An Engineering Approach to Linear Algebra

The book is full of physical analogies and contains many worked and unworked examples, integrated with the text.

W. W. Sawyer (Author)

9780521093330, Cambridge University Press

Paperback / softback, published 11 January 2009

316 pages
24.6 x 18.9 x 1.7 cm, 0.57 kg

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.

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.

Subject Areas: Algebra [PBF]