Indiana University of Pennsylvania

Indiana, PA 15705

Course Number: MA 123??

Course Title: Calculus I

Credits: 4 semester hours

Prerequisites: Algebra, geometry and trigonometry. (MA 110 or the equivalent)

Text: Calculus with Analytic Geometry (Early Transcendental Version), 4th Ed.

by Edwards and Penney, Prentice Hall.

Technology: TI 92 calculator

Revised: 10/96

Catalog Description: Intended for math and science majors, coverage includes: functions, limits, continuity, derivatives, applications of derivative, integrals and applications of the integral. (Trigonometric, exponential and logarithmic functions are included throughout the course.)

Course Outline/Schedule:

Coverage: Chapters 2 through 8 with the exception of 4.2 and 8.5, with chapter 7 assimilated into earlier chapters.

CHAPTER 1 Functions and Graphs (1 hour)

The instructor should prepare a brief review of concepts related to functions and their graphs as well as an introduction to calculus. (Use your own discretion here.)

Possible problems to assign may include some of the following:

1.1 Functions and Real Numbers

Problems pp. 11-13 (1, 4, 6, 10, 13, 14, 16, 17, 25, 27, 29, 39, 42, 47, 54, 57, 61, 69)

1.2 The Coordinate Plane and Straight Lines

Problems pp. 22-23 (3, 6, 8, 10, 14, 19, 22, 25, 29, 35, 36, 43)

1.3 Graphs of Equations and Functions

Problems pp. 30-31 (3, 4, 9, 10, 13, 23, 27, 35, 41, 43, 49, 53, 55)

1.4 A Brief Catalog of Functions

Problems pp. 40-41 (5, 9, 13, 16, 22, 23, 28, 31, 34)

1.5 A Preview What Is Calculus?

NOTE STUDENTS SHOULD BE ADVISED TO LOOK OVER AND WORK SOME OF THE MISCELLANEOUS PROBLEMS ON PAGES 47-48.

CHAPTER 2 PRELUDE TO CALCULUS (4 hours)

Possible problems to assign may include some of the following

2.1 Tangent Lines and the Derivative - A First Look

Problems pp. 57-59 (3, 5, 8, 11, 15, 18, 21, 24, 28, 31, 35, 36, 37, 38, 42, 46, 49)

2.2 The Limit Concept

Problems p. 69 (1-29 odd, 32, 35, 38, 40, 41, 43, 46, 49, 51)

2.3 More about Limits

Problems pp. 80-81 (1-27 odd, 30, 34, 35, 41, 48, 49, 55, 61, 64, 66)

2.4 The Concept of Continuity

Problems pp. 90-91 (2, 6, 8, 11, 18, 21, 27, 33, 39, 44, 47, 52, 54, 57, 59, 62, 67)

NOTE: POSSIBLE REVIEW PROBLEMS MAY BE FOUND IN THE MISCELLANEOUS PROBLEMS SECTION ON PAGES 92-93.

CHAPTER 3 THE DERIVATIVE (10 hours)

3.1 The Derivative and Rates of Change

Problems pp. 105-106 (2, 3, 5, 9, 14, 17, 20, 23, 24, 29, 31, 35, 37, 39, 43, 45)

3.2 Basic Differentiation Rules

Problems pp. 115-117 (1-71 every other odd)

3.3 The Chain Rule

Problems pp. 124-125 (1-63 odd - OR every other odd)

3.4 Derivatives of Algebraic Functions

Problems pp. 129-131 (1-59 odd -OR every other odd)

3.5 Maxima and Minima of Functions on Closed Intervals

Problems pp. 138-139 (1-51 odd)

3.6 Applied Maximum-Minimum Problems

Problems pp. 149-154 (1-7odd,11,12,14, 16, 19, 21, 25-27, 30, 33, 335, 38, 42, 46-48)

3.7 Derivatives of Trigonometric Functions

Problems pp. 161-164 (1-71 e.o.o.)

3.8 Exponential and Logarithmic Functions (NOTE: Add problems from 7.2 & 7.3)

Problems pp. 173-174 (1-57 e.o.o.)

