The new edition of this highly acclaimed textbook contains several major additions, including more than four hundred new exercises (with hints and answers). To match the mathematical preparation of current senior college and university entrants, the authors have included a preliminary chapter covering areas such as polynomial equations, trigonometric identities, coordinate geometry, partial fractions, binomial expansions, induction, and the proof of necessary and sufficient conditions. Elsewhere, matrix decompositions, nearly-singular matrices and non-square sets of linear equations are treated in detail. The presentation of probability has been reorganised and greatly extended, and includes all physically important distributions. New topics covered in a separate statistics chapter include estimator efficiency, distributions of samples, t- and F-tests for comparing means and variances, applications of the chi-squared distribution, and maximum likelihood and least-squares fitting. In other chapters the following topics have been added: linear recurrence relations, curvature, envelopes, curve-sketching, and more refined numerical methods.
Prefaces; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics; Index.
From reviews of previous editions: '...a great scientific textbook. It is a tour de force ... to write mathematical sections that are both complete and at an appropriate academic level. The authors have clearly succeeded in this challenge, making this a remarkable pedagogical book ... The choice of exercises is excellent and possibly the best feature of the book. In summary, this textbook is a great reference at undergraduate levels, particularly for those who like to teach or learn using lots of examples and exercises.' R. Botet, European Journal of Physics
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