Course: Numerical Methods for Engineers
Modules:
Course Overview, Week One Introduction, Binary Numbers | Lecture 1, Double Precision | Lecture 2, MATLAB as a Calculator | Lecture 3, Scripts and Functions | Lecture 4, Vectors | Lecture 5, Line Plots | Lecture 6, Matrices | Lecture 7, Logicals | Lecture 8, Conditionals | Lecture 9, Loops | Lecture 10, Logistic Map (Part A) | Lecture 11, Logistic Map (Part B) | Lecture 12
Week Two Introduction, Bisection Method | Lecture 13, Newton's Method | Lecture 14, Secant Method | Lecture 15, Order of Convergence| Lecture 16, Convergence of Newton's Method | Lecture 17, Fractals from Newton's Method | Lecture 18, Coding the Newton Fractal | Lecture 19, Root-Finding in MATLAB | Lecture 20, Feigenbaum Delta (Part A) | Lecture 21, Feigenbaum Delta (Part B) | Lecture 22, Feigenbaum Delta (Part C) | Lecture 23
Week Three Introduction, Gaussian Elimination without Pivoting | Lecture 24, Gaussian Elimination with Partial Pivoting | Lecture 25, LU Decomposition with Partial Pivoting | Lecture 26, Operation Counts | Lecture 27, Operation Counts for Gaussian Elimination | Lecture 28, Operation Counts for Forward and Backward Substitution | Lecture 29, Eigenvalue Power Method | Lecture 30, Eigenvalue Power Method (Example) |Lecture 31, Matrix Algebra in MATLAB | Lecture 32, Systems of Nonlinear Equations | Lecture 33, Systems of Nonlinear Equations (Example) | Lecture 34, Fractals from the Lorenz Equations | Lecture 35
Week  Four Introduction, Midpoint Rule | Lecture 36, Trapezoidal Rule | Lecture 37, Simpson's Rule | Lecture 38, Composite Quadrature Rules | Lecture 39, Gaussian Quadrature | Lecture 40, Adaptive Quadrature | Lecture 41, Quadrature in MATLAB | Lecture 42, Interpolation | Lecture 43, Cubic Spline Interpolation (Part A) | Lecture 44, Cubic Spline Interpolation (Part B) | Lecture 45, Interpolation in MATLAB | Lecture 46, Bessel Functions and their Zeros | Lecture 47
Week Five Introduction, Euler Method | Lecture 48, Modified Euler Method | Lecture 49, Runge-Kutta Methods | Lecture 50, Second-Order Runge-Kutta Methods | Lecture 51, Higher-Order Runge-Kutta Methods | Lecture 52, Higher-Order ODEs and Systems | Lecture 53, Adaptive Runge-Kutta Method | Lecture 54, Integrating ODEs in MATLAB (Part A) | Lecture 55, Integrating ODEs in MATLAB (Part B) | Lecture 56, Shooting Method for Boundary Value Problems | Lecture 57, The Two-Body Problem (Part A) | Lecture 58, The Two-Body Problem (Part B) | Lecture 59
Week Six Introduction, Boundary and Initial Value Problems | Lecture 60, Central Difference Approximation | Lecture 61, Discrete Laplace Equation | Lecture 62, Natural Ordering | Lecture 63, Matrix Formulation | Lecture 64, MATLAB Solution of the Laplace Equation (Direct Method) | Lecture 65, Jacobi, Gauss-Seidel and SOR Methods | Lecture 66, Red-Black Ordering | Lecture 67, MATLAB Solution of the Laplace Equation (Iterative Method) | Lecture 68, Explicit Methods for Solving the Diffusion Equation | Lecture 69, Von Neumann Stability Analysis of the FTCS Scheme | Lecture 70, Implicit Methods for Solving the Diffusion Equation | Lecture 71, Crank-Nicolson Method for the Diffusion Equation | Lecture 72, MATLAB Solution of the Diffusion Equation | Lecture 73, Two-Dimensional Diffusion Equation | Lecture 74, Concluding Remarks