Math 140 - Calculus I

Credits: 4

Description: This course is an introduction to differential and integral calculus. It begins with a short review of basic concepts surrounding the notion of a function. Then it introduces the important concept of the limit of a function, and uses it to study continuity and the tangent problem. The solution to the tangent problem leads to the study of derivatives and their applications. Then it considers the area problem and its solution, the definite integral. The course concludes with the calculus of elementary transcendental functions.

Pre-Requisites: A suitable score on Math placement test C, or completion of MATH 130 within the past semester with a grade of B or higher.

Note: A student who has received credit for either MATH 134 or MATH 135 may not take MATH 140 for credit without the explicit permission of the department and then only for two credits.

Frequency: Offered every semester (Fall - Spring - Summer).

Current Textbook: Single Variable Calculus. 6th Edition, by James Stewart, published by Brooks/Cole, 2008. ISBN: 0495011606. Check with your instructor to make sure this is the textbook used for your section.

Chapter 1: Functions and Models.

1.1 Four Ways to Represent a Function.
1.2 Mathematical Models: A Catalog of Essential Functions.
1.3 New Functions from Old Functions.

Chapter 2: Limits.

2.1 The Tangent and Velocity Problems.
2.2 The Limit of a Function.
2.3 Calculating Limits Using the Limit Laws.
2.5 Continuity.

Chapter 3: Derivatives.

3.1 Derivatives and Rates of Change.
3.2 The Derivative as a Function.
3.3 Differentiation Formulas.
3.4 Derivatives of Trigonometric Functions.
3.5 The Chain Rule.
3.6 Implicit Differentiation.
3.7 Rates of Change in the Natural and Social Sciences.
3.8 Related Rates.
3.9 Linear Approximations and Differentials.

Chapter 4: Applications of Differentiation.

4.1 Maximum and Minimum Values.
4.2 The Mean Value Theorem.
4.3 How Derivatives Affect the Shape of a Graph.
4.4 Limits at Infinity; Horizontal Asymptotes.
4.5 Summary of Curve Sketching.
4.7 Optimization Problems.
4.8 Newton's Method.
4.9 Antiderivatives.

Chapter 5: Integrals.

5.1 Areas and Distances.
5.2 The Definite Integral.
5.3 The Fundamental Theorem of Calculus.
5.4 Indefinite Integrals and the Net Change Theorem.
5.5 The Substitution Rule.

Chapter 6: Applications of Integration.

6.1 Areas between Curves.
6.2 Volumes.

Chapter 7: Inverse Functions.

7.1 Inverse Functions.
7.2 Exponential Functions and Their Derivatives.
7.3 Logarithmic Functions.
7.4 Derivatives of Logarithmic Functions.