IR 101101 Discrete Matematics and Linear Algebra
IR 101201 Calculus 1
IR 201101 Calculus 2
After completion of the course the students should
- be able to sketch the graph of polar coordinates equations and parametric curves.
- know the connection between a parametric curve and the motion of a particle given by the position vector.
- know how to caltulate the velocity vector and the acceleration vector of moving particles.
- be able to find the equation for the tangent line and calculate area of surfaces related to curves defined by parametic or polar equations.
- know the formula for the arc length and differential and know how to calulate the length of curves given by parametric equations.
- be able to calculate double and trippel integral.
- know about spherical and cylindrical coordinates and to do calculations i these coordinate systems.
- be able to calculate area, volum and moments by use of multiple integral.
- know about directional derivative, gradient vector, divergence and circulation of a vector field.
- know how to calculate line integral and surface integral.
- know the theorem of Green, Gauss and Stoke and be able to do calculations using these theorems.
- be able to find particular solutions of partial differential equations of first and second order by d'Alembert solution and by separation the variables.
- know how to derive the one-dimensional heat equation and the one-dimensional wave equation and be able to find particular solutions under given boundary conditions.
- be able to find particular solutions of the two-dimensional Laplace equation under given boundary conditions.
Coordinate:
- polar, cylindrical and spherical coordinates
- calculate area of surfaces related to curves defined by parametic or polar equations
Plan curves and curves in space:
- Position vector, velocity vector and accelration vector
-arc length
- Curvature of plane curves
- Curvature of space curves
- How to integrate and derivate vector functions
- Line integral along curves
- Fundamental theorem for line integrals
Surfaces in space:
- Cylinders and quadric surfaces
- Surfaces of revolution
Multiple integrals:
- Double and trippel integral
- Calculating areal and volum by use of double integral
- Double integral in polar coordinates
- Areal of surfaces in space
- Surface integral
- Trippel integral in cartesial, cylindrical and spherical coordinates with applications.
Vector calculus:
- Gradient vector
- Direction derivative. Potential function, conservative fields
- Divergens and curl of vector fields
- Greens theorem
- The divergence theorem
- Stokes theorem
Partial differential equations:
- Partial differential equations of first and second order.
- One-dimensional heat equation. One-dimensional wave equation
- d'Alembert solution
- Laplaces equation
Lectures and problem solvings
At the beginning of the course the professor can decide if the students have to do some obligatory problems.
