Single Variable Calculus

### Limits

- Calculating Limits Expressly. Calculating the limit of a function at certain values.
- Finding Limits Numerically. Using For Loops to calculate the limit of a value numerically.

### Differentiation

- Taking the Derivative of a Function. Calculating the derivatives of functions.
- Higher Order Derivatives. Calculating higher order derivatives.
- Implicit Differentiation. Using Sage to do implicit differentiation.
- Newtons Method with Python. Newtons Method in Sage with Python.

### Integration

- Indefinite Integrals. Calculating indefinite integrals.
- Definite Integrals. Calculating definite integrals.
- Numerical Integration. Calculating definite integrals using numerical approximation.
- Partial Fractions. Calculating partial fraction decompositions.
- Using Infinity in Sage and for Improper Integrals. Sage's symbol for infinity and its use in an improper integral.
- The sage assume Command and Integrals Using sage's assume command to evaluate integrals with variable limits.

### Sequences, Series, and Taylor Polynomials

- Taylor Polynomials. Computing Taylor polynomials.