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## Thursday, June 26, 2008

### Engineering Mathematics I

Engineering Mathematics I

Objective

This course covers calculus of one variable, techniques of differentiation and integration and their applications. Sequences and series and some of the convergence tests. Extension of the concepts of differentiation and integration to two and more variables by the study of partial differentiation. Taylor series, Maclaurin series and Fourier series. Concepts of complex functions and vectors. Concepts of probability, distributions, mean, variance.

Syllabus

1. Calculus of One Variable ( 7 hrs)
Functions, inverse trigonometric functions and principal values, hyperbolic and inverse hyperbolic functions, graphs.
Concepts of continuity and differentiability. Mean-value theorem. Taylor’s series expansion. Integration by parts.

2. Sequences and Series ( 6 hrs)
Sequences of real numbers, monotone sequence, convergence and limits.
Infinite series, convergence tests, addition and multiplication of series. Power series, radius of convergence, term-by-term integration and differentiation.

3. Partial Differentiation ( 6hrs)
Functions of several variables, continuity and partial derivatives. Total differentials, approximate calculations using differentials. Chain rule. Implicit differentiation. Series representation of functions, Taylor’s Theorem.
Extremum problems, without and with constraints, Lagrange multipliers, global extremum.

4. Complex Function and Vector Algebra ( 6 hours)
DeMoivre’s theorem, powers and roots of complex numbers. Euler formula. Elementary functions of a complex variable, polynomials, rational, exponential, trigonometric, hyperbolic, logarithmic, inverse trigonometric and inverse hyperbolic functions.
Dot and cross products, triple products, lines and planes.
Vectors in Rn space, addition and scalar multiplication, linear combination of vectors, idea of linear dependence and independence.

5. Fourier Series ( 5 hours)
Periodic functions, trigonometric series. Fourier series, functions of period 2p, Fourier coefficients, Parsevals theorem, Functions of arbitrary period, even and odd functions. Half range expansion. Complex form of Fourier series.

6. Probability ( 5 hours)
Probability space. Probability theorems. Conditional probability and independence. Random variables, discrete and continuous distributions, mean and variance. Bernouli, Binomial, Poisson, hypergeometric, exponential, normal distributions and their characteristics. Examples involving experimental measurement and reliability.

Final exam:
60%

Coursework:
Test 1 20%
Test 2 20%

References
1. Lecture Notes Series – Engineering Mathematics Volume 1 (2nd edition), Pearson Prentice Hall, 2006.( main reference)

2. Calculus - 6th edition, James Stewart, Thomson Learning - Brooks/Cole, 2008.

3. Thomas' Calculus - 10th edition, Finney, Weir and Giordano, Addison-Wesley Publishing, 2001.

4. Calculus - A New Horizon - 6th edition, Howard Anton, John Wiley & Sons Inc, 1999.

5. Modern Engineering Mathematics - 3rd edition, Glyn James, Prentice Hall, 2001.

6. Advanced Engineering Mathematics - 8th edition, Erwin Kreysig, John Wiley & Sons Inc, 1999.

7. Probability and Statistics for Engineers and Scientists - 7th edition, R.E.Walpole, R.H.Myers, S.L.Myres and K. Ye, Prentice Hall, 2002.

8. Schaum's 3000 Solved Problems in Calculus, E. Mendelson, McGraw Hill, 1990.