Introduction to Differentiation

La duración total del curso es de 13 horas.

1. Introduction.
   • Overview of Differential Calculus.
   • Importance and applications of differentiation in various fields.
   • Brief history of calculus and key contributors.
2. Limits and Instantaneous Gradient of a Curve
   • Concept of limits and their significance in calculus.
   • Techniques for calculating limits.
   • Understanding instantaneous rate of change and gradient of a curve.
3. Derivarion of Differential Formula
   • Fundamental definition of the derivative.
   • Derivation process and notation.
   • Interpretation of the derivative as a slope of the tangent line.
4. Differentitation of Polynomial Functions
   • Basic rules of differentiation (power rule, constant rule, sum rule).
   • Step-by-step differentiation of polynomial functions.
   • Examples and practice problems.
5. Tangent and Normal Lines.
   • Definition and equations of tangent and normal lines.
   • Finding the tangent and normal lines to a curve at a given point.
   • Applications of tangent and normal lines in problem-solving.
6. Characterization of Polynoial Curves.
   • Analyzing the behavior of polynomial functions using derivatives.
   • Identifying critical points, inflection points, and intervals of increase/decrease.
   • Graphical representation and interpretation.
7. Maximum and Minimum Values.
   • Finding local and global extrema of functions.
   • First and second derivative tests.
   • Application of maximum and minimum values in real-world problems.
8. Differential as Rate of Charge.
   • Understanding the derivative as a rate of change.
   • Applications in physics, economics, biology, and other fields.
   • Solving real-life problems using the concept of rate of change.

1. Dominio de operaciones básicas con números reales y polinomios.
2. Comprensión de conceptos geométricos básicos.
3. Entendimiento de funciones lineales, cuadráticas, exponenciales y logarítmicas.
4. Actitud positiva hacia el aprendizaje de nuevas ideas y conceptos matemáticos.

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.