#### 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

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**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.