This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

# Calculus 1: course

### From Mathematics Is A Science

## 1 Description

This is a traditional first semester course in introductory calculus. The main goal is some familiarity with the derivative and its applications.

## 2 Prerequisites

## 3 Lectures

- Preview of calculus: part 1
- Preview of calculus: part 2
- Preview of calculus: part 3
- Limits: part 1
- Limits: part 2
- Limits: part 3
- Introduction to continuity
- Continuity of functions
- Limits at infinity: part 1
- Limits at infinity: part 2
- Derivative as a limit
- Derivative as a function
- Differentiation without limits: part 1
- Differentiation without limits: part 2
- Differentiation without limits: part 3
- Differentiation without limits: part 4
- Applications of the derivative
- Implicit differentiation
- Rates of change
- Radar gun: the math
- Exponential models
- Linear approximations
- Differentials
- Maximum and minimum values of functions
- Using derivative to find extreme values
- Derivative reflects behavior of the function
- Using derivative to study monotonicity
- Using derivative to study concavity
- Resolving indeterminate expressions
- Plotting the graph of a function
- Applications of derivative: optimization
- Reversing differentiation: antiderivatives
- Integral: introduction
- Integral: definition
- Integral: properties
- Derivative and integral: Fundamental Theorem of Calculus
- Computing integrals

## 4 Exams

## 5 Notes

The content came from this complete set of handwritten lectures.

Calculus by Stewart was used.

An alternative approach to studying calculus is to start with Differential calculus and then proceed to Integral calculus.