| Objectives |
| To
further strengthen the understanding and applications of mathematical concepts
in optimization, complex numbers and random variables in the engineering
context. |
| References/Textbooks |
|
E. Kreyszig,
"Advance Engineering Mathematics", John Wiley & Sons.
K. A.
Stroud, "Engineering Mathematics", ELBS.
K. A.
Stroud, "Further Engineering Mathematics", ELBS
|
| Contents |
Chapter
1 Optimization
-
Linear programming: objective function,
constraints, slack variable. Solution using graphical method and simplex
techniques. Dual and primal problems. Post-optimal analysis.
-
Dynamic programming: solution of
routing problem by stages. Review and implication of computational process.
Solution of the resource allocation problem and the equipment replacement
model. Continuous state variables.
-
Minimization (Lagrange multipliers),
non-linear programming, combinatorial problems.
|
Chapter
2 Functions of a Complex Variable
-
Analytic functions: limits and
derivatives, Cauchy-Riemann equations. Integration: integrals, Cauchy's
theorem and integral representation of derivatives of all orders.
-
Series: Taylor and Laurent series.
Uniform convergence, term by term differentiation, domain of convergence
and classification of singularities.
-
Contour integration: the residue
theorem, evaluation of integrals of single valued and multi-valued functions.
-
Conformal mapping: application
for solving Laplace's equation.
-
Asymptotic evaluation of integrals:
the methods of steepest descent and stationary phase.
|
Chapter
3 Calculus of Variations
-
The Euler equation, geodesics,
the brachistochrone problem. Cycloids, first integrals of the Euler equation,
several dependent variables, isoperimetric problems, variational notation.
|
Chapter
4 Random Variables and Stochastic Processes
-
Review of probability theory. Random
variables, distributions and densities. Functions of one and multiple variables,
expected values, dispersion moments. Stochastic processes: basic concepts.
Discrete-time and continuous-time Stochastic processes. Estimation and
Detection.
|
| Revised
Lecture Notes/Lecture Slides |
|
|
| Revised
Tutorial Questions and Solutions |
|
|
| Test
Questions and Solutions |
|
|
| Supplements |
|
|
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