Calculus theory

1. Proofs
   1. Mistakes regarding proofs
2. Algebra and properties of numbers
   1. Mistakes regarding algebra
   2. Properties of powers
   3. Properties of roots
   4. Properties of the absolute value
   5. Completing the square and long division
   6. Properties of the real numbers
3. 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
4. Polar coordinates and parametric curves
   1. Polar coordinates
   2. Parametric curves
5. Limits and continuity
   1. Mistakes regarding limits
   2. Limit and continuity of a single variable function
   3. Limit and continuity of a multivariable function
   4. Properties of limits
6. Differentiation and derivatives
   1. Mistakes regarding derivatives
   2. Defining the derivative