This section contains documents that could not be made accessible to screen reader software. A "#" symbol is used to denote such documents.

Amazon logo Help support MIT OpenCourseWare by shopping at! MIT OpenCourseWare offers direct links to to purchase the books cited in this course. Click on the Amazon logo to the left of any citation and purchase the book from, and MIT OpenCourseWare will receive up to 10% of all purchases you make. Your support will enable MIT to continue offering open access to MIT courses.


Most of the readings and all practice problems are from the course text:

Amazon logo Knowles, J. K. Linear Vector Spaces and Cartesian Tensors. New York, NY: Oxford University Press, 1998. ISBN: 9780195112542.

Abeyaratne, Rohan. Lecture Notes on the Mechanics of Elastic Solids. Vol. 1, A Brief Review of Some Mathematical Preliminaries. Free e-book, 2006. (PDF - 1.4 MB)#

Further References

Amazon logo Gel'fand, I. M. Lectures on Linear Algebra. New York, NY: Dover, 1989. ISBN: 9780486660820.

Amazon logo Halmos, P. R. Finite Dimensional Vector Spaces. Princeton, NJ: Van Nostrand-Reinhold, 1958. ISBN: 9780387900933.

Gel'fand, I. M., and S. V. Fomin. Calculus of Variations. Englewood Cliffs, NJ: Prentice Hall, 1963.

Amazon logo Giaquinta, M., and S. Hilderbrandt. Calculus of Variations I. New York, NY: Springer, 1996. ISBN: 9780387506258.

Amazon logo Troutman, J. L. Variational Calculus with Elementary Convexity. New York, NY: Springer-Verlag, 1983. ISBN: 9780387907710.

1 Vector space, linear independence, dimension of a vector space, basis for vector space, components of a vector pp. 1-8 Problems 1.1-1.11
2 Scalar product, length of vector, distance between vectors, angle between vectors, orthonormal basis pp. 9-17 Problems 1.12-1.20
3 Linear transformations, invariant subspace, eigenvalue problem pp. 18-20 and 23-26 Problems 2.1, 2.3, 2.6, and 2.17 (except questions about singular/non-singular/inverse transforms)
4 Null space, singular/non-singular linear transformations, inverse, components of a linear transformation Chapter 2 Problems 2.1-2.5, 2.8, 2.9, 2.11, and 2.15-2.17
5 Components of a linear transformation, components in different bases, scalar invariants, cartesian tensors, symmetric tensors, skew-symmetric tensors pp. 27-32 and 42-46 Problems 3.1-3.12
6 Eigenvalues of a symmetric tensor, principal basis, positive-definite tensor, orthogonal tensor, proper/improper, orthogonal tensor pp. 42-52 (except tensor products) and 56-57 Problems 3.13-3.18, 3.20, and 3.24-3.26
7 Tensor product of 2 vectors, polar decomposition of a non-singular tensor

pp. 44 and 57-59

Also read chapters 2 and 3 in Abeyaratne, Rohan. Lecture Notes on the Mechanics of Elastic Solids.

Problems 3.3-3.7, 3.11-3.16, 3.22, and 3.23