Calculus theory: Difference between revisions

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# '''Functions'''
 
## [[Mistakes regarding functions]]
* '''Functions'''
## [[Defining a function]]
<div style="width:100%; float:left; padding-bottom:1.5em;">
## [[Operations with functions]]
<div style="width: 50%; float:right;">
## [[Visualising the domain of a function]]
* [[Graphs of trigonometric functions]]
## [[Graph of single variable functions]]
* [[Transforming the graph of functions]]
## [[Transforming the graph of functions]]
* [[Linear algebra and deforming graphs of functions]]
## [[Linear algebra and deforming graphs of functions]]
* [[Guessing the graphs of single variable functions]]
## [[Guessing the graphs of single variable functions]]
* [[Guessing the graphs of multivariable functions]]
## [[Guessing the graphs of multivariable functions]]
* [[Level curves and level surfaces]]
## [[Level curves and level surfaces]]
</div>
# '''Polar coordinates and parametric curves'''
<div style="width: 50%; float:right;">
## [[Mistakes regarding polar coordinates]]
* [[Mistakes regarding graphs]]
## [[Mistakes regarding parametric curves]]
* [[Mistakes regarding functions]]
## [[Polar coordinates]]
* [[Defining a function]]
## [[Parametric curves]]
* [[Operations with functions]]
## [[Parametrization of curves]] (add graphs with vectors?)
* [[Visualising the domain of a function]]
# '''Limits and continuity'''
* [[Graphs of the parabola, exp and log]]
## [[Mistakes regarding limits]]
</div>
## [[Informal limit and continuity of a single variable function]]
</div>
## [[Formal limit and continuity of a single variable function]]
 
## [[Limit and continuity of a multivariable function]]
* '''Limits and continuity'''
## [[Properties of limits]]
<div style="width:100%; float:left; padding-bottom:1.5em;">
## [[Limits at or with infinity]]
<div style="width: 50%; float:right;">
## [[Theorems covering limits and continuity of functions]]
* [[Properties of limits]]
## [[Informal discussion of the Euler's constant]]
* [[Limits at or with infinity]]
# '''Differentiation and derivatives'''
* [[Theorems covering limits and continuity of functions]]
## [[Mistakes regarding derivatives]]
* [[Informal discussion of the Euler's constant]]
## [[Defining the derivative]]
</div>
## [[Partial derivatives and direction]]
<div style="width: 50%; float:right;">
## [[Defining the gradient]]
* [[Mistakes regarding limits]]
## [[Conditions for differentiability for a single variable]]
* [[Informal limit and continuity of a single variable function]]
## [[Conditions for differentiability for many variables]]
* [[Formal limit and continuity of a single variable function]]
## [[Linear approximation for one variable]]
* [[Limit and continuity of a multivariable function]]
## [[Linear approximation for two variables]]
</div>
## [[Derivative formulas]]
</div>
## [[Derivative of logarithm and exponential]]
 
## [[Derivative of trigonometric functions]]
* '''Differentiation and derivatives'''
## [[Derivative of inverse functions]]
<div style="width:100%; float:left; padding-bottom:1.5em;">
## [[Chain rule for single variable functions]] (incomplete at the end)
<div style="width: 50%; float:right;">
## [[Chain rule for multivariable functions]]
* [[Linear approximation for two variables]]
## [[Implicit differentiation]]
* [[Derivative formulas]]
# '''Applications of differentiation'''
* [[Derivative of logarithm and exponential]]
## [[Increasing and decreasing functions]]
* [[Derivative of trigonometric functions]]
## [[Extreme values of a function]]
* [[Derivative of inverse functions]]
## [[Finding extreme values of a single variable function]]
* [[Chain rule for single variable functions]]
## [[Finding critical points of a single variable function]]
* [[Chain rule for multivariable functions]]
## [[l'Hospital rule]]
* [[Implicit differentiation]]
## [[Finding extreme values of a multivariable function]]
</div>
## [[Finding critical points of a multivariable function]]
<div style="width: 50%; float:right;">
# '''Integration and total change'''
* [[Mistakes regarding derivatives]]
* [[Defining the derivative]]
* [[Partial derivatives and direction]]
* [[Defining the gradient]]
* [[Conditions for differentiability for a single variable]]
* [[Conditions for differentiability for many variables]]
* [[A sufficient condition for differentiability for many variables]]
* [[Linear approximation for one variable]]
</div>
</div>
 
* '''Applications of differentiation'''
<div style="width:100%; float:left; padding-bottom:1.5em;">
<div style="width: 50%; float:left;">
* [[Increasing and decreasing functions]]
* [[Extreme values of a function]]
* [[Finding extreme values of a single variable function]]
* [[Finding critical points of a single variable function]]
</div>
<div style="width: 50%; float:right;">
* [[l'Hospital rule]]
* [[Finding extreme values of a multivariable function]]
* [[Finding critical points of a multivariable function]]
* [[Lagrange multipliers]]
</div>
</div>
 
* '''Integration and total change'''

Latest revision as of 15:28, 1 September 2022

  • Functions
  • Limits and continuity
  • Differentiation and derivatives
  • Applications of differentiation
  • Integration and total change
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