Calculus I

1. Limits of sequences of numbers
2. Limits of functions
3. Continuity of a function

1. Introduction to Derivatives
2. Derivatives of some functions
3. Derivatives of combinations and compositions of functions

1. Extreme values of functions
2. Optimization of functions
3. Rate of change

1. Integration as reverse process of differentiation
2. Techniques of integration
3. Definite integrals, area and fundamental theorem of calculus
4. Applications of Integral calculus

Keys

1. Work with inequalities
2. Work with absolute values
3. Visualization of intervals
4. Understand the delta-epsilon definition of a limit
   Key: given a function f, we would like to find and interval delta (domain) which controls the behavior of f (within epsion of the range).

Theories

1. Identity function
2. Constant function
3. Multiplication of a constant and a function
4. Sum of two functions
5. Difference of two functions
6. Product of two functions
7. Quotient of two functions
8. Power of a function
9. Polynomial of a function