Description

Introduction to calculus, including functions, limits, continuity, derivatives and applications of the derivative, sketching of graphs of functions, introduction to definite and indefinite integrals, and calculation of area. The course is especially recommended for science and mathematics majors. Credit will be granted for only one of the following: MATH 140 or MATH 136 or MATH 120.

Prerequisites

Permission of the department based on 3 1/2 years of college preparatory mathematics (including trigonometry) and either a satisfactory score on the mathematics placement examination or completion of Math 115 with a grade of C or better.

Topics

Chapter 1. Functions

Brief review of major topics in precalculus

Chapter 2. Limits and Continuity

Limits, one sided and infinite limits
Tangent lines and velocity
Continuity, the Intermediate Value Theorem, and the Bisection Method

Chapter 3. Derivatives

Derivatives, including the Chain Rule
Implicit differentiation
Related rates
Approximation of derivatives and the Newton-Raphson method

Chapter 4. Applications of the Derivative

Maximum and minimum values, and the Maximum-Minimum Theorem
Mean Value Theorem and its applications
Exponential growth and decay
Analysis of graphs of functions

Chapter 5. The Integral

Definite and indefinite integrals
The Fundamental Theorem of Calculus
Integration by substitution
Natural logarithmic function
Area

Chapter 10. Curves in the plane

Basic properties of parabolas, ellipses and hyperbolas

Calculator Programs

The course includes an introduction to a few numerical methods, such as Newton's Method for solving nonlinear equations and Riemann sums for approximating integrals. For such methods, it is convenient to use a computer or calculator. Programs for Riemann sums on a TI-83 or TI-84 calculator may be found here. Programs for Newton's method may be found here.