# Mount Holyoke College

# Math 151: Calculus IA

# Syllabus

### Functions (Chapter 1)

- General notion of function. Domain. Range. Functions in one variable.
Three ways to represent a function.
- Linear functions.
- Power functions. Polynomials. Rational functions.
- Exponential functions.
- Inverse functions. Logarithms.
- Trigonometric functions.

### Derivative (Chapter 2)

- Speed, velocity and derivative.
- The derivative function.
- Second derivative and its interpretations.

### Short-cuts to differentiation (Chapter 4)

- Differentiation of polynomials.
- Differentiation of exponents.
- Differentiation of trigonometric functions.
- The product and quotient rules.
- The chain rule.
- Derivative of the inverse function.
- Implicit function.
- Linear approximation.

### Applications (Chapter 5)

- Using the first and second derivatives.
- Optimizations.
- Newton's method

### Integral (Chapter 3)

- Notion of definite integral.
- Areas.
- The fundamental theorem of Calculus (The Newton-Leibniz formula).