• Elementary functions - Invertible functions. Exponential function and logarithm. Sine and cosine functions and their inverse. Tangent and cotangent functions and their inverse.
• Limits and functions in a topological space. Topological spaces. Examples of topological spaces. Notable metric and topological spaces. Function limits. Theorems of uniqueness of the limit, of the compound function and of the restriction. Special cases of expanded R and R.
• Continuous functions - Definitions and first examples. Calculation of limits for substitution. Theorems on continuous functions.
• Derivation - Incremental ratio and derivative . Examples. Derivable functions. Left derivative, right derivative. Theorem of the left and right derivative. Tangent to a curve.
• Examples and applications in geology - Sedimentation frequency.
• Rules of derivation - Linearity theorem. Derivative of the product and the quotient. Derivative of the compound function. Derivative of the inverse function. Derivatives of elementary functions. Derivatives of order superior to the first.
• Applications of differential calculus - Increment, decrescence, maxima and minima. Increasing, decreasing, strictly increasing and strictly decreasing function. Relative and absolute maxima and minima.Transmissions on the derivative in the points of crescenza and decrescence, maxima and minima.
• Notable theorems on the derivative - Rolle's theorem. Lagrange's theorem and its consequences. Cauchy's theorem. Theorems of the Hospital. Taylor's formula with the rest of Peano. Taylor's formula with the rest of Lagrange. Use of the Taylor formula for the theorems related to growth, decrescence, maxima and minima and for the approximate calculation of the values ​​assumed by a function.
• Complements and exercises on derivation - Asymptotes. Convex and concave functions. Flexed. Theorems for the search for points of concavity and convexity and inflections. Study of the graph of a function. Calculation of limits with the help of Hospital theorems and Taylor's formula.
• Integrals of functions with a variable. Definition and geometric interpretation. Some properties of integrals. Comparison and average theorem. Applications of the integral. The fundamental theorem of integral calculus. Theorems on primitives.
• Examples and applications in geology - Sedimentation accumulation