# 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:
• 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.