 32. Signals, noise, and noisy signals --
32.3. Mathematical and statistical description of noise --
32.4. Auto- and cross-correlation functions --
32.5. Detection of signals in noise --
32.6. White noise --
32.7. Concluding remarks --
Problems --
33. Digital filters --
33.1. Introduction --
33.2. Fourier transform methods --
33.3. Constant-coefficient digital filters --
33.4. Other filter design methods --
33.5. Summary of main results and concluding remarks --
Problems --
34. Introduction to estimation theory --
34.1. Introduction --
34.2. Estimation of a constant --
34.3. Taking into account the changes in the underlying model --
34.4. Further methods --
34.5. Concluding remarks --
Problems --
35. Linear programming and optimization --
35.1. Basic ideas of linear programming --
35.2. Simplex method --
35.3. Non-linear optimization ; gradient methods --
35.4. Gradient method for two variables --
35.5. A practical gradient method for any number of variables --
35.6. Optimization with constraints, the Lagrange multiplier method --
Problems --
36. Laplace transforms --
36.1. Defining the Laplace transform --
36.2. Inverse Laplace transforms --
36.3. Solving differential equations with Laplace transforms --
36.4. Laplace transforms and transfer functions --
Problems --
37. Networks --
37.1. Graphs and networks --
37.2. Types of network --
37.3. Finding cheapest paths --
37.4. Critical path analysis --
Problems --
38. Simulation with particles --
38.1. Types of problem --
38.2. Binary systems --
38.3. An electron in a magnetic field --
38.4. N-body problems --
38.5. Molecular dynamics --
38.6. Modelling plasmas --
38.7. Collisionless particle-in-cell model --
Problems. 39. Chaos and physical calculations --
39.1. The nature of chaos --
39.2. An example from population studies --
39.3. Other aspects of chaos --
Problem --
Appendices --
Appendix 1. Table of integrals --
Appendix 2. Inverse Fourier transform --
Appendix 3. Fourier transform of a sampled signal --
Appendix 4. Derivation of the discrete and inverse discrete Fourier transforms --
Appendix 5. Program OSCILLAT --
Appendix 6. Program EXPLICIT --
Appendix 7. Program HEATCRNI --
Appendix 8. Program SIMPLATE --
Appendix 9. Program STRING1 --
Appendix 10. Program DRUM --
Appendix 11. Program SHOOT --
Appendix 12. Program DRUNKARD --
Appendix 13. Program POLYMER --
Appendix 14. Program METROPOLIS --
Appendix 15. Program REACTOR --
Appendix 16. Program LESLIE --
Appendix 17. Eigenvalues and eigenvectors of Hermitian matrices --
Appendix 18. Distance of a point from a line --
Appendix 19. Program MULGAUSS --
Appendix 20. Program MCINT --
Appendix 21. Program GS --
Appendix 22. Second moments for uniform and Gaussian noise --
Appendix 23. Convolution theorem --
Appendix 24. Output from a filter when the input is a cosine --
Appendix 25. Program GRADMAX --
Appendix 26. Program NETWORK --
Appendix 27. Program GRAVBODY --
Appendix 28. Program ELECLENS --
Appendix 29. Program CLUSTER --
Appendix 30. Program FLUIDYN --
Appendix 31. Condition for collisionless PIC --
Appendix 32. Program PLASMA1 --
References and further reading --
Solutions to exercises and problems --
Index.
Responsibility: Michael M. Woolfson, Malcolm S. Woolfson.
