MVVC Week 4 – Problem Set Assignments and Learning Goals

Reading:

• • Boas 5.1 Introduction
  • Boas 5.2 Double and Triple Integrals
  • Boas 5.3: Applications of Integration; Single and Multiple Integrals

Learning Goals:

0. Review and reinforce material from single variable integral calculus: finding anti-derivatives/evaluating indefinite integrals and evaluating definite integrals with simple integrands using inspection, u-substitution (including trig substitutions), and integration by parts, and for more complicated integrands, using a table of integrals and a computer algebra system.
1. Given a double integral over a rectangular or general region, sketch the region of integration by hand or computer. Use the sketch or inspection to determine the new limits of integration if the order of integration is changed. Carry out an analogous process for triple and other multiple integrals.
2. Evaluate a given multiple integral using the techniques described in 0. above. When necessary, switch the order of integration using the techniques described in 1. above.
3. Translate physical situations given by verbal descriptions or sketches into suitable multiple integrals, particularly those involving area, volume, arc length, surface area, mass, center of mass and centroid, and moments of inertia.

MVVC Problem Set, Week 4:

• 5.2: 20 & 23; 27 & 28 & 30 & 31; 33 & 35; 42 & 44; 43 & 45
• 5.3: 7 & 9; 10 &11; 19 & 20 & 29
• Note: this has more problems than on previous sets; my hope is to have quite a bit of time in class on Wednesday for CSS groups to work together.

To see which problem(s) you’ve been assigned to contribute to the Collaborative Solution Set, visit this shared Google folder and navigate to the appropriate subject and assignment in the directory structure. This is also the document to which you will post your solutions by Friday 6pm.