An engineering approach to linear algebra
著者
書誌事項
An engineering approach to linear algebra
University Press, 1972
- : pbk
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内容説明・目次
内容説明
Professor Sawyer's book is based on a course given to the majority of engineering students in their first year at Toronto University. Its aim is to present the important ideas in linear algebra to students of average ability whose principal interests lie outside the field of mathematics; as such it will be of interest to students in other disciplines as well as engineering. The emphasis throughout is on imparting an understanding of the significance of the mathematical techniques and great care has therefore been taken to being out the underlying ideas embodied in the formal calculations. In those places where a rigorous treatment would be very long and wearisome, an explanation rather than a complete proof is provided, the reader being warned that in a more formal treatment such results would need to be be proved. The book is full of physical analogies (many from fields outside the realm of engineering) and contains many worked and unworked examples, integrated with the text.
目次
- Preface
- 1. Mathematics and engineers
- 2. Mappings
- 3. The nature of generalisation
- 4. Symbolic conditions for linearity
- 5. Graphical representation
- 6. Vectors in a plane
- 7. Bases
- 8. Calculations in a vector space
- 9. Change of axes
- 10. Specification of a linear mapping
- 11. Transformations
- 12. Choice of basis
- 13. Complex numbers
- 14. Calculations with complex numbers
- 15. Complex numbers and trigonometry
- 16. Trigonometry and exponentials
- 17. Complex numbers: terminology
- 19. The logic of complex numbers
- 20. The algebra of transformations
- 21. Subtraction of transformations' 22. Matrix notation
- 23. An application of matrix multiplication
- 24. An application of linearity
- 25. procedure for finding invariant lines, eigenvectors and eigenvalues
- 26. Determinant and inverse
- 27. Properties of determinants
- 28. Matrices other than square
- partitions
- 29. Subscript and summation notation
- 30. Row and column vectors
- 31. Affine and Euclidean geometry
- 32. Scalar products
- 33. Transpose
- quadratic forms
- 34. Maximum and minimum principles
- 35. Formal laws of matrix algebra
- 36. Orthogonal transformations
- 37. Finding the simplest expressions for quadratic forms
- 38. Principal axes and eigenvectors
- 39. Lines, planes and subspaces
- vector product
- 40. Null space, column space, row space of a matrix
- 42. Illustrating the importance of orthogonal matrices
- 43. Linear programming
- 44. Linear programming, continued
- Answers
- Index.
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