Master Calculus 1: Basic-To-Advanced Course

La duración total del curso es de 7 horas.

1. Introduction.
   • Overview of calculus and its significance in mathematics and sciences.
   • Fundamental concepts such as functions, rates of change, and slopes.
   • Functions Reading and Exercises.
2. Limits.
   • Understanding the concept of limits and their notation.
   • Evaluating limits algebraically, graphically, and numerically.
   • Special limits including limits at infinity and indeterminate forms.
   • Continuity of functions and the Intermediate Value Theorem.
3. Derivatives.
   • Definition of derivatives using limits.
   • Computing derivatives of polynomial, exponential, logarithmic, and trigonometric functions.
   • Rules of differentiation: product rule, quotient rule, and chain rule.
4. Applications of derivatives.
   • Finding extrema and points of inflection using first and second derivative tests.
   • Optimization problems: maximizing/minimizing functions subject to constraints.
   • Introduction to Local Extrema.
   • Explain about Tangent Lines, Linear approximation, differential…
   • Definition of Rolle’s Theorem and Mean Value Theorem.
   • Graphing equations using derivatives.
5. Antiderivatives.
   • Introduction to antiderivatives and indefinite integrals.
   • Techniques of integration: substitution, integration by parts, trigonometric substitution.
   • Riemann sums.

1. Familiaridad con álgebra básica y funciones matemáticas.
2. Conocimiento sólido de trigonometría y geometría analítica.
3. Comprensión de límites y conceptos básicos de cálculo.
4. Capacidad para resolver problemas matemáticos utilizando derivadas e integrales.
5. Disponibilidad para dedicar tiempo a estudiar y completar ejercicios prácticos.

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.