Syllabus
*Vectors and vector operations.
Columns, rows and matrices. Points, vectors, forms and operators. Scalar and vector product.
* Geometry and motion in Euclidian space
Distance. Isometries of Euclidian space. Geometry of curves and surfaces. Velocity and acceleration in inercial and noninercial frames.
* Differential calculus.
Derivative of elementery functions. Leibniz rule. Functions of many varibles. Total diferential.
* Integral calculus
Geometrical and physical meaning of the Riemann integral, methods of integration. Volume and surface integrals.
* Differential equations
Solution of the differential equation, existence and uniqueness of the solution. The first inegral, integral of energy. The solution of systems of linear differential equations by the separation of variables.
* Differential operators.
Gradient, divergence, curl, Laplace operator and their geometric and physical meaning. Gauss and Stokes theorems
* Tensors.
Definition of a tensor, coordinates of tensors and their physical meaning.
Annotation
Mathematical methods used in the introductory physics course.