Description

An introduction to calculus for students in the biological, social and management sciences and architecture. Applications of calculus to these disciplines form an important part of the course. Concrete calculations are emphasized and provide an opportunity to practice algebraic skills introduced in earlier courses. Credit will only be given for one of Math 140 and Math 220.

Prerequisites

MATH 112 or MATH 113 or MATH 115 or satisfactory score on the Math Department placement exam.

Topics

The Derivative

Slopes
Derivatives
Rules for differentiation
Rate of change

Applications of the Derivative

Graphs and relation with derivatives
Curve sketching
Optimization problems

Techniques of Differentiation

Product rule
Quotient rule
Chain rule

The Exponential and Logarithm Functions

Definitions and properties of exponential function
Definitions and properties of natural log
Derivatives of log and exponential functions

Applications of the Exponential and Logarithm Functions

Exponential growth and decay
Compound interest

Integration

Antidifferentiation,
Area
Approximation by Riemann sums
The fundamental theorem of calculus
Applications of the definite integral

Functions of Several Variables

Partial derivatives
Max-Min
Lagrange multipliers
Least squares