Calculus I

1. Introduction to limits of functions
2. Tangent lines and rates of change
3. Continuity of a function
4. Exercises

1. Concepts
2. Exercises

1. Concepts
2. Exercises

1. Concavity
2. Asymptotes
3. Infection points
4. Curve sketching

Exercises

Vectors

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

Appliction in 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