1. PEM2046 Engineering Mathematics IV PEM2046 Engineering Mathematics IV Final Review Trimester 3 2001/2002 Session

2. All Rights Reserved 2002 by dktk What’s inside here? Topic Highlights Final Examination Format

3. All Rights Reserved 2002 by dktk Topic Highlights

4. All Rights Reserved 2002 by dktk Chapter 1 Optimization Solving LP using Simplex Method The Primal and the Dual Problem Sensitivity Analysis Nonlinear Programming Dynamic Programming

5. All Rights Reserved 2002 by dktk Chapter 2 Functions of a Complex Variable Contour Integrals Cauchy’s Integral Formula and Derivatives of Analytic Functions Taylor and Maclaurin Series Laurent Series Zeros and Classification of Singularities Residue Theory

6. All Rights Reserved 2002 by dktk Chapter 3 Calculus of Variations Euler's Equation –The integral curve for this equation is called extremals. It should be noted that the functional would only attain its extremum on extremals. System of Euler's Equations N.B.: Euler Lagrange Equation = Euler's Equations

7. All Rights Reserved 2002 by dktk Chapter 4 Random Variables and Stochastic Processes Random Variables Properties of Probability Marginal Probability Conditional Probability Independent Random Variables Variance and Covariance –Value of covariance can be positive or negative. The sign of the covariance indicates whether the relationship between two dependent random variables is positive or negative. If X and Y are statistically independent, the covariance is zero (which means X and Y are uncorrelated).

8. All Rights Reserved 2002 by dktk Cont’d: Chapter 4 Random Variables and Stochastic Processes Stochastic Processes State Classification of a Markov Chain CommunicationPeriodicity Recurrence and Transient

9. All Rights Reserved 2002 by dktk Final Examination Format

10. All Rights Reserved 2002 by dktk Attempt Four out of Six questions. Chapter 1 1.5 Questions Chapter 2 1.5 Questions Chapter 3 1 Question Chapter 4 2 Questions

11. All Rights Reserved 2002 by dktk Good luck in the Final Examination… All the sources are taken from Malacca Campus. All the guidelines given above are only for references. Students are advised to study most of the material given by lecturer.