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   schema:datePublished "2007" ;
   schema:description "1. Useful formulae and relationships -- 1.1. Relationships for triangles -- 1.2. Trigonometric relationships -- 1.3. The binomial expansion (theorem) -- 1.4. The exponential e -- 1.5. Natural logarithms -- 1.6. Two-dimensional coordinate systems -- Problems -- 2. Dimensions and dimensional analysis -- 2.1. Basic units and dimensions -- 2.2. Dimensional homogeneity -- 2.3. Dimensional analysis -- 2.4. Electrical and magnetic units -- Problems -- 3. Sequences and series -- 3.1. Arithmetic series -- 3.2. Geometric series -- 3.3. Harmonic series -- 3.4. Tests for convergence -- 3.5. Power series -- Problems -- 4. Differentiation -- 4.1. The basic idea of a derivative -- 4.2. Chain rule -- 4.3. Product rule -- 4.4. Quotient rule -- 4.5. Maxima, minima, and higher-order derivatives -- 4.6. Expressing ex as a power series in x -- 4.7. Taylor's theorem -- Problems -- 5. Integration -- 5.1. Indefinite and definite integrals -- 5.2. Techniques of evaluating integrals -- 5.3. Substitution method -- 5.4. Partial fractions -- 5.5. Integration by parts -- 5.6. Integrating powers of cos x and sin x -- 5.7. The definite integral : area under the curve -- Problems -- 6. Complex numbers -- 6.1. Definition of a complex number -- 6.2. Argand diagram -- 6.3. Ways of describing a complex number -- 6.4. De Moivre's theorem -- 6.5. Complex conjugate -- 6.6. Division and reduction to real-plus-imaginary form -- 6.7. Modulus-argument form as an aid to integration -- 6.8. Circuits with alternating currents and voltages -- Problems."@en ;
   schema:description "21. Quantum mechanics I : Schrödinger wave equation and observations -- 21.1. Transition from classical to modern physics : a brief history -- 21.2. Intuitive derivation of the Schrödinger wave equation -- 21.3. A particle in a one-dimensional box -- 21.4. Observations and operators -- 21.5. A square box and degeneracy -- 21.6. Probabilities of measurements -- 21.7. Simple harmonic oscillator -- 21.8. Three-dimensional simple harmonic oscillator -- 21.9. The free particle -- 21.10. Compatible and incompatible measurements -- 21.11. A potential barrier -- 21.12. Tunnelling -- 21.13. Other methods of solving the TISWE -- Problems -- 22. The Maxwell-Boltzmann distribution -- 22.1. Deriving the Maxwell-Boltzmann distribution -- 22.2. Retention of a planetary atmosphere -- 22.3. Nuclear fusion in stars -- Problems -- 23. The Monte Carlo method -- 23.1. Origin of the method -- 23.2. Random walk -- 23.3. A simple polymer model -- 23.4. Uniform distribution within a sphere and random directions -- 23.5. Generation of random numbers for non-uniform deviates -- 23.6. Equation of state of a liquid -- 23.7. Simulation of a fluid by the Monte Carlo method -- 23.8. Modelling a nuclear reactor -- 23.9. Description of a simple model reactor -- 23.10. A cautionary tale -- Problems -- 24. Matrices II -- 24.1. Population studies -- 24.2. Eigenvalues and eigenvectors -- 24.3. Diagonalization of a matrix -- 24.4. A vibrating system -- Problems."@en ;
   schema:description "32. Signals, noise, and noisy signals -- 32.3. Mathematical and statistical description of noise -- 32.4. Auto- and cross-correlation functions -- 32.5. Detection of signals in noise -- 32.6. White noise -- 32.7. Concluding remarks -- Problems -- 33. Digital filters -- 33.1. Introduction -- 33.2. Fourier transform methods -- 33.3. Constant-coefficient digital filters -- 33.4. Other filter design methods -- 33.5. Summary of main results and concluding remarks -- Problems -- 34. Introduction to estimation theory -- 34.1. Introduction -- 34.2. Estimation of a constant -- 34.3. Taking into account the changes in the underlying model -- 34.4. Further methods -- 34.5. Concluding remarks -- Problems -- 35. Linear programming and optimization -- 35.1. Basic ideas of linear programming -- 35.2. Simplex method -- 35.3. Non-linear optimization ; gradient methods -- 35.4. Gradient method for two variables -- 35.5. A practical gradient method for any number of variables -- 35.6. Optimization with constraints, the Lagrange multiplier method -- Problems -- 36. Laplace transforms -- 36.1. Defining the Laplace transform -- 36.2. Inverse Laplace transforms -- 36.3. Solving differential equations with Laplace transforms -- 36.4. Laplace transforms and transfer functions -- Problems -- 37. Networks -- 37.1. Graphs and networks -- 37.2. Types of network -- 37.3. Finding cheapest paths -- 37.4. Critical path analysis -- Problems -- 38. Simulation with particles -- 38.1. Types of problem -- 38.2. Binary systems -- 38.3. An electron in a magnetic field -- 38.4. N-body problems -- 38.5. Molecular dynamics -- 38.6. Modelling plasmas -- 38.7. Collisionless particle-in-cell model -- Problems."@en ;
