Algorithmization of Engineering Computations 

Topic 1 
Introduction to working with the Matlab program system: Entering variables, vectors and matrices, managing variable in Matlab, grafiphic output, creating scripts. 

Topic 2 
Fundamentals of algorithmization: Properties of algorithms, elementary algorithms. 

Topic 3 
Calculation of function values: Calculation of the value of a polynomial, tabulated functions, drawing the graph of a targeted function, determining the maximum of a discretized function. 

Topic 4 
Solving nonlinear algebraic equations: Iteration, iterative methods of solving nonlinear algebraic equations. 

Topic 5 
Sorting algorithms: Bubble sort, Select sort, Insert sort, Quick sort, Shell sort. 

Topic 6 
Systems of linear
equations: Direct methods of solving systems of linear equations 
solving a triangular system, Gaussian and GaussJordan elimination
method,
LU and Cholesky decomposition. 

Topic 7 

Topic 8 
Numerical integration of a definite integral: Rectangle, trapezoid, Simpson's and Romberg's methods of numerical integration, Adaptive integration, Gaussian method. 

Topic 9 
Numerical derivation: Finite difference method, numerical differentiation with a variable difference, partial derivatives. 

Topic 10 
Solving differential equations: Ordinary differential equations of the first order, Euler's method, RungeKutta method, Leapfrog method. 

Topic 11 
Interpolation and approximation: Linear interpolation, Lagrange interpolation, Newton's interpolation, aproximation bz the method of least squares  linear and by mth degree polynomial. 
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