Advanced Engineering Mathematics for ME

Reference:

Bird, J. (2013). Understanding engineering mathematics. Routledge.

1. Numerical Methods Foundations: introduction, discrete algebra, accuracy, and error analysis.
   
   

2. Numerical Analysis for Engineering: applications and the Taylor series as a core tool.
   
   

3. Matrix and Vector Review: matrix operations, vectors, determinants, and rank.  Pages 531-541  (Bird, 2013)
   
   

4. Solving Linear Systems: numerical techniques for systems of linear equations.
   
   

5. Root-Finding Methods: numerical approaches for solving equations.
   
   

6. Approximation and Optimization: interpolation, least-squares approximation, curve fitting, and optimization basics.
   
   

7. Numerical Differentiation: finite-difference methods and related techniques.
   
   

8. Numerical Integration: quadrature methods and time-integration approaches (including Runge–Kutta methods).
   
   

9. Nonlinear Systems: numerical solution techniques for nonlinear equations.
   
   

10. Numerical Solutions for ODEs: solving ordinary differential equations and systems of ODEs.
    
    

11. Numerical Solutions for PDEs: partial differential equations (advanced topic; may be optional).
    
    

12. Programming Applications: computer programming exercises, worked examples, and implementation practice.