Lecture Notes on
"Scientific Computing with MATLAB"

1. Introduction into MATLAB computing
• Computations of variables and arrays (vectors)
• Branch statements and loops
• Mathematical functions and M-files
• Reading and writing operations
• Plotting operations and MATLAB graphics
• Errors of MATLAB numerical computations


2. Matrix computations and MATLAB linear algebra
• Two-dimensional arrays (matrices) and matrix operations
• Block and band matrices, structures and cells
• MATLAB linear algebra
• Ill-conditioned and sparse matrices
• Plotting of functions of two variables


3. Numerical algorithms with MATLAB
• Polynomials and polynomial interpolation
• Least square curve fitting
• Piecewise polynomial interpolation
• Trigonometric interpolation
• Two-dimensional interpolation and errors of interpolating polynomials


4. Mathematical modeling with MATLAB
• Finite difference approximations for numerical derivatives
• Summation rules for numerical integration
• Initial-value problems for differential equations
• Root finding algorithms and minimization problems