Error analysis, Types of error, Sources of error, Norms of vectors and matrices, Computer arithmetic, Condition number of a matrix, Significant digits and loss of significant digits, Floating point arithmetic, Binary and decimal representation, Single and double precision
Interpolation: Newton forward and backward difference formula for interpolation, Central difference interpolation formulae, Lagrange’s interpolation, Error in interpolation, Linear least square approximation, Interpolation versus least square approximation, Relevant engineering case studies
Derivation of numerical differentiation of first order and second order derivatives using two points, three points, and five points formulas along with its application in engineering, Relevant case studies
Numerical integration: Trapezoidal rule, Simpson’s rules, Composite Trapezoidal Simpson Rules and Romberg integration, Applications of numerical in engineering, Relevant case studies
Solution of system of linear algebraic equations, Gauss elimination method
LU factorization, Tridiagonal solver
Applications of these methods in engineering disciplines, Relevant case studies
Numerical Solution of nonlinear equations: Bisection method, Newton’s method, Secant method, Convergence analysis of these methods
Newton’s method for system of nonlinear equations
Solution of system of linear equations by Jacobi, Gauss Seidel and SOR methods, Applications of these methods in engineering disciplines, Relevant case studies
Euler’s method and its variations, Taylor’s higher order methods, Error analysis, Consistency, stability and convergence
Runge-Kutta methods of order 2, 3, and 4, Stiff ODEs, Consistency, stability and convergence
Linear multistep methods, Numerical solution of system of ODEs
Numerical solution of BVPs by Finite Difference Method
Applications in engineering: Some relevant case studies
Eigenvalues and Eigenvectors of matrix: power method,
Inverse power method, Shifted inverse power method.
Applications of eigenvalues in engineering disciplines.
Unconstrained Optimization,
Golden search ratio, Lagrange Multipliers,
Method of steepest descent
Applications of optimization in engineering disciplines
Lectures (audio/video aids), Written Assignments/ Quizzes, Tutorials, Case Studies relevant to engineering disciplines, Semester Project, Guest Speaker, Industrial/ Field Visits, Group discussion, Report Writing
Mid Term, Report writing/ Presentation, Assignments, Project Report, Quizzes, Final Term
Numerical Analysis: By Richard L. Burden, J. Douglas Faires, Latest Edition
Numerical methods for scientist and engineers by R.W. Hamming (Latest Edition)
Numerical methods for Engineers by Steven C. Chapra and R. P. Canale(Latest Edition)
There are 133 total credit hours to complete the Software Engineering degree.