Maria Shea Terrell

CAN GOOD QUESTIONS AND PEER DISCUSSION IMPROVE CALCULUS INSTRUCTION

ABSTRACT Preliminary report of the results of a project 1 to introduce peer instruction into a multi-section first semester calculus course taught largely by novice instructors. This paper summarizes the instructional approaches instructors chose to use, and the subsequent results of student performance on common exams throughout the course of the term. 1 Support for the Good Questions project was provided by the National Science Foundations Course, Curriculum, and Laboratory Improvement Program under grant DUE-0231154. Opinions expressed are those of the authors and not necessarily those of the Foundation.

Multivariable Calculus with Applications

p.106 the last line change k to h p.163 Problem 4.6 (c) change gx1 to bgx1 p.164 Problem 4.11 (a) change z to z p.169 line −4 change rz to rw p.177 lines 6,7 change R(X−A) to R(A,X−A) p.357 line 5 change u) to u0 p.361 line −2 change curlF1 = 0 to curlF2 = 0 p.366 8.35 (a) and (b) 0 should be bold p.371 line 3 0 should be bold p.377 line 11 change [contrary to (8.27)] to [contrary to (8.26)] p.378 line 14 change ρ(x(t)x, t) = ρ(x0.0) to ρ(x(t), t) = ρ(x0.0) p.441 3.51(b) change V(X(t), t)) to V(X(t), t) in 4 places delete ) in C2). change Vt(X(t), t)) to Vt(X(t), t) change X′′(X(t), t) to X′′(t) p.464 8.7(c) two zeros [0 = · · · ] and [· · · = 0] should be bold the integral signs should be printed full-size p.467 8.35 (a) and (b) zeros should be bold p.475 9.49 (c) change row labels X, Y , Z to Ex, Ey, Ez

Line and surface integrals

We use integrals to find the total amount of some quantity on a curve or surface in space. Examples include total mass of a wire, work along a curve, total charge on a surface, and flux across a surface.

More about differentiation

This chapter describes applications of the derivative to methods for finding extreme values of functions of several variables, and to methods for approximating functions of several variables by polynomials.

Vectors and matrices

The mathematical description of aspects of the natural world requires a collection of numbers. For example, a position on the surface of the earth is described by two numbers, latitude and longitude. To specify a position above the earth requires a third number, the altitude. To describe the state of a gas we have to specify its density and temperature; if it is a mixture of gases like oxygen and nitrogen, we have to specify their proportion. Such situations are abstracted in the concept of a vector.

Applications to motion

The concepts and techniques of calculus are indispensable for the description and study of dynamics, the science of motion in space under the action of forces. Both were created by Isaac Newton in the late seventeenth century and they revolutionized both mathematics and physics. In this chapter we describe the basic concepts and laws of the dynamics of point masses and deduce some of their mathematical consequences.

Divergence and Stokes’ Theorems and conservation laws

Green’s and Stokes’ Theorems are extensions to functions of several variables of the relation between differentiation and integration.

Partial Differential Equations

In this chapter we derive the laws governing the vibration of a stretched string and a stretched membrane, and the equations governing the propagation of heat. Like the laws of conservation of mass, momentum and energy studied in the previous chapter, and like the electromagnetism laws, these laws are expressed as partial differential equations. We derive some properties and some solutions of these equations. We also state the Schrodinger equation of quantum mechanics, derive a property of the solutions and explain the physical meaning of this property.

Applications of the Derivative

We present five applications of the calculus: 1. Atmospheric pressure in a gravitational field 2. Motion in a gravitational field 3. Newton’s method for finding the zeros of a function 4. The reflection and refraction of light 5. Rates of change in economics

Numbers and Limits

This chapter introduces basic concepts and properties of numbers that are necessary prerequisites for defining the calculus concepts of limit, derivative, and integral.