Applied Mathematics: Operations Research Topics

 

- Operations Research Modeling approach

- Linear Programming

- The Simplex Method

- Other Algorithms for Linear Programming

*Dual Simplex Method

*Parametric Linear Programming

*The Upper Bound Technique

*Interior-Point Algorithm

*Goal Programming

- Duality Theory and Sensitivity Analysis

- Transportation and Assignment Problems

- Network Optimization Models

- Dynamic Programming

- Integer Programming

- Non-linear Programming

- Heuristic Programming

- Game Theory

- Decision Analysis

- Queuing Theory

- Inventory Theory

- Simulation Modeling

Applied Mathematics: Numerical Analysis Topics

 

- Errors in Numerical Computations

- Solutions of Equations in One Variable

- Solving Linear Systems of Equations

*Direct Methods

*Iterative Methods

- Solutions of Non-leanear Equations

- Interpolation

- Approximation Theory

- Approximating Eigenvalues

- Numerical Differentiation

- Numerical Integration

- Numerical methods to Ordinary Differential Equations

*Initial value problems

*Systems of Ordinary Differential Equations

*Boundary value problems

- Numerical methods to Partial Differential Equations

- Optimization

Mathematics: Algebra Topics

- Algebra Essentials

*Numbers and Arithmetics

*Mathematical Induction

*sequences and series

*Exponents and Notations

*Radicals and Rational Exponents

*Polynomails

*The binomial Theorem

*Rational Expressions

*Permutations and combinations

- Equations and Inequalities

*Linear Equations

*Complex numbers

*Quadratic Equations

*Other Types of Equations

*Linear Inequalities and Absolute Value Inequalities

- Functions

*Function Notation

*Domain and Range

*Composition of Functions

*Transformation of Functions

*Absolute Value Functions

*Inverses and radical Functions

*Exponential function

*Linear Functions

*Polynomail Functions

*Rational Functions

*Quadratic Functions

*Exponential Functions 

*Logarithmic Functions

*Periodic Functions

*Trigonometric Functions

- System of Equations and Inequalities

*System of Linear Equations

*System of NonLinear Equations and Inequalities

*Partial Fraction

*Matrices

*Determinants

*Solving System of Equations

Paradigm of Mathematics Courses

Paradigm of Mathematics Courses

• Algebra
• Differential Calculus I
• Mechanics I, Statics
• Analytic Geometry
• Integral Calculus I
• Mechanics I, Dynamics
• Linear Algebra
• Differential Calculus II
• Mechanics II, Dynamics of Particle
• Solid Geometry
• Integral Calculus II
• Mechanics II, Dynamics of Solid Bodies
• Differential Equations
• Numerical Analysis I & II
• Operations Research I & II
• Probabilities and Statistics

Algebra and Geometry

• Mathematical Induction
• Partial Fraction
• Series
• Determinant and Matrix
• Linear equations
• Nonlinear equations
• Coordinate system
• Conic sections
• Euclidean vector
• Surfaces and Quadric Surfaces
• Ruled Surface

Differential and Integral calculus

• Function of one real variable
• Limits of functions
• Continuity
• Derivative
• Taylor series
• Indefinite integral
• Definite integral
• Improper integral
• Numerical integration

Newtonian Mechanics

• Statics in plane
• Application on equilibrium of 2D Force Systems
• Statics in space
• Friction
• Center of gravity and centroid
• Virtual work
• Kinematic of a particle in a straight line
• Kinematic of a particle in a plane
• Relative motion in plane
• Kinetics of a particle
• Simple harmonic motion
• Projectile motion
• Dynamics of rigid body in a plane

Analytical Mechanics

• Dynamics of a particles in 3D Dimensions
• Rotating Axes
• Component of velocity and acceleration in different coordinate systems
• Foucault’s pendulum
• Dynamic of rigid body in three dimensions
• Eulerian angles
• Moment on inertia
• Equation of motion of rigid body
• Euler equations
• Generalized coordinate
• Lagrange Equations
• Hamilton functions
• Routh Equations
• Sturm–Louwville equation
• Invariants
• Hamilton–Jacobi equation

