Lecture Mathematics B

Thursday at 8 am in C12

Basic information

Topics for oral exam

Slides from lecture

Syllabus here

  1. Vectors and matrices, matrix arithmetic, dot product. Linear independence of vectors and rank of a matrix.
  2. Systems of linear algebraic equations. Determinant of a matrix, cross product.
  3. Inverse matrices. Eigenvalues of a matrix. Geometry in the plane and three-dimensional space.
  4. Euclidean space, metric, norm, properties of subsets of the Eucidean space.
  5. Functions of several variables. Partial derivatives, partial derivatives of compositions of functions. Directional derivatives, gradient of a function. Total differential, tangent plane.
  6. Taylor polynomial of functions of two variables. Newton’s method for a system of two non-linear equations of two variables.
  7. Extrema of functions of two variables. Least square method.
  8. Implicitly defined functions of a single and several variables, derivatives of implicitly defined functions.
  9. Parametric curves, tangent vector to a curve, smooth curve, orientation and a sum of curves.
  10. Vector field in the plane and space. Curvilinear integral of a vector field and its physical meaning.
  11. Path independence of the curvilinear integral of a vector field. Scalar potential of a vector field. Differential forms and their integrals.
  12. Double integral and its geometrical meaning. Fubini theorem. Substitution for double integral. Polar coordinates.
  13. Laplace integral. Revision and discussion.
  14. Systems of two first order differential equations. Solving autonomous systems of differential equations with constant coefficients. Predator-prey model.

Consultations – by agreement personal or email