Calculus theory

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. Polar coordinates
   2. Parametric curves
   3. Parametrization of curves
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. Defining partial derivatives
   4. Conditions for differentiability
   5. Linear approximation for one variable
   6. Linear approximation for two variables
   7. Derivative formulas
   8. Derivative of trigonometric functions
   9. Chain rule for single variable functions
   10. Chain rule for multivariable functions
   11. Implicit differentiation
5. Applications of differentiation
   1. Increasing and decreasing functions
   2. Extreme values of a function
   3. Finding extreme values of a function
   4. Finding critical points of a function