APPLIED MATHEMATICS 2- SET 1- Q AND A

SKU: MATH2LA-02
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APPLIED MATHEMATICS 2-SET1


This module unifies linear algebra with analytical series techniques to model, analyse, and solve engineering problems. Linear algebra, eigenvalues and eigenvectors with applications to first and second order systems of differential equations. Sequences and series, convergence tests. Power series with applications to ordinary differential equations with variable coefficients. Fourier series with applications to partial differential equations such as potential, heat and wave equations.


Set 1- Topics

1.    Eigenvalue Eigenvector Method

2.    Repeated Eigenvalue Solutions

3.    Non-Homogeneous Linear Systems

4.    Second Order Linear Systems

5.    Sequences

6.    Series

7.    Series with non-negative terms


Module Objectives:

  • Perform core linear algebra operations: vector/matrix algebra, determinants, rank, inverses, LU/QR factorization.
  • Solve linear systems Ax = b; interpret solution spaces (column, null, row spaces) and conditioning.
  • Compute and interpret eigenvalues/eigenvectors; distinguish algebraic vs geometric multiplicity; assess diagonalizability/defectiveness.
  • Model and solve second-order systems Mx″ + Cx′ + Kx; reduce to first-order form; analyze modes, damping, resonance, and stability.
  • Classify equilibria and sketch phase portraits; relate eigenstructure to physical behavior in engineering systems.
  • Analyze sequences and series; apply nth-term, comparison, limit comparison, ratio, root, alternating, and integral tests for convergence.
  • Construct and manipulate power series; find radii/intervals of convergence; solve linear ODEs with variable coefficients via Frobenius/power series.
  • Develop Fourier series (real/complex, even/odd, half/quarter-range); use orthogonality and Parseval’s identity.
  • Apply separation of variables and Fourier series to solve canonical PDEs (heat, wave,


Prescribed Textbooks

·       Edwards, C.H., Penney, D.E. and Calvis, D.T., 2004. Differential equations and boundary value problems

·       Zill, D. G. (2016). Differential equations with boundary-value problems.