Calculus part 1: Limits and continuity

La duración total del curso es de 60 horas.

1. Introduction.
   • Overview of the course objectives and structure.
   • Importance of calculus in understanding mathematical functions.
2. Basic notions and elementary fuctions.
   • Mathematical notation and symbols used in calculus.
   • Definitions and properties of elementary functions.
3. The nature of the set of real numbers.
   • Definition and properties of the set of real numbers.
   • Axiom of completeness and implications for calculus.
   • Basic operations and relations in the set of real numbers.
4. Sequences and their limits.
   • Definition and types of sequences (arithmetic, geometric, harmonic, etc.).
   • Convergence and divergence of sequences.
   • Weierstrass’ Theorem.
   • Limit of a sequence: formal definition and examples.
   • Limit laws for sequences.
   • Computing limits from the definition.
5. Limit of a function in a point.
   • Definition of the limit of a function at a point.
   • Calculation of limits using algebraic techniques.
   • Squeeze theorem and its applications.
   • One-sided limits and their significance.
   • Continuity of polynomials, rational functions, and power functions.
6. Infinite limits and limits in the infinities.
   • Definition and evaluation of infinite limits.
   • Horizontal and vertical asymptotes.
   • Limits at infinity and their interpretations.
7. Continuity and discontinuities.
   • Definition of continuity at a point and on an interval.
   • Types of discontinuities.
   • Behavior of functions around points of discontinuity.
8. Properties of continuous functions.
   • The Max-Min Theorem.
   • Boundedness theorem for continuous functions.
   • Uniform continuity and its implications.
9. Graphing functions.
   • Techniques for graphing functions of one variable.
   • Determining domain and range of functions.
   • Behavior near points of discontinuity and asymptotes.

1. Familiaridad con notación matemática básica, lógica, conjuntos y demostraciones matemáticas.
2. Conocimiento de funciones polinómicas y racionales.
3. Dominio de conceptos trigonométricos.
4. Comprensión de funciones exponenciales y logarítmicas.

La realización del curso será completamente on-line y evaluado a través de un examen. Una vez superado el mismo, podrás recibir tu título, válido para toda España.

Una vez hayas completado el curso, puede realizar el test relacionado y obtener tu título.