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Numerical methods in civil engineering homework help

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The exhaustive list of topics in Numerical Methods in Civil Engineering in which we provide Help with Homework Assignment and Help with Project is as follows:

  • Numerical Methods:
    • Numerical methods.
    • Sources of error in numerical solutions: truncation error, round off error.
    • Order of accuracy - Taylor series expansion.
  • Direct Solution of Linear systems:
    • Gauss elimination
    • Gauss Jordan elimination.
    • Pivoting
    • Inaccuracies due to pivoting.
    • Factorization
    • Cholesky decomposition.
    • Diagonal dominance
    • Condition number
    • Ill conditioned matrices
    • Singularity and singular value decomposition.
    • Banded matrices
    • Storage schemes for banded matrices
    • Skyline solver.
  • Iterative solution of Linear systems:
    • Jacobi iteration.
    • Gauss Seidel iteration.
    • Convergence criteria.
  •  Direct Solution of Non Linear systems:
    • Newton Raphson iterations to find roots of a 1D nonlinear equation.
    • Generalization to multiple dimensions.
    • Newton Iterations
    • Quasi Newton iterations.
    • Local and global minimum
    • Rates of convergence
    • Convergence criteria.
  • Iterative Solution of Non Linear systems:
    • Conjugate gradient.
    • Preconditioning.
  •   Partial Differential Equations:
    • Partial differential equations.
    • First and second order equations.
    • Analytical solutions.
    • Method of characteristics.
  • Numerical Differentiation:
    • Difference operators (forward, backward and central difference).
    • Stability and accuracy of solutions.
    • Application of finite difference operators to solve initial and boundary value problems.
  • Finite Element Method as a method to solve partial differential equations:·
    • Strong form of the differential equation.
    • Weak form.
    • Galerkin method: the finite element approximation.
    • Interpolation functions: smoothness, continuity, completeness, Lagrange polynomials.
    • Numerical quadrature: Trapezoidal rule, simpsons rule,Gauss quadrature.
  • Numerical integration of time dependent partial differential equations:
    • Parabolic equations: algorithms - stability
    • Consistency and convergence
    • Lax equivalence theorem.
    • Hyperbolic equations: algorithms - Newmark's method
    • Stability and accuracy
    • Convergence
    • Multi-step methods.
  • Numerical solutions of integral equations:
    • Types of integral equations.
    • Fredholm integral equations of the first and second kind.
    • Fredholm's Alternative theorem.
    • Collocation and Galerkin methods for solving integral equations.