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Look Inside An Engineering Approach to Linear Algebra

An Engineering Approach to Linear Algebra


  • Date Published: January 2009
  • availability: Available
  • format: Paperback
  • isbn: 9780521093330


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About the Authors
  • 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.

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    Product details

    • Date Published: January 2009
    • format: Paperback
    • isbn: 9780521093330
    • length: 316 pages
    • dimensions: 246 x 189 x 17 mm
    • weight: 0.57kg
    • availability: Available
  • Table of Contents

    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
    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

  • Author

    W. W. Sawyer

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