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MINISTRY OF EDUCATION AND SCIENCE OF THE REPUBLIC OF KAZAKHSTAN

Almaty University of Power Engineering and Telecommunications

Department of Higher Mathematics

Numerical methods and computer realization

Laboratory work №3

Subject: The problem of mathematical analysis

Laboratory work №4

Subject: The problem of integral calculus, operational calculus and differential equations

Option №1

Done by: the student of group EE-14-1

Akhmet.Z.

Checked by: Zhanuzakova D.T.

Almaty, 2015

Task 1. Given function f(x) and a point x=a.

  1. Compute the two-sided limit of the function at the point indicated;

  2. Calculate the left-sided limit at the point indicated;

  3. Calculate the right-sided limit at the point indicated;

  4. Conclude that the discontinuity of the function at x=a and type of fracture.

Implementation of the task

Task 2. Calculate the function f(x):

  1. f’(x);

  2. f’(x0);

  3. f’’(x);

  4. f’’(x0).

Implementation of the task

Task 3. Draw the graph of the function

Implementation of the task

Task 4. Plot parametrically given function f(x).

Implementation of the task

Task 5. Draw the graph of polar coordinates.

Implementation of the task

Task 6. Draw the graph of the function y=f(x) in the Cartesian coordinate system. Built in the same coordinate system tangent and normal function of this at the specified point.

Implementation of the task

Task 7. Show graph of this function, find the derivative, find the zeros of the derivative (stationary points), find the coordinates of extreme points.

Implementation of the task

Task 8. Three-dimensional surface plot.

Implementation of the task

Task 1. Calculate undefined integral . Build three graphs from the family of primitive.

Implementation of the task

Task 2. Calculate defined integral.

(1;2)

Implementation of the task

Task 3. Find image of the function(laplace).

Implementation of the task

Task 4. Find original of the function(invlaplace).

Implementation of the task

Task 5. Solve differential equations using operation calculus(Laplace transform).

Implementation of the task

Task 6. Solve system of differential equations using operation calculus.

Implementation of the task

Task 7. Solve differential equition using procedures Given and Odesolve. Build the graph of solution. Find the value of the solution at he piont x=2.

Implementation of the task

Task 8. Solve differential equation of second order. Build the graph of solution. Create a table of argument and value of function.

Implementation of the task

Task 9. Solve the differential equation by procedure Given/Odesolve. Initial condition for all option: x1(0)=2 x2(0)=1. Create a table of argument and value of function. Find value of function at the point t=3.4. Built graph of function.

Implementation of the task

Task 10. Solve the differential equation by procedure rkfixed. Create a table of argument and value of function. Build the graph of solution.

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