Below are some references on the various topics covered in the class. It is not necessary for the students to consult these references. But if the student wants to learn beyond what is covered in the class, the following references could be good starting points.
The Finite Element Method: Linear Statics and Dynamics Finite Element Analysis, by T. J. R. Hughes
Publisher: Dover Publications; (2000)
ISBN: 0486411818
An Introduction to the Finite Element Method, by J. N. Reddy
Publisher: McGraw-Hill Science/Engineering/Math; 3rd edition (2005)
ISBN: 0072466855
Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics, by D. Braess
Publisher: Cambridge University Press; (2007)
ISBN: 0521705185
Finite Element Methods for Flow Problems, by J. Donea and A. Huereta
Publisher: John Wiley & Sons Ltd.; (2003)
ISBN: 0471496669
Note: The books on Mathematical Theory of FEM have more advanced treatments than what we discuss in this course. These books assume some knowledge in Mathematical Analysis, and Partial Differential Equations. If a student is very curious on the mathematical aspects of FEM, one can approach the following books. If you want me to recommend a book, I suggest the book by Oden and Reddy as it is quite approachable to engineering students with strong mathematics background.
The Mathematical Theory of Finite Element Methods; by S. C. Brenner and L. R. Scott
Publisher: Springer; 3rd edition (2007)
ISBN: 0387759336
Mixed and Hybrid Finite Element Method; by F. Brezzi and M. Fortin
Publisher: Springer; 1st edition (1991)
ISBN: 0387975829
The Finite Element Method for Elliptic Problems; by P. G. Ciarlet
Publisher: SIAM; 2nd edition (2002)
ISBN:0898715148
Theory and Practice of Finite Elements; by A. Ern and J.-L. Guermond
Publisher: Springer; 1st edition (2004)
ISBN: 0387205748
An Introduction to the Mathematical Theory of Finite Elements; by J. T. Oden and J. N. Reddy
Publisher: Dover Publications; (2011)
ISBN: 0486462994
Kronecker Products and Matrix Calculus: With Applications, by A. Graham
Publisher: Ellis Horwood Lrd; (1981)
ISBN: 0853123918
Matrix Calculus and Kronecker Product: A Practical Approach to Linear and Multilinear Algebra, by W.-H. Steeb and Y. Hardy
Publisher: World Scientific Publishing Company; (2011)
ISBN: 9814335312
Problems and Solutions In Introductory and Advanced Matrix Calculus, by W.-H. Steeb
Publisher: World Scientific Publishing; (2006)
ISBN: 9812702024
Applied Partial Differential Equations, J. D. Logan
Publisher: Springer (Undergraduate Texts in Mathematics); 2nd edition (2004)
ISBN: 0387209530
Introduction to Linear Algebra, by G. Strang
Publisher: Wellesley Cambridge Press; (2009)
ISBN: 0980232716
Linear Algebra: An Introductory Approach, by C. W. Curtis
Publisher: Springer (Undergraduate Texts in Mathematics); (1984)
ISBN: 0387909923
Finite Dimensional Vector Spaces, by P. R. Halmos (A classical! It is proof-oriented, and can be hard for engineering students.)
Publisher: Springer; (1993)
ISBN: 0387900934
Matrix Computations, by G. H. Golub and Trefethen and C. F. Van Loan
Publisher: The John Hopkins University Press; (1996)
ISBN: 0801854149
Numerical Linear Algebra, by L. N. Trefethen and D. Bau III
Publisher: SIAM; (1997)
ISBN: 0898713617
Scientific Computing, by M. T. Heath
Publisher: McGraw-Hill Companies; 2nd edition (2002)
ISBN: 0072399104
C Programming Language, by D. W. Kernighan and D. M. Ritchie
Publisher: Prentice Hall PTR; 2nd edition (1988)
ISBN: 0131103628
The C++ Programming Language, by B. Stroustrup
Publisher: Addison-Wesley; 3rd edition (1997)
ISBN: 0201327554
A Primer on Scientific Programming with Python, by H. P. Langtangen
Publisher: Springer; 2nd edition (2011)
ISBN: 978-3-642-18365-2