   schema:description "12. Probability and statistics -- 12.1. What is probability? -- 12.2. Combining probabilities -- 12.3. Making selections -- 12.4. The birthday problem -- 12.5. Bayes' theorem -- 12.6. Too much information? -- 12.7. Mean ; variance and standard deviation ; median -- 12.8. Combining different estimates -- Problems -- 13. Coordinate systems and multiple integration -- 13.1. Two-dimensional coordinate systems -- 13.2. Integration in a rectangular Cartesian system -- 13.3. Integration with polar coordinates -- 13.4. Changing coordinate systems -- 13.5. Three-dimensional coordinate systems -- 13.6. Integration in three dimensions -- 13.7. Moments of inertia -- 13.8. Parallel-axis theorem -- 13.9. Perpendicular-axis theorem -- Problems -- 14. Distributions -- 14.1. Kinds of distribution -- 14.2. Firing at a target -- 14.3. Normal distribution -- 14.4. Binomial distribution -- 14.5. Poisson distribution -- Problems -- 15. Hyperbolic functions -- 15.1. Definitions -- 15.2. Relationships linking hyperbolic functions -- 15.3. Differentiation of hyperbolic functions -- 15.4. Taylor expansions of sinh x and cosh x -- 15.5. Integration involving hyperbolic functions -- 15.6. Comments about analytical functions -- Problems -- 16. Vector analysis -- 16.1. Scalar and vector fields -- 16.2. Gradient (grad) and del operators -- 16.3. Conservative fields -- 16.4. Divergence (div) -- 16.5. Laplacian operator -- 16.6. Curl of a vector field -- 16.7. Maxwell's equations and the speed of light -- Problems."@en ;
   schema:description "17. Fourier analysis -- 17.1. Signals -- 17.2. The nature of signals -- 17.3. Amplitude-frequency diagrams -- 17.4. Fourier transform -- 17.5. The d-function, d(x) -- 17.6. Inverse Fourier transform -- 17.7. Several cosine signals -- 17.8. Parseval's theorem -- 17.9. Fourier series -- 17.10. Determination of the Fourier coefficients a₀, {an}, and {bn} -- 17.11. Fourier or waveform synthesis -- 17.12. Power in periodic signals -- 17.13. Complex form for the Fourier series -- 17.14. Amplitude and phase spectrum -- 17.15. Alternative variables for Fourier analysis -- 17.16. Applications in physics -- 17.17. Summary -- Problems -- 18. Introduction to digital signal processing -- 18.1. More on sampling -- 18.2. Discrete Fourier transform (DFT) -- 18.3. Some concluding remarks -- Problems -- 19. Numerical methods for ordinary differential equations -- 19.1. The need for numerical methods -- 19.2. Euler methods -- 19.3. Runge-Kutta method -- 19.4. Numerov method -- Problems -- 20. Applications of partial differential equations -- 20.1. Types of partial differential equation -- 20.2. Finite differences -- 20.3. Diffusion -- 20.4. Explicit method -- 20.5. The Crank-Nicholson method -- 20.6. Poisson's and Laplace's equations -- 20.7. Numerical solution of a hot-plate problem -- 20.8. Boundary conditions for hot-plate problems -- 20.9. Wave equation -- 20.10. Finite-difference approach for a vibrating string -- 20.11. Two-dimensional vibrations -- Problems."@en ;
   schema:description "25. Quantum mechanics II : Angular momentum and spin -- 25.1. Measurement of angular momentum -- 25.2. The hydrogen atom -- 25.3. Electron spin -- 25.4. Many-electron systems -- Problems -- 26. Sampling theory -- 26.1. Samples -- 26.2. Sampling proportions -- 26.3. The significance of differences -- Problems -- 27. Straight-line relationships and the linear correlation coefficient -- 27.1. General considerations -- 27.2. Lines of regression -- 27.3. A numerical application -- 27.4. The linear correlation coefficient -- 27.5. A general least-squares straight line -- 27.6. Linearization of other forms of relationship -- Problems -- 28. Interpolation -- 28.1. Applications of interpolation -- 28.2. Linear interpolation -- 28.3. Parabolic interpolation -- 28.4. Gauss interpolation formula -- 28.5. Cubic spline interpolation -- 28.6. Multidimensional interpolation -- 28.7. Extrapolation -- Problems -- 29. Quadrature -- 29.1. Definite integrals -- 29.2. Trapezium method -- 29.3. Simpson's method (rule) -- 29.4. Romberg method -- 29.5. Gauss quadrature -- 29.6. Multidimensional quadrature -- 29.7. Monte Carlo integration -- Problems -- 30. Linear equations -- 30.1. Interpretation of linearly dependent and incompatible equations -- 30.2. Gauss elimination method -- 30.3. Conditioning of a set of equations -- 30.4. Gauss-Seidel method -- 30.5. Homogeneous equations -- 30.6. Least-squares solutions -- 30.7. Refinement procedures using least squares -- Problems -- 31. Numerical solution of equations -- 31.1. The nature of equations -- 31.2. Fixed-point iteration method -- 31.3. Newton-Raphson method -- Problems -- 32. Signals and noise -- 32.1. Introduction."@en ;
   schema:description "7. Ordinary differential equations -- 7.1. Types of ordinary differential equation -- 7.2. Separation of variables -- 7.3. Homogeneous equations -- 7.4. The integrating factor -- 7.5. Linear constant-coefficient equations -- 7.6. Simple harmonic motion -- 7.7. Damped simple harmonic motion -- 7.8. Forced vibrations -- 7.9. An LCR circuit -- Problems -- 8. Matrices I and determinants -- 8.1. Definition of a matrix -- 8.2. Operations of matrix algebra -- 8.3. Types of matrix -- 8.4. Applications to lens systems -- 8.5. Application to special relativity -- 8.6. Determinants -- 8.7. Types of determinant -- 8.8. Inverse matrix -- 8.9. Linear equations -- Problems -- 9. Vector algebra -- 9.1. Scalar and vector quantities -- 9.2. Products of vectors -- 9.3. Vector representations of some rotational quantities -- 9.4. Linear dependence and independence -- 9.5. A straight line in vector form -- 9.6. A plane in vector form -- 9.7. Distance of a point from a plane -- 9.8. Relationships between lines and planes -- 9.9. Differentiation of vectors -- 9.10. Motion under a central force -- Problems -- 10. Conic sections and orbits -- 10.1. Kepler and Newton -- 10.2. Conic sections and the cone -- 10.3. The circle and the ellipse -- 10.4. The parabola -- 10.5. The hyperbola -- 10.6. The orbits of planets and Kepler's laws -- 10.7. The dynamics of orbits -- 10.8. Alpha-particle scattering -- Problems -- 11. Partial differentiation -- 11.1. What is partial differentiation? -- 11.2. Higher partial derivatives -- 11.3. The total derivative -- 11.4 Partial differentiation and thermodynamics -- 11.5. Taylor series for a function of two variables -- 11.6. Maxima and minima in a multidimensional space -- Problems."@en ;
   schema:description "39. Chaos and physical calculations -- 39.1. The nature of chaos -- 39.2. An example from population studies -- 39.3. Other aspects of chaos -- Problem -- Appendices -- Appendix 1. Table of integrals -- Appendix 2. Inverse Fourier transform -- Appendix 3. Fourier transform of a sampled signal -- Appendix 4. Derivation of the discrete and inverse discrete Fourier transforms -- Appendix 5. Program OSCILLAT -- Appendix 6. Program EXPLICIT -- Appendix 7. Program HEATCRNI -- Appendix 8. Program SIMPLATE -- Appendix 9. Program STRING1 -- Appendix 10. Program DRUM -- Appendix 11. Program SHOOT -- Appendix 12. Program DRUNKARD -- Appendix 13. Program POLYMER -- Appendix 14. Program METROPOLIS -- Appendix 15. Program REACTOR -- Appendix 16. Program LESLIE -- Appendix 17. Eigenvalues and eigenvectors of Hermitian matrices -- Appendix 18. Distance of a point from a line -- Appendix 19. Program MULGAUSS -- Appendix 20. Program MCINT -- Appendix 21. Program GS -- Appendix 22. Second moments for uniform and Gaussian noise -- Appendix 23. Convolution theorem -- Appendix 24. Output from a filter when the input is a cosine -- Appendix 25. Program GRADMAX -- Appendix 26. Program NETWORK -- Appendix 27. Program GRAVBODY -- Appendix 28. Program ELECLENS -- Appendix 29. Program CLUSTER -- Appendix 30. Program FLUIDYN -- Appendix 31. Condition for collisionless PIC -- Appendix 32. Program PLASMA1 -- References and further reading -- Solutions to exercises and problems -- Index."@en ;
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