IN BRIEF Definition of multiple integrals: integration of functions of multiple real variables. Types of integrals: double integrals and triple integrals. Applications: calculation of areas and volumes of irregular shapes, evaluation of the mass of objects with variable density. Use in mechanics: calculation of moments of inertia by analogy with double integrals. Techniques: importance of … Read more
IN BRIEF Use interactive games to make learning fun. Integrate hands-on activities, such as cooking, to teach quantities. Incorporate educational books that address mathematics in an accessible way. Utilize everyday objects for counting and measuring exercises. Create a stimulating environment with appropriate tools, like dice and cards. Creating a mathematics learning workshop at home can … Read more
IN BRIEF Geometric transformations: Mechanisms for modifying figures in the plane. Main types: Translation, Rotation, Reflection, Homothety. Bijectivity: Unique association between original points and image points. Conservations: Lengths, angles, areas, and alignments preserved during transformations. Varied applications: Used in various fields such as physics and computer science. Pedagogical approach: Presentation and exercises in student textbooks. … Read more
IN BRIEF Read carefully the statement to fully understand the problem. Rephrase the problem to grasp its essence. Develop a strategy to determine the appropriate method. Put into practice the chosen strategy and carry out the necessary calculations. Verify that the solution found is coherent and relevant. The resolution of simple mathematical problems is an … Read more
IN BRIEF Definition of place value in decimal numbers. Difference between whole numbers and decimal numbers. Importance of digits after the decimal point (tenths, hundredths, etc.). Concept of truncation and approximate value. Writing decimal numbers in expanded form. Place value charts to organize values. In the field of mathematics, understanding decimal numbers and their place … Read more
IN BRIEF Differential equations: fundamental in applied mathematics. Homogeneous solutions: functions of the form x ↦ λe−A(x). Cauchy problem: method of variation of the constant. Linear equations: of order 1 and 2, rewritten in canonical form. Numerical resolution: approach for solutions by series. Variation method: development of particular solutions. Applications: usefulness in various industrial fields. … Read more
IN BRIEF Applied Mathematics : Essential foundation for robotics. Predictive Models : Used in the design of robotic movements. Algorithms : Designed using mathematics to guide robotic actions. Machine Learning : Integrated to enhance the intelligence of robots. Geometry : Fundamental for understanding space and movement. Trajectories : Mathematical modeling of movements. Educational Robots : … Read more
IN BRIEF Applied mathematics to quantum mechanics Use of complex numbers to model wave-like phenomena Emission of electrons from metallic materials under light radiation Applications of group theory to describe the symmetries of physical systems Solutions described by periodic vibration modes Impact of mathematics on advances in quantum physics Mathematics plays a fundamental role in … Read more
IN BRIEF Mathematical logic as the foundation of philosophical thought. Relationship between mathematics and philosophy through the centuries. Influence of modern philosophers on mathematics. The philosophy of mathematics and its foundations. Contributions from figures like Descartes and Pascal. Abstraction and generalization in reasoning. Kant’s approaches to the independence of mathematics. Mathematics, as a rigorous discipline, … Read more
IN BRIEF Set ℕ: Natural integers (0, 1, 2, …) Set ℤ: Relative integers (positive and negative) Set ℚ: Rational numbers (fractions) Set ℝ: Real numbers including irrationals Set ℝ⁺: Positive real numbers Set ℝ⁻: Negative real numbers Use of the number line to represent the sets Importance of properties and relationships between the sets … Read more