Syllabus of lecture
Mathematical analysis
Real functions of one real variable. Definition, graph. Bounded functions, monotonic, even, odd and periodic functions.
One-to-one functions, inverse and composite functions. Elementary functions (including inverse trigonometric functions).
Limit of a function, infinite limit of a function. Limit at an improper point. Continuous and discontinuous functions.
Differential calculus of functions of one real variable. Derivative of a function, its geometrical and physical
meaning. Derivative rules.
Derivative of elementary functions.
Differential of a function. Derivative of higher orders. l’Hospital rule.
Relation between derivative and monotonicity, convexity and concavity of a function.
Extrema of a function. Asymptotes. Plot graph of a function.
Linear algebra
Linear algebra. Matrices. Matrix operations. Rank of a matrix. Inverse.
Determinants, properties of a determinant.
Solution of systems of linear equations. Frobenius theorem. Cramer’s rule. Gaussian elimination algorithm.
Analytic geometry.
Affine space. Euclidean space. Scalar, cross and triple product of vectors, properties.
Equation of a plane, line in E3. Relative position problems.
Metric or distance problems.
Mathematical analysis
Real functions of one real variable. Definition, graph. Bounded functions, monotonic, even, odd and periodic functions.
One-to-one functions, inverse and composite functions. Elementary functions (including inverse trigonometric functions).
Limit of a function, infinite limit of a function. Limit at an improper point. Continuous and discontinuous functions.
Differential calculus of functions of one real variable. Derivative of a function, its geometrical and physical
meaning. Derivative rules.
Derivative of elementary functions.
Differential of a function. Derivative of higher orders. l’Hospital rule.
Relation between derivative and monotonicity, convexity and concavity of a function.
Extrema of a function. Asymptotes. Plot graph of a function.
Linear algebra
Linear algebra. Matrices. Matrix operations. Rank of a matrix. Inverse.
Determinants, properties of a determinant.
Solution of systems of linear equations. Frobenius theorem. Cramer’s rule. Gaussian elimination algorithm.
Analytic geometry.
Affine space. Euclidean space. Scalar, cross and triple product of vectors, properties.
Equation of a plane, line in E3. Relative position problems.
Metric or distance problems.