Mathematics Department

Indiana University of Pennsylvania

Indiana, PA 15705

Course Number: MA 124??

Course Title: Calculus I

Credits: 4 semester hours

P rerequisites: 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 c alculator

Revised: 10/96

Catalog Description:

The second of a two semester sequence for math and science majors. Topics include: techniques of integration, sequences and series, Taylor polynomials, calculus of functions of sev eral variables, polar coordinates, multiple integrals.

Course Outline/Schedule:

Coverage: Chapters 9 through 15 with the some exceptions noted below. Chapter 10 material on polar coordinates will be incorporated into chapter 15 wi th polar integrals and chapter 12 material on vectors and parametric curves will be merged with chapter 13 as noted.

CHAPTER 9 TECHNIQUES OF INTEGRATION (4 hours)

The main focus here is on use of tables, integration by parts. Additional sections at the instructor's discretion. Possible problems to assign may include some of the following:

9.1 Introduction

9.2 Integral Tables and Simple Substitutions

Problems pp. 487-488 1-29 every other odd, 31-35 odd, 37-49 eoo.

9.3 Trigonometric I ntegrals (play up the fact that these are substitutions.)

Problems pp. 495-496 1-45 eoo, 49, 51

9.4 Integration by Parts

Problems pp. 501-502 1-31 odd, 37, 41, 43, 47, 51

9.8 Improper Integrals

Problems pp. 529-531 1-23 odd, 25, 26, 27

CHAPTER 10 POLAR COORDINATES AND CONIC SECTIONS (Integrated later.)

CHAPTER 11 INFINITE SERIES (7 hours)

11.1 Introduction

11.2 Infinite Sequences

Problems p. 587 1-35 odd 40, 44

11.3 Infinite Series and Convergence

Pr oblems pp. 596-507 1-29 odd (e.o.o would suffice) 31,33, 47, 49. Avoid 36-40

11.4 Taylor Series and Taylor Polynomials

Problems pp. 610-611 1-19 odd (1, 7, 13, 15 suffice) 23, 27, 31, 35. Avoid 32, 37

11.5 Integral test Just using for p-test. light on these if any. Many involve partial fractions.

Problems pp. 617-618 2,3,4, 17, 25 are ok.

11.6 Comparison test. Since we usually use limit comparison instead, light on these too.

Problems pp. 623-624 1, 5, 7, 9 are strai ght forward.

11.7 Alternating Series and Absolute Convergence

Problems p. 631 1-32 odd are ok. Could do: 1, 3, 5, 7, 9, 11, 13, 15, 17, 29, 33, 37

11.8 Power Series

Problems p. 641 1-19 odd are ok. 1, 3, 9, 13, 15, 21, 23, 27, 31, 33, 37

CHAPTER 12 PARAMETRIC CURVES AND VECTORS IN THE PLANE

Integrated into chapter 13 with vectors in 3-D.

CHAPTER 13 VECTORS, CURVES AND SURFACES IN SPACE (5 hours)

Here we work in the vectors in the plane from chapter 12 at the same time. < p>Cover 12.3 & 13.1 concurrently

12.3 Vectors in the Plane

Problems p. 675 1, 5, 9, 11, 15, 17, 19, 23, 25, 33, 35

13.1 Rectangular Coordinates and 3-D Vectors

Problems pp. 700-701 1, 5, 6, 10, 11, 15, (17, 19, 21)?, 31, 43, 52

13.2 The Vector Product of Two Vectors

Problems pp. 708-709 1, 3, 11, 13, 15, 21, 22

13.3 Lines and Planes in Space

They will not have seen parametric equations yet, so we use the parametric form of lines to introduce the concept.

Problems p. 715 3, 5, 9, 11, 15, 19, 23, 25, 33

Cover 12.4 & 13.4 concurrently: vector valued parametric curves.

12.4 Motion and Vector Valued Functions

Problems pp. 682-683 3, 5, 9, 13, 19, (projectile?0 25, 27, 41

13.4 Curves and Motion in Space

Problems pp. 720-721 3, 5, 11, 15, 17, 27?

13.5 Omit

13.6 Omit

12.1 Parametric Curves

Problems p. 659 1, 3, 7, 9. (angle between curves?)

12.2 omit

CHAPTER 14 PARTIAL DIFFERENTIATION (8 hours)

14.1 Introduction

14.2 Functio ns of Several Variables

Problems pp. 761-762 3, 4, 15, 19, 21, 25, 27, 37, 40, 41. (Omit 31-36, since we omit 13.6)

14.3 Limits and Continuity

Problems pp. 767-768 3, 5, 7, 9, 11, 17, 19, 21, 27

14.4 Partial Derivatives

Problems pp . 774-775 1-19 odd, 21, 23, 31, 35, 43(long), 45, 47a.

14.5 Maxima and Minima of Functions of Several Variables

Problems pp. 784-785 1, 7, 11*, 15, 19, 21, 23, 31, 35...more? 55

14.6 omit

14.7 The Chain Rule

Problems pp. 800-801 5, 7, 11 , 13, 21, 26, 29

14.8 Directional Derivatives and the Gradient Vector

Problems pp. 809-810 1, 3, 7, 11, 15, 18, 21, 23, 27, 35, 42, 43

14.9 Lagrange Multipliers and Constrained Maximum-Minimum Problems

Problems pp. 818-819 3, 7, 15, 18

14. 10 The Second Derivative Test for Functions of Two Variables

Problems pp. 827-828 5, 7, 13, 21, 23

CHAPTER 15 MULTIPLE INTEGRALS (9 hours)

Here we work in other coordinate systems (polar, cylindrical, spherical) as needed.

15.1 Double Inte grals

Problems p. 839 1-29 odd are ok. Perhaps e.o.o

15.2 Double Integrals over More General Regions

Problems pp. 845-846 1, 3, 9, 11, 15, 20, 21

15.3 Area and Volume by Double Integration

Problems pp. 851-852 11, 13, 21, 27, 33. (om it areas by double integral)

15.5 omit

15.6 Triple Integrals

Problems pp. 876-877 1, 5, 9 centroids, moments?

10.2 Polar Coordinates

Problems pp. 548-549 1, 2, 11, 13, 21, 19, 29-38 39-51eoo (use techn) 53, 55, 57

10.3 Area Computation s in Polar Coordinates

Problems pp. 554-555 1, 5, 13, 16, 19, 23

13.7 Cylindrical and Spherical Coordinates

Problems pp. 747-748 1, 59, 9, 11, 13, 15, 25, 27, 33

15.4 Double Integrals in Polar Coordinates

Problems pp. 858-859 (omit area s using double integrals) 9, 11, 13, 17, 26, 29

15.7 Integration in Cylindrical and Spherical Coordinates

Problems pp. 884-885 some

Reading Program: The following should be required reading.

1. Morris Kline: The Creation of the C alculus.

2. Philip J Davis and Reuben Hersh: Introduction, Overture, Chapter 1 and Chapter 6 from The Mathematical Experience.