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Text: G.B. Thomas, Jr., M.D. Weir, and J. Hass, Thomas' Calculus. Early Transcendentals, 13th Edition, 2014.

General information:

50 min written exam. No laptops, gadgets, tablets, smartphones, calculators, etc.

Subject:

Multiple integration - the material considered in the last part of the course (Sections 15.5 - 15.7).

The concepts which should be under your unconditional control:

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

Contents:

1. Finding the mass (or a moment) of a planar non-homogeneous lamina
2. Finding by triple integration the volume of a solid bounded by surfaces
3. Formulation and evaluation of a triple integral in cylindrical coordinates (2 problems)
4. Formulation and evaluation of a triple integral in spherical coordinates
5. A bonus.

Sample problems:

1. 15.5: ## 23-36
2. 15.6: ## 11-20
3. 15.7: ## 43-62, 67-82

General information:

50 min written exam. No laptops, gadgets, tablets, smartphones, calculators, etc.

Subject:

Extreme values/multivariable optimization (Section 14.7) and double integration (Sections 15.1 to 15.4) - the material considered in the second part of the course.

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 integral of f(x, y) over region R (2 problems)
3. Evaluation of an iterated integral with reversed order of integration
4. Finding the volume of a 3D solid
5. Evaluation of a double integral over the region defined by polar functions
6. A bonus

Sample problems:

1. 14.7: ## 1 - 30
2. 15.1: ## 15 - 22, 15.2: ## 19 - 28
3. 15.2: ## 47 - 54
4. 15.2: ## 57- 66
5. 15.4: ## 9 - 22

General information:

50 min written exam. No laptops, gadgets, tablets, smartphones, calculators, etc.

Subject:

Partial derivatives and associated topics - the material considered in the course so far (i.e., Sections 14.1 to 14.6).

The concepts which should be under your unconditional control:

• Domain of a multivariable function
• Limits of functions of several varibales
• Partial derivatives of the first and higher orders; mixed derivatives
• The Chain Rule for functions of several variables
• Gradient & directional derivatives
• Tangent plane
• Incremental approximation

Contents:

1. Problem on finding a domain of a multivariable function
2. Sketching level curves
3. Finding the limit of a function of two variables
4. Computation of partial derivatives of the first order
5. Computation of partial derivatives of the second order
6. Finding partial derivatives of a composite functions with the Chain
7. Computation of a directional derivative of a function in a particular direction at a give point
8. A bonus

Sample problems:

1. 14.1 ## 5-12
2. 14.1 ## 37-48
3. 14.2 ## 1-12
4. 14.3 ## 23-34
5. 14.3 ## 41-49
6. 14.4 ## 1-10
7. 14.5 ##11-18

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Last modified: Fri, Apr 28, 2017