Escalera de Matemáticas · Universidad

Cálculo 1: Límites y Derivadas

Límites, la derivada como razón de cambio, las reglas de derivación y sus aplicaciones, de la optimización a las primeras integrales.

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54 temas en 5 unidades. Se apoya en Precálculo y Trigonometría. Lleva a Cálculo 2: Integrales y Series. ¿No estás seguro de que sea el curso adecuado? Encuentra tu peldaño.

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Unidad 1 Limits

12 temas

Understand limits from graphs, compute them with algebra, and define them precisely.

  1. Limits from Both Sides
  2. One-Sided Limits
  3. Infinite Limits and Vertical Asymptotes
  4. Limit Laws
  5. Limits by Factoring and Canceling
  6. Limits by Rationalizing
  7. The Squeeze Theorem
  8. Special Trigonometric Limits
  9. Continuity
  10. The Intermediate Value Theorem
  11. Limits at Infinity and Horizontal Asymptotes
  12. The Precise Definition of a Limit

Unidad 2 The Derivative

6 temas

Go from average to instantaneous rate of change, and define the derivative as a limit.

  1. From Average to Instantaneous Rate
  2. The Derivative at a Point
  3. Tangent Lines
  4. The Derivative as a Function
  5. Where Derivatives Fail to Exist
  6. Leibniz Notation and Units

Unidad 3 Differentiation Rules

11 temas

Differentiate powers, products, quotients, compositions, and trig, exponential and log functions.

  1. Constant, Power and Sum Rules
  2. The Product Rule
  3. The Quotient Rule
  4. Derivatives of Trig Functions
  5. Higher Derivatives
  6. The Chain Rule
  7. Chain Rule with Several Layers
  8. Derivatives of Exponential and Log Functions
  9. Implicit Differentiation
  10. Derivatives of Inverse Functions and Inverse Trig
  11. Logarithmic Differentiation

Unidad 4 Applications of Derivatives

11 temas

Use derivatives for motion, related rates, approximation, graph shape and optimization.

  1. Position, Velocity and Acceleration
  2. Related Rates
  3. Linear Approximation and Differentials
  4. Critical Points and Absolute Extrema
  5. The Mean Value Theorem
  6. Increasing, Decreasing and the First Derivative Test
  7. Concavity and the Second Derivative Test
  8. Curve Sketching
  9. Optimization
  10. L'Hôpital's Rule
  11. Newton's Method

Unidad 5 Integrals

14 temas

Find antiderivatives, build definite integrals from sums, and use the Fundamental Theorem and substitution.

  1. Antiderivatives
  2. Antiderivatives with Initial Conditions
  3. Approximating Area with Rectangles
  4. Riemann Sums
  5. The Definite Integral
  6. Properties of Definite Integrals
  7. Accumulation Functions and FTC Part 1
  8. Evaluating Integrals with FTC Part 2
  9. Net Change and Total Distance
  10. Average Value of a Function
  11. Integration by Substitution
  12. Substitution in Definite Integrals
  13. Integrals Giving Exponentials and Logarithms
  14. Integrals Giving Inverse Trig Functions