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Level 1 · 36 lessons

Calculus I: Differential Calculus

Limits, continuity and derivatives of functions of one real variable.

Course content

Unit 0Course overview

  1. 01Syllabus of Calculus I

Unit 1Limits and Continuity

  1. 02Limits and continuity: introduction
  2. 03Limit of functions of a real variable
  3. 04Algebra of limitsWith account
  4. 05The squeeze theorem and trigonometric limitsWith account
  5. 06One-sided limitsWith account
  6. 07Limits as the variable tends to infinityWith account
  7. 08Infinite limitsWith account
  8. 09Asymptotes and curve sketching techniquesWith account
  9. 10Limit and continuityWith account
  10. 11Continuity of the elementary functions and standard limitsWith account
  11. 12Equivalent infinitesimals and infinitely large functionsWith account
  12. 13Limits and continuity: synthesis and challengesWith account

Unit 2Derivatives

  1. 14Derivadas: introducciónAvailable in SpanishSubscriptionWith account
  2. 15La derivada como el límite de una funciónAvailable in Spanish
  3. 16Reglas de derivaciónAvailable in SpanishSubscriptionWith account
  4. 17Derivadas de las funciones elementalesAvailable in SpanishSubscriptionWith account
  5. 18Regla de la cadena para la derivada de la composición de funcionesAvailable in SpanishSubscriptionWith account
  6. 19Teorema del valor intermedioAvailable in SpanishSubscriptionWith account
  7. 20Derivada de la función inversa y derivación implícitaAvailable in SpanishSubscriptionWith account
  8. 21La variable en el exponente y la derivación logarítmicaAvailable in SpanishSubscriptionWith account
  9. 22Derivadas sucesivas y diferencialAvailable in SpanishSubscriptionWith account
  10. 23Razones de cambio y tasas relacionadasAvailable in SpanishSubscriptionWith account
  11. 24Derivadas: síntesis y desafíosAvailable in SpanishSubscriptionWith account

Unit 3Applications of Derivatives

  1. 25Aplicaciones de las derivadas: introducciónAvailable in SpanishSubscriptionWith account
  2. 26Teorema de Weierstrass de los valores extremosAvailable in SpanishSubscriptionWith account
  3. 27Teoremas de Fermat, Rolle, Lagrange y CauchyAvailable in SpanishSubscriptionWith account
  4. 28Regla de L'HôpitalAvailable in SpanishSubscriptionWith account
  5. 29Monotonía y criterio de la primera derivadaAvailable in SpanishSubscriptionWith account
  6. 30Máximos y mínimos de una funciónAvailable in SpanishSubscriptionWith account
  7. 31Concavidad, convexidad y puntos de inflexiónAvailable in SpanishSubscriptionWith account
  8. 32Curvatura y radio de curvaturaAvailable in SpanishSubscriptionWith account
  9. 33Problemas de optimizaciónAvailable in SpanishSubscriptionWith account
  10. 34El método de Newton-RaphsonAvailable in SpanishSubscriptionWith account
  11. 35Aplicaciones de las derivadas: síntesis y desafíosAvailable in SpanishSubscriptionWith account

Unit 4Course closing

  1. 36Balance final de Cálculo IAvailable in SpanishSubscriptionWith account