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by K. F. Riley, M. P. Hobson and S. J. Bence

Edition: 2ND 02Copyright: 2002

Publisher: Cambridge University Press

Published: 2002

International: No

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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 reorganized 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.

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 ordinary differential equations

16. Series solutions of ordinary differential equations

17. Eigenfunction methods for differential equations

18. Partial differential equations: general and particular

19. Partial differential equations: separation of variables and other methods

20. Complex variables

21. Tensors

22. Calculus of variations

23. Integral equations

24. Group Theory

25. Representation theory

26. Probability

27. Statistics

28. Numerical methods

Appendix

Index.

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Summary

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 reorganized 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.

Table of Contents

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 ordinary differential equations

16. Series solutions of ordinary differential equations

17. Eigenfunction methods for differential equations

18. Partial differential equations: general and particular

19. Partial differential equations: separation of variables and other methods

20. Complex variables

21. Tensors

22. Calculus of variations

23. Integral equations

24. Group Theory

25. Representation theory

26. Probability

27. Statistics

28. Numerical methods

Appendix

Index.

Publisher Info

Publisher: Cambridge University Press

Published: 2002

International: No

Published: 2002

International: No

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 ordinary differential equations

16. Series solutions of ordinary differential equations

17. Eigenfunction methods for differential equations

18. Partial differential equations: general and particular

19. Partial differential equations: separation of variables and other methods

20. Complex variables

21. Tensors

22. Calculus of variations

23. Integral equations

24. Group Theory

25. Representation theory

26. Probability

27. Statistics

28. Numerical methods

Appendix

Index.