Lecture Notes on “Scientific Computing with MATLAB”

**Contents**

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

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