ES 202- Mathematics for Engineers

Zülfü Aşık, Office: AE-H107; e-mail: azulfu@metu.edu.tr

Course Information

TENTATIVE OUTLINE

PART I/ VECTOR ANALYSIS

1. Introduction to vectors, vector spaces and linear algebra, linear independence, basis, orthogonality, vector norms.
2. Vector calculus: Parametric representation of  a curve and surface, vector differentiation along a curve, fundamentals of differential geometry, Frennet-Serret formulas.
3. Gradient, divergence and curl.
4. Line, surface, volume integrals.
5. Integral theorems: Green, Gauss and Stokes' theorem.

PART II/ FUNDAMENTALS OF LINEAR ALGEBRA

6. Matrices, matrix operations, special matrices, determinant and inverse of a matrix by adjoint matrix.
7. Elementary row and column operations, echelon forms, rank and norms of a matrix, complete solution of a system of equations (GEM), Gauss-Jordan method, determinant and inverse of a matrix by adjoint matrix.
8. Linear transformation and change of bases.
9. Characteristic value problems and related theorems, eigenvalues and corresponding eigenvectors. Applications: diagonalization, modal matrix, quadratic forms.
10. Special topics.

TEXT BOOK

• Kreyszig, E., Advanced Engineering Mathematics, John Wiley & Sons, (ed. 1988, chapters: 6,7,8,9 or ed. 1993, chapters 7,8,9).

REFERENCES

• Wylie, C.R., Advanced Engineering Mathematics, McGraw Hill, (ed. 1988, chapters: 3,11,12,13 or ed. 1995, chapters 3,13,15)
• O'Neil, P.V., Advanced Engineering Mathematics, Wadsworth Publishing Company, (ed. 1988, chapters 11, 12, 13, 14, 15, 16)
• Apostol, M.T., Calculus: Volumes I and II, Blaisdel Publishing Company, 1967.
• Cambell. H., Linear Algebra with Applications, Prentice Hall, 1980.
• Hoffmann, K. and Kunze R., Linear Algebra, Prentice Hall, 1980.
• Fraleigh, J.B. and R.Beauregard, Linear Algebra, Addison-Wesley Publishing Company, 1990.

There will be 55% 2 term exams; 35% final and remaining 10% will be shared between attendance, quiz, and/or homework assignments. There will be only one and a common make-up exam after the final .

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