# 11.3 Solids Of Revolution Washerap Calculus

## Professor Shannon Gracey

The Fundamental Theorem of Calculus 5 2.1. The Fundamental Theorem of Calculus I 5 2.2. The Fundamental Theorem of Calculus II 6 3. Change of variable or the substitution rule 7 Chapter 2. Applications of Integration I 9 1. Area between curves 9 2. Volumes by cylindrical shells 12 4. Average value of a function 16. This lesson reviews how to find volumes of solids of revolution by disks (one function over the x-axis) and washers (two functions). We also work out one example where there are two bounding. The basic method is slicing a solid into pieces of known cross-sectional area; solids of revolution are a special case. 11.3-11.4: Polar coordinates; areas in polar coordinates. 1 2: Complex numbers and complex exponentials: De Moivre s theorem, complex roots, and Euler s formula.

## Office Hours  ## Course Description  Covers analytic geometry, vectors, and vector-valued functions. Includes functions of several variables, vector calculus, surfaces and surface integrals, partial derivatives, multiple integrals, line integrals, and Green's Theorem. Requires graphing calculator.

## Prerequisite

MATH 251

### Recommended Preparation

RDG 56 or the equivalent skill level as determined by the Southwestern College Reading Assessment or equivalent

## ANNOTATED LECTURE PDF FILES (BY DATE)

 WEEK 1 LECTURES: 1/121/14 WEEK 7 LECTURES: 2/23 WEEK 13 LECTURES: 4/44/64/8 WEEK 2 LECTURES: 1/191/21 WEEK 8 LECTURES: 2/283/23/4 WEEK 14 LECTURES: 4/114/13 WEEK 3 LECTURES: 1/241/261/28 WEEK 9 LECTURES: 3/73/93/11 WEEK 15 LECTURES: 4/274/29 WEEK 4 LECTURES: 1/312/4 WEEK 10 LECTURES: 3/143/163/18 WEEK 16 LECTURES: 5/25/45/6 WEEK 5 LECTURES: 2/72/92/11 WEEK 11 LECTURES: no class 3/23 and 3/25-out-of-class assignment due 3/28 WEEK 17 LECTURES: 5/9 5/13 WEEK 6 LECTURES: 2/142/16 WEEK 12 LECTURES: 3/304/1 WEEK 18 LECTURES:

## IN-CLASS WORKSHEETS WS 14.1

## SOLUTIONS:

### 11.3 Solids Of Revolution Washerap Calculus Calculator

EXAMS

 EXAM 1 EXAM 2 EXAM 3 EXAM 5

HANDOUTS:

## Course Objectives

1. Student will apply the concepts learned in the previous two courses to functions of two or more variables.
Uefaempty spaces the blog. 2. Student will perform operations on vectors and vector-valued functions and will use them in applications to lines and planes in space, velocity and acceleration, and loci in space.
3. Student will evaluate partial and directional derivatives, differentials, and apply these to extrema of functions and tangent planes and normal lines.
4. Student will evaluate multiple integrals and use them in applications to areas and volume, including tranformations to polar, cylindrical, and spherical systems.
5. Student will evaluate line integrals and surface integrals, use vector fields and use Green's Theorem and the Divergence Theorem as applications of vector calculus.
6. Student will demonstrate the ability to graph a variety of surfaces in 3-space, including quadric surfaces, cylinders, and solids of revolutions.

## Student Learning Outcomes

### Upon successful completion of Math 252, the student should be able to:

• State and apply basic definitions, properties, and theorems of multivariable Calculus
• Apply vector operations in two and three dimensions and use vector methods to analyze plane and space curves, and curvilinear motion
• Apply standard techniques of multivariable calculus, both differential and integral, to solve selected applied problems
• Apply standard techniques of vector analysis to analyze and solve problems involving vector fields and (line, surface, or flux) integrals

### 11.3 Solids Of Revolution

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