1. Differential calculus of multivariable functions
Real functions of several variables.
Limits and continuity.
Partial derivative, gradient and directional derivative, total differential.
Differentials of higher orders, Taylor polynomials, Taylor's theorem.
Implicit function theorem.
Local, constrained and global extrema. Lagrange multipliers method.
2. Integration of multivariable functions
Riemann double and triple integrals.
Fubini theorem.
Substitution theorem for double and triple integrals.
Applications of double and triple integrals.
Real functions of several variables.
Limits and continuity.
Partial derivative, gradient and directional derivative, total differential.
Differentials of higher orders, Taylor polynomials, Taylor's theorem.
Implicit function theorem.
Local, constrained and global extrema. Lagrange multipliers method.
2. Integration of multivariable functions
Riemann double and triple integrals.
Fubini theorem.
Substitution theorem for double and triple integrals.
Applications of double and triple integrals.