Calculus theory: Difference between revisions

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## [[Mistakes regarding derivatives]]
## [[Mistakes regarding derivatives]]
## [[Defining the derivative]]
## [[Defining the derivative]]
## [[Derivatives of logarithm and exponential]]
## [[Partial derivatives and direction]]
## [[Partial derivatives and direction]]
## [[Defining the gradient]]
## [[Defining the gradient]]
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## [[Linear approximation for two variables]]
## [[Linear approximation for two variables]]
## [[Derivative formulas]]
## [[Derivative formulas]]
## [[Derivative of logarithm and exponential]]
## [[Derivative of trigonometric functions]]
## [[Derivative of trigonometric functions]]
## [[Chain rule for single variable functions]] (incomplete at the end)
## [[Chain rule for single variable functions]] (incomplete at the end)

Revision as of 00:05, 5 April 2022

  1. Functions
    1. Mistakes regarding functions
    2. Defining a function
    3. Operations with functions
    4. Visualising the domain of a function
    5. Graph of single variable functions
    6. Transforming the graph of functions
    7. Linear algebra and deforming graphs of functions
    8. Guessing the graphs of single variable functions
    9. Guessing the graphs of multivariable functions
    10. Level curves and level surfaces
  2. Polar coordinates and parametric curves
    1. Mistakes regarding polar coordinates
    2. Mistakes regarding parametric curves
    3. Polar coordinates
    4. Parametric curves
    5. Parametrization of curves (add graphs with vectors?)
  3. Limits and continuity
    1. Mistakes regarding limits
    2. Informal limit and continuity of a single variable function
    3. Formal limit and continuity of a single variable function
    4. Limit and continuity of a multivariable function
    5. Properties of limits
    6. Limits at or with infinity
    7. Theorems covering limits and continuity of functions
  4. Differentiation and derivatives
    1. Mistakes regarding derivatives
    2. Defining the derivative
    3. Partial derivatives and direction
    4. Defining the gradient
    5. Conditions for differentiability for a single variable
    6. Conditions for differentiability for many variables
    7. Linear approximation for one variable
    8. Linear approximation for two variables
    9. Derivative formulas
    10. Derivative of logarithm and exponential
    11. Derivative of trigonometric functions
    12. Chain rule for single variable functions (incomplete at the end)
    13. Chain rule for multivariable functions
    14. Implicit differentiation
  5. Applications of differentiation
    1. Increasing and decreasing functions
    2. Extreme values of a function
    3. Finding extreme values of a single variable function
    4. Finding critical points of a single variable function
    5. l'Hospital rule
    6. Finding extreme values of a multivariable function
    7. Finding critical points of a multivariable function
  6. Integration and total change
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