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Text: Calculus. Early Transcendental Version by C.H. Edwards and D.E. Penney, 7th Edition, 2008

General information:

Open-text open-notes event. Calculators are not allowed (and not needed - no complex arithmetic operations are involved).

Subject:

Multiple integration - the material considered in the last part of the course (Sections 13.5 - 13.8).

The concepts which should be under your unconditional control:

• Applications of double integrals: mass, moments, center of mass, moments of inertia, surface area.
• Triple integrals as iterated integrals; finding mass, center of mass, volume, moments of inertia with triple integrals
• Change of variables in triple integration - integration in cylindrical and spherical coordinates

Contents:

1. Finding the mass (or a moment) of a planar non-homogeneous lamina
2. Evaluating the triple integral of a given function over a given solid region
3. Finding by triple integration the volume of a solid bounded by surfaces
4. Finding the mass (or the volume, or a moment of inertia) of a solid conveniently characterized in cylindrical coordinates
5. A bonus.

Sample problems:

1. 13.5: ## 21, 23, 25
2. 13.6: ## 3, 7, 10 (512/3)
3. 13.6: ## 11, 13, 19
4. 13.7: ## 5, 9, 13

General information:

Open-text open-notes closed-solution-manual event. Calculators are not allowed as they are not required for anything in this test.

Subject:

Multivariable optimization (Sections 12.5 & 12.10) and double integration - the material considered in the second part of the course (Sections 13.1 to 13.4).

The concepts which should be under your unconditional control:

• Absolute (global) and relative (local) extrema; horizontal tangent plane
• Critical points; Second Derivative Test
• Successive partial integration; iterated integrals
• Double integral over rectangular and non-rectangular regions
• Change of order of integration
• Area and volume by double integration
• Double integrals in polar coordinates; integration over the regions formed by polar functions.

Contents:

1. Determination and classification of critical points
2. Evaluation of an iterated integral
3. Evaluation of an iterated integral with reversed order of integration
4. Finding the volume of a 3D solid
5. Evaluation of an integral over the region defined by polar functions
6. A bonus.

Sample problems:

1. 12.10: ## 13, 15
2. 13.1: ## 27, 29
3. 13.2: ## 23, 31
4. 13.3: ## 21, 23
5. 13.4: ## 15, 17

General information:

Open-text open-notes event. Calculators are not allowed (and not required for any calculation - there are no big numbers, no trig functions of non-standard angles, etc.).

Subject:

Partial derivatives and associated topics - the material considered in the course so far (i.e., Chapter 12 - Sections 12.2 to 12.4 and 12.6 to 12.8).

The concepts which should be under your unconditional control:

• Domain of a multivariable function
• Partial derivatives of the first and higher orders; mixed derivatives
• Incremental approximation
• Tangent plane
• Gradient; directional derivatives
• Chain rule

Contents:

1. Problem on finding a domain of a multivariable function
2. Computation of partial derivatives of the first order
3. Computation of partial derivatives of the second order
4. Problem about the differential
5. Finding partial derivatives of composite functions with the Chain Rule (2 problems)
6. Computation of the gradient of a function at a point
7. Computation of a directional derivative of a function in a particular direction at a give point
8. A bonus.

Sample problems:

1. 12.2: ## 11, 15
2. 12.4: ## 7, 19
3. 12.4: ## 21, 25
4. 12.6: ## 13, 15
5. 12.7: ## 1, 7
6. 12.8: ## 3, 9
7. 12.8: ## 15, 19

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Last modified: Wed, Apr 16, 2014