Linear algebra and Solid geometry

• Vector Spaces
• Linear Transformations
• Eigenvalues and Eigenvectors
• Inner product spaces
• Bilinear and quadratic forms
• Applications in Geometry

Advanced Calculus

• Functions of several real variables
• Partial derivatives
• Maxima and minima
• Multiple integrals
• Line and surface integral
• Using MATLAB Program

Differential Equations

• Formation of ordinary differential equations(ODE’S)
• ODE’S of first order and first degree
• ODE’S of first order and higher degrees
• Applications
• Linear ODE’S of higher orders with constant coefficients and its applications
• Linear ODE’S of higher orders with variant coefficients
• Partial differential equations

Probabilities and Statistics

• Sample Space
• Random Variables
• Some Discrete distributions
• Some Continuous distributions
• Bivariate and multivariate random variables
• Some special Bivariate distributions
• Mathematical Expectation
• Least squared concept
• Correlation and regression
• Statistical tests most useful to software engineering
• T-test, ANOVA and chi-squared
• Design of experiments and testing of hypotheses
• Statistical analysis of data from a variety of sources.
• Applications of statistics to performance analysis
• reliability engineering
• Usability engineering
• Cost estimation

Discrete mathematics

• Sets
• Relations
• Functions
• Mathematical logic
• Group Theory
• Counting Theory
• Probability
• Mathematical Induction
• Recurrence Relations
• Graph Theory
• Trees
• Boolean Algebra

Operations Research

• Linear Programming
• Non-linear programming
• Geometric Programming
• Dynamic Programming
• Integer Programming
• Game Theory
• Decision Analysis
• Queuing Theory
• Inventory Theory

Numerical Analysis

• Errors in Numerical Computations
• Solutions of Non-Linear equations
• Direct Methods for solving linear systems
• Iterative Methods for solving linear systems
• Interpolation Approximations
• Polynomial Approximations
• Numerical differential
• Numerical Integration
• Numerical methods for differential equations
• Approximation theory

Mathematical and statistical Packages

• Using Mathematica
• Using MATLAB
• Using in Matrices
• Using in Functions
• Using in Graphics
• Using in Data Fitting
• Applied statistics

University/College Computer Science Program

Mathematics

• Algebra
• Differential Calculus I
• Mechanics I, Statics
• Analytic Geometry
• Integral Calculus I
• Mechanics I, Dynamics
• Linear Algebra
• Differential Calculus II
• Mechanics II, Dynamics of Particle
• Solid Geometry
• Integral Calculus II
• Mechanics II, Dynamics of Solid Bodies
• Differential Equations
• Numerical Analysis I & II
• Operations Research I & II
• Probabilities and Statistics

Physics

• Properties of Matter
• Electricity and Magnetism
• Heat and Thermodynamics
• Geometric Optics and Acoustics
• Electricity and AC Current
• Physical Optics
• Physics of Vibrations and Waves
• Principles of Modern Physics
• Introduction to Physical Electronics
• Physics of Semiconductors and Applications
• Digital Logic Circuits
• Physical Measurements Using Computer

Computer Science

• Principles of Computer Science
• Fundamentals of Programming Languages
• Scientific Computation I & II
• Theoretical Foundation of Computer Science
• Formal Language and Automata
• Computer Systems and Architecture
• Microprocessors and Communication Circuits
• Operating Systems
• File Structures
• Computer Networks
• Data Communications
• Compilers
• Systems Simulations
• Algorithms
• Data Structure and Databases
• Data Mining
• Artificial Intelligence
• Distributed Computing
• Object-Oriented Programming and C++

Others

• History of Science
• Business Management
• Scientific Thinking
• English