Test Preview

Text: G.B. Thomas, Jr., M.D. Weir, and J. Hass, Thomas' Calculus. Early Transcendentals, 14th Edition, 2018.

General information: Open-text & open-notes event. No Solution Manual, laptop, tablets, etc. Calculators are not allowed (and not required for calculations in this test).

Subjects: Area in Polar Coordinates; Vectors & Vector Operations; Geometry with Vectors

Concepts which should be under unconditional control:

• Area bounded by polar functions
• Vectors; elementary operations on vectors
• Magnitude of a vector; basis unit vectors; unit vector
• Dot product; angle between two vectors
• Cross product; areas of a triangle; volume of parallelepiped
• Lines in space; parametric equations
• Planes in space and their linear equations; normal vector
• Vector-valued functions and operations with them

Contents (#2 consists of two questions):

1. Problem about area of the region bounded by polar function(s)
2. Basic operations with vectors in the plane and in space
3. Determination of the angle between the vectors (no calculator will be needed)
4. Finding the cross product of two vectors
5. Geometrical problem: area
6. Geometrical problem: volume
7. Finding parametric equations of a line in space
8. Finding a standard equation of a plane in space
--------------------
9. Bonus problem

Sample problems:

1. 11.5: 1 - 18
2. 12.2: 1 - 8, 21, 22
3. 12.3: 9 - 14
4. 12.4: 1 - 8
5. 12.4: 15 - 18; 12: 25(a), 26(a) (p. 758)
6. 12.4: 19 - 22; 12: 25(b), 26(b) (p. 758)
7. 12.5: 1 - 12
8. 12.5: 21 - 26; 12: 37, 38 (p. 758)

Help Session - Test Preview: Wednesday, March 4, 2020

4:00 - 6:00 pm: SH202

General information: Open-text & open-notes event. No Solution Manual, laptop, tablets, etc. Calculators are not allowed (and not required for elementary calculations in this test).

Subjects: Infinite Series with Negative Terms. Parametric Representations & Polar Coordinates.

Concepts which should be under unconditional control:

• Series with real terms; alternating series
• Absolute and conditional convergence of series with real terms
• Power series
• Taylor polynomials & Taylor series
• The remainder; errors of polynomial approximations
• Parametric equations and their graphs; area of the region bounded by a parametric curve; length of a parametric curve
• Polar coordinates; conversion from/to polar forms
• Typical polar curves - cardioids, limacons, rose curves, and lemniscates

Contents:

1. Convergence of a series with real numbers
2. Convergence of a power series
3. Taylor series/polynomial (with remainder) of a function at a point
4. Graph of a parametric curve (or its Cartesian equivalent)
5. Area of a region bounded by (or an arc length of) a parametric curve
6. Conversion of a polar equation to a Cartesian one
7. Conversion of a Cartesian equation to a polar one
8. Sketch of a graph of a polar function
-------------------
9. Bonus problem

Sample problems:

1. 10.6: 15 - 44
2. 10.7: 1 - 36
3. 10.8: 1 - 10
4. 11.1: 1 - 18
5. 11.2: 21 - 30
6. 11.3: 27 - 52
7. 11.3: 53 - 66
8. 11.4: 1 - 12

Help Session - Test Preview: Monday, February 17, 2020

5:00 - 6:00 pm: SH202

General information: Open-text & open-notes event. No Solution Manuals, laptops, tablets, calculators, etc.

Subjects: Indeterminate Forms & Improper Integrals. Infinite Sequences & Infinite Series with Non-Negative Terms.

Concepts which should be under unconditional control:

• Indeterminate forms (0/0, oo/oo); l'Hopital's Rule; techniques for other indeterminate forms
• Importer integrals: integrands with infinite domain and infinite range
• Infinite sequences and their convergence
• Infinite series and their convergence
• Geometric series, harmonic series, p-series and their properties
• Series with positive terms; convergence tests: integral test, comparison test, limit comparison test

Contents (No 1 contains two problems, No 5 - three, No 7 - two):

1. Limits of indeterminate forms
2. Improper integral
3. General term of a sequence
4. Convergence of a sequence
5. Infinite series - convergence, sum of convergence, divergence
6. Convergence of an infinite series - the Integral Test
7. Convergence of an infinite series - Comparison Tests
-------------------
8. Bonus problem

Sample problems:

1. Section 4.5: 7 - 50
2. Section 8.8: 1 - 34
3. Section 10.1: 13 - 30
4. Section 10.1: 31 - 100
5. Section 10.2: 7 - 22; 10.3: 13 - 46
6. Section 10.3: 1 - 12
7. Section 10.4: 1 - 56

Test Preview Help Session: Thursday, January 30, 2020

5:00 - 6:00 pm: SH202

[ Back to Calc III Info Page ]

---

vadim@wpi.edu

Last modified: Tue, March 3, 2020