Differential and Integral Calculus
Faculty of Mechanical Engineering
Field of Study: Mechanical Engineering
Lectures 15 h, Practices 15 h
The range of the test no. 1- 29.11.2019 (maximum 12 points):
Task. 1. Calculate the surface area of a region limited by given curves (List 1 Task 3).
Task. 2. Calculate the length of a given curve (List 1 Task 4) or the lateral area of a given solid of revolution (List 1 Task 6).
Task. 3. Calculate the volume of a given solid of revolution (List 1 Task 5).
Lists of Tasks:
1. Improper Integral and its Applications;
Properties of n-dimensional
of Several Variable Functions, Continuity;
Derivatives, Gradient, Total Differential, Directional Derivative, Tangent Plane;
Higher Order Derivatives, Hessian Matrix;
Differential Calculus for Vector Valued Functions, Jacobian Matrix;
of Several Variable Function and Its Applications;
8. Introduction and First Definitions on Ordinary Differential Equations;
9. First Order Differential Equations (Separable Equations, Homogeneous Equations);
10. Linear Nonhomogeneous Equation First Order;
11. Higher Order Linear Equations (Homogeneous Linear Equations with Constant Coefficients);
12. Non-Homogeneous Linear Equations, Method of Undetermined Coefficients, Method of Variation of Parameters, Linear Independence and the Wronskian.
1.1. E. Zakon, Mathematical Analysis I, The Trillia Group, 2004
2.2. B. S. Schroder, Mathematical Analysis: A Concise Introduction, JohnWiley&Sons,2008
3. 3.G.M. Fichtenholz, Course in the Differential and Integral Calculus vol. I, II, III, Nauka, Moscow, 1969.
4.4. B. Sikora, E. Łobos, A First Course in Calculus, Wydawnictwo Politechniki ¦l±skiej.