Calculus theory

• Functions

• Graphs of trigonometric functions
• Transforming the graph of functions
• Linear algebra and deforming graphs of functions
• Guessing the graphs of single variable functions
• Guessing the graphs of multivariable functions
• Level curves and level surfaces

• Mistakes regarding graphs
• Mistakes regarding functions
• Defining a function
• Operations with functions
• Visualising the domain of a function
• Graphs of the parabola, exp and log

• Limits and continuity

• Properties of limits
• Limits at or with infinity
• Theorems covering limits and continuity of functions
• Informal discussion of the Euler's constant

• Mistakes regarding limits
• Informal limit and continuity of a single variable function
• Formal limit and continuity of a single variable function
• Limit and continuity of a multivariable function

• Differentiation and derivatives

• Linear approximation for two variables
• Derivative formulas
• Derivative of logarithm and exponential
• Derivative of trigonometric functions
• Derivative of inverse functions
• Chain rule for single variable functions
• Chain rule for multivariable functions
• Implicit differentiation

• 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

• Applications of differentiation

• 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

• l'Hospital rule
• Finding extreme values of a multivariable function
• Finding critical points of a multivariable function
• Lagrange multipliers

• Integration and total change