DEPARTMENT OF MATHEMATICS AND STATISTICS

UNIVERSITY OF MASSACHUSETTS AT AMHERST

MATHEMATICS 127 COURSE OUTLINE FALL 1998

TEXT: **Calculus & Its Applications**, by Goldstein, Lay and Schneider, 8th edition,

published by Prentice Hall

Chapter 0 - Functions

0.1 Functions and Their Graphs

0.2 Some Important Functions

0.3 The Algebra of Functions

0.4 Zeros of Functions--The Quadratic Formula and Factoring

0.5 Exponents and Power Functions

0.6 Functions and Graphs in Applications

Chapter 1 - The Derivative

1.1 The Slope of a Straight Line

1.2 The Slope of a Curve at a Point

1.3 The Derivative

1.4 Limits and the Derivative

1.5 Differentiability and Continuity

1.6 Some Rules for Differentiation

1.7 More About Derivatives

1.8 The Derivative as a Rate of Change

Chapter 2 - Applications of the Derivative

2.1 Describing Graphs and Functions

2.2 The First and Second Derivative Rules

2.3 Curve Sketching (Introduction)

2.4 Curve Sketching (Conclusion)

2.5 Optimization Problems

2.6 Further Optimization Problems

2.7 Applications of Calculus to Business and Economics

Chapter 3 - Techniques of Differentiation

3.1 The Product and Quotient Rules

3.2 The Chain Rule and the General Power Rule

3.3 Implicit Differentiation and Related Rates

Chapter 4 - The Exponential and Natural Logarithm Functions

4.1 Exponential Functions

4.2 The Exponential Function e^{x}

4.3 Differentiation of Exponential Functions

4.4 The Natural Logarithm Function

Chapter 4 - The Exponential and Natural Logarithm Functions - continued

4.5 The Derivative of 1n x

4.6 Properties of the Natural Logarithm Function

Chapter 5 - Applications of the Exponential and Natural Logarithm Functions

5.1 Exponential Growth and Decay

5.2 Compound Interest

- Applications of the Natural Logarithm Function to Economics
- Further Exponential Models

Chapter 6 - The Definite Integral

6.1 Antidifferentiation

6.2 Areas and Riemann Sums

6.3 Definite Integrals and the Fundamental Theorem

6.4 Areas in the *xy*-Plane

6.5 Applications of the Definite Integral

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Your grade will be determined by the following formula:

Two 1 1/2 hour exams (25% each)

In class homework and/or quizzes (20%)

Final exam - 2 hours (30%)

Exam 1 6:30pm - 8:00 Thursday, October 22

Make-up 6:30pm - 8:00} Wednesday, October 21

Exam 2 6:30pm - 8:00 Tuesday, November 24 (Section 5 is in Room: Bart 65).

Make-up 6:30pm - 8:00 Monday, November 23 (Section 5 is in Room: Morril 2 room 131)

Final 8:00am - 10:00am Monday, December 21 (Section 5 is in BART 65)

__All__ exams are multiple choice.

Calculators need to be used on all exams.