Mathematics 1 1200-1MATH1Z

List of topics:
Sequences and limits of sequences: definitions, various
criteria for convergence.
Continuity of functions; limits of functions. Differentiality;
definition of derivative; counting derivatives by definition
and by using differentiation rules.
Investigation of functions (critical points and monotonicity;
inflection points and convexity; asymptotes).
Simultaneously, applying the new piece of knowledge:
revision of definitions and properties of basic functions (sine,
cosine, tangent, cotangent, logarithm, exponential, roots).
Introduction of cyclometric functions (arc-functions).
Primal function. Integration as an inverse operation to
2differentiation.
Calculation of indefinite integrals.
Vectors on a plane and in space; operations on vectors; scalar
product, vector product.
Systems of linear equations as an introduction to matrices;
Cramer's formulas; eigenvalues of matrices; determinants;
operations on matrices, especially - matrix multiplication;
inverse matrix; diagonalization of matrices. Vector product
using matrix determinants.
Optimization tasks.
Taylor formula and Taylor series.