Fundamentals of Mathematics and Physics for Agriculture

Foundamentals of Calculus

Numeric sets, operations with numbers (natural numbers, integers, fractions). Powers with integer and real exponents and their properties. Roots and powers with rational exponents and their properties. Scientific notation. Absolute value and its properties.
First and second-degree equations and inequalities, zero-product property, fractional equations and inequalities, simple irrational equations and inequalities, systems of equations and inequalities.
Percentage and proportions and their use in solving applied exercises.
Elements of analytic geometry: Cartesian coordinates, points in the plane, distance between points in the plane, midpoint of a segment, equation of a line, slope, parallel lines, and perpendicular lines, intersection of lines.
Trigonometric circle and angle definition. Degrees and radians. Sine, cosine, and tangent of an angle and their properties, values of sine, cosine, and tangent for special angles, associated angles, solving simple trigonometric equations and inequalities. Solving right triangles, Carnot's Theorem, and the Law of Sines and their application to real problems. Elements of plane and solid geometry.
Exponentials and logarithms: definition and properties. Solving simple logarithmic and exponential equations and inequalities. Logarithmic and exponential functions (with their graphs). Exponential growth, pH of a solution, population dynamics, and the application of logarithms and exponentials to real problems.
Functions of a real variable and graphing a function. Graphs of elementary functions (lines, power functions with positive and negative exponents, roots, absolute value, exponential functions, logarithmic functions, trigonometric functions).
Increasing and decreasing functions. Maxima and minima. Even/odd functions and symmetries of their graphs. Creating new graphs from known ones. Constructing and reading graphs of functions, also in reference to real situations.

Elements of Statistics

What is Statistics and its purpose: definition, basic concepts, the language of statistics.
Collecting and organizing data: sampling techniques, datasets, tables, and graphs, frequency distributions, graphical representation of statistical data.
Summarizing data: central tendency measures for unitary and grouped data (mean, median, and mode); measures of dispersion for unitary and grouped data (range, mean absolute deviation, variance, standard deviation, interquartile range).
Analyzing data: Univariate analysis (shape of the distribution, boxplot) and bivariate analysis (scatter plots and correlation, least squares method, regression line).

Elements of Physics

Fundamental and derived physical quantities. Units of measurement in the International System. Examples of dimensional analysis.
Cartesian plane, reference system, vectors. Position and average velocity. Uniform linear motion. Angular velocity and uniform circular motion. Concept of acceleration and force. Fundamental law of dynamics. Weight force and gravitational acceleration. Frictional forces.
Work. Work-energy theorem. Mechanical power.
Statics of fluids and the concept of pressure. Flow rate and conservation of mass. Viscous friction and head loss.
Temperature and thermometers. Thermal equilibrium and heat transfer. Specific heat and thermal energy. Principle of conservation of energy.
Electric charge, Coulomb's law. Potential difference and electric current. Electrical measurements. Electrical resistance and Ohm's first law. Resistors in series and parallel. Electrical power. Joule's effect.
Concept of electromagnetic wave, frequency, wavelength. Spectrum and visible light. Visible, IR, UV radiation, and interaction with matter. Solar radiation and incident energy on a surface.

Attendance is strongly recommended