2nd Year Syallabus (3th Sem & 4th Sem)

Advanced Engineering Mathematics

Probability and Statistics-1

1. Random Variables:

   • Discrete: Countable outcomes.
   • Continuous: Measurable outcomes.

2. Probability Basics:

   • Probability Distribution Function: Describes likelihood.
   • Mathematical Expectations: Mean and variance.

Probability and Statistics-2

1. Distributions:

   • Binomial: Success/failure scenarios.
   • Poisson: Events in fixed intervals.
   • Normal: Bell-shaped curve.
   • Uniform: Equal likelihood for all.
   • Exponential: Time between events.

2. Correlation and Regression:

   • Correlation Coefficients: Measure relationships.
   • Regression: Predicting one variable based on another.

Optimization Techniques-1

1. Basics:

   • Historical Development: Evolution of optimization.
   • Engineering Applications: Real-world uses.

2. Single and Multi-variable Optimization:

   • Constraints: Conditions on variables.
   • Equality and Inequality Constraints.

Optimization Techniques-2

1. Linear Programming:

   • Introduction: Basics of linear programming.
   • Methods: Simplex, Big-M, Two Phase.
   • Duality: Dual solutions and significance.

2. Applications:

   • Transportation and Assignment Problems.

Numerical Methods

1. Interpolation:

   • Newton’s and Lagrange’s: Predicting missing values.
   • Gauss’s and Stirling’s: Fine-tuning interpolation.

2. Differentiation and Integration:

   • Numerical Differentiation: Approximating derivatives.
   • Numerical Integration: Approximating definite integrals.

3. Ordinary Differential Equations:

   • Euler, Modified Euler, Runge-Kutta, Milne’s PC: Solving real-world problems.