Mathematics III

COURSE CONTENT

1. Basic notions of ODEs. 1st order ODEs (ODEs with separable variables, homogeneous ODEs, linear ODEs, Bernoulli equations, Ricatti equations, exact ODEs, ODEs that can be reduced to exact, d’ Alembert-Lagrange equations), orthogonal trajectories. Geometric and physical applications.
2. Linear ODEs of higher order, homogeneous and nonhomogeneous, with constant or nonconstant coefficients. Euler ODEs. Reduction method. Boundary value problems. Applications
3. Systems of ODEs (Reduction to one ODE, diagonalization method, General solutions using eigenvlaues and eigenvectors). Applications
4. Laplace transform, Delta function, Heaviside function and their application to the solution of ODEs and systems of ODEs.

LEARNING OUTCOMES

The course is the basic course whereordinary  differential equations are introduced to the students, together with analytic methods of their solutions.

During the course, the basic ideas of ordinary differential equations are introduced, together with their applications in problems relevant to mechanical engineering. Basic methodologies are demonstrated for finding explicit analytical solutions of ordinary differential equations. Moreover, an introduction to the Laplace  transform is carried out with an emphasis to their use for solving specific classes of differential equations.

By the end of this course the student will be able to:

• Recognize basic problems of a mechanical engineer which can be modelled by ordinary differential equations.
• Find explicitly analytical solutions of ordinary differential equations.
• Use the Laplace transform.