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
