# Mount Holyoke College

# Math 200: Calculus IIA

# Syllabus

### Antiderivatives (Chapter 6)

- Antiderivatives. Notion and formulas for simplest functions.
- Simple differential equations.
- Second Fundamental Theorem of Calculus. Definite integrals with a
variable as the upper limit.

### Integration (Chapter 7)

- Integration by substitution.
- Integration by parts.
- Practice on integration.
- Approximations of definite integrals.
- Improper integrals.

### Applications (Chapter 8)

- Applications of integrals to geometry.
- Applications of integrals to physics.
- Complex numbers. Functions in complex variable.

### Approximation and series (Chapter 9)

- Taylor series.
- Series. Geometric series. Convergency.
- Fourier series.

### Differential equations (Chapter 10)

- Differential equations. Basic notions. Slope fields.
- Separation of variables.
- Second-order differential equations.
- Linear second-order ODEs with constant coefficients.