AND pp. 418-419 (1-31 e.o.o, 51, 55); pp. 425-426 (1-35 e.o.o, 55, 59, 63)

3.9 Differentiation and Related Rates

Problems pp. 180-183 (1-27 odd, 35, 37, 45, 49, 55, 59, 63)

3.10 Successive Approximations and NewtonÕs Method

Problems pp. 192-194 (3, 7, 11, 17, 18, 21, 25, 29, 31, 34, 37, 38)

CHAPTER 4 ADDITIONAL APPLICATIONS OF THE DERIVATIVE (4 hours)

Possible problems to assign may include some of the following:

4.3 Increasing and Decreasing Functions and the Mean Value Theorem

Probs pp. 218-20 (3,4,8,9,12, 15, 18, 21, 22, 25, 26, 30, 33, 36, 38, 43, 44, 49, 55, 57)

4.4 The First Derivative Test & 4.5 Simple Curve Sketching

Problems pp. 228-230 (1, 7, 11, 15, 18, 21, 23, 27, 30, 33, 36, 44, 46)

AND pp. 237-238 (2, 3, 7, 11, 15, 19, 20, 29, 39, 43)

4.6 Higher Derivatives and Concavity

Probs pp. 250-253 (2,3,8,9,13, 17, 21, 23, 27, 30, 35, 38, 41, 47, 51, 65, 73,77,80, 81)

4.7 Curve Sketching and Asymptotes

Problems pp. 261-262 (1-29 odd, 34, 41, 47, 55)

CHAPTER 5 THE INTEGRAL (7 hours)

Possible problems to assign may include some of the following:

5.1 Introduction

5.2 Antiderivatives and Initial Value Problems

Problems pp. 278-280 (1-29odd, 35-45 odd, 47,49,57, 65)

5.3 Elementary Area Computations (light coverage)

Problems pp. 290-291 (1,5,9,13,17,19,23,25,35,37)

5.4 Riemann Sums and the Integral (light coverage)

Problems pp. 298-299 (1,5,9,11,15,43,45,47)

5.5 Evaluation of Integrals (light coverage, emphasize Fund. Thm of Calc in 5.6)

Problems pp. 307-308 (1-35 odd)

5.6 Average Values and the Fundamental Theorem of Calculus

Problems pp. 316-318 (1, 5, 9, 11, 13-27 odd, 29, 31, 35, 41, 43, 45, 51-59 odd)

5.7 Integration by Substitution

Problems pp. 323-325 (1-43 odd, 45, 46, 49)

5.8 Areas of Plane Regions

Problems pp. 332-334 (1, 4, 5, 10, 11, 13, 15, 18, 20, 21-41 odd, 45)

5.9 Numerical Integration

Problems pp. 345-347 (1, 3, 5, 13, 15, 17, 21, 23)

CHAPTER 6 APPLICATIONS OF THE INTEGRAL (6 hours)

Possible problems to assign may include some of the following:

6.1 Setting up Integral Formulas

Problems pp. 359-360 (1, 5, 9, 11, 13, 15, 19, 21, 25, 27, 29, 31, 33, 34, 37)

6.2 Volumes by the Method of Cross Sections

Problems pp. 368-371 (1-25 odd, 29, 31, 33, 34, 39, 43)

6.3 Volume by the Method of Cylindrical Shells

Problems pp. 377-378 (1-9 odd, 15, 17, 19, 23, 25, 31, 35)

6.4 Arc Length and Surface Area of Revolution (optional)

Problems pp. 386-387 (1-9 odd, 11, 12, 15, 17, 18, 21, 23, 27, 29, 31, 35)

6.5 Separable Differential Equations

Problems pp. 394-395 (1-19 odd, 21, 23, 27, 29, 21, 33)

Problems pp. 441-442 (3, 5, 10, 13, 15, 17, 19)

6.6 Force and Work

Problems pp. 403-405 (1-13 odd, 17, 19, 23, 25, 29, 31)

CHAPTER 7 MORE EXPONENTIAL AND LOGARITHMIC FUNCTIONS (Omitted)

Note: Problems from sections 7.2, 7.3 and 7.5 included in sections on derivatives and integrals.

CHAPTER 8 FURTHER CALCULUS OF TRANSCENDENTAL FUNCTIONS (3 hours)

Possible problems to assign may include some of the following:

8.1 Introduction

8.2 Inverse Trigonometric Functions

Problems pp. 461-462 (1-25 odd, 27, 31-55 odd, 59, 61, 63)

8.3 Indeterminate Forms and L'Hopital's Rule

Problems pp. 466-467 (1-47 odd)

8.4 Additional Indeterminate Forms

Problems pp. 471-472 (1-33 odd, 39)

Reading Program: The following articles should be required reading.

1. Judith Grabiner: The Changing Concept of Change: The derivative from Fermat to Weierstrass.

2. Lars Garding: The Heroic Century.

3. Eric Temple Bell: On the Seashore.