Sets. Main examples of sets of numbers.
Real numbers, neighborhoods, absolute value.
Upper and lower bounds,
Sup, inf, maximum, minimum of a set. Completeness of R.
Functions. Injective (One-to-one) and surjective functions. Monotonic and invertible (bijective) functions. Graph of a function. Symmetries of graphs. Convex functions. Main examples of functions: powers,
exponential, logarithm, sine, cosine, tangent,
arctangent. Hyperbolic functions.
Limit of a sequence. Some theorems about limits. Algebraic properties of limits. Indeterminate forms. Series. Generalized harmonic series. Geometric series. Criteria for convergence of a series. Simple and absolute convergence.
Limit of a function. Continuous functions. Main theorems about limits. Algebraic properties of limits. Indeterminate forms.
Derivatives. Differentiation rules. Main theorems about derivatives. Maxima, minima and critical points. Monotonic and convex functions. Inflection points. Landau's Notation "Big O / little o".
Taylor expansions. Taylor series.
Definite integrals. Integral function. Main theorems about integration. Methods for the evaluation of integrals. Integration by parts and by substitution. Integration of some classes of fundamental functions. Improper integrals.
Ordinary differential equations. Cauchy Problem for for
explicit ordinary differential equations. Existence and uniqueness theorems. First order linear differential equations. Linear differential equations with constant coefficients. Systems of differential equations with constant coefficients.
The Laplace transform