Math 107 Fall 2007 Course Update and Cumulative Homework List

Transcription

1 Math 107 Fall 2007 Course Update and Cumulative Homework List Date: 8/27 Sections: 5.4 Log: Review of course policies. The mean value theorem for definite integrals. The fundamental theorem of calculus, parts I and II. Assignment: Read about total area (last two pages of section 5.4) and do problems odd. Date: 8/29 Sections: 5.5 Log: Indefinite and definite integrals by substitution. Assignment: Section 5.5, problems odd, 55, 57, 67. Date: 8/31 Sections: 7.1 Log: Integration by parts (IBP). Assignment: Section 7.1, 1-23 odd, 43, 45. Review: Section 5.5, odd. Notes: Quiz 1 will be given on Thursday, 9/6. It will cover sections 5.5 and 7.1. Date: 9/5 Sections: 7.2 Log: Trigonometric integrals. Assignment: Section 7.2, 5-37 odd. Read example 7. Date: 9/7 Sections: 7.3 Log: Trigonometric substitutions. Assignment: Section 7.3, 1-23 odd, 29, 31. Notes: Quiz 2, over 7.3 and 7.4, will be given on Thursday, 9/13. Date: 9/10 Sections: 7.4 Log: The partial fraction decomposition of a rational function. Assignment: Section 7.4, 1-23 odd, 29 35, 50.

2 Date: 9/12 Sections: 7.5 Log: Tables of integrals, computer algebra systems and special functions. Assignment: Section 7.5, 1, 9, odd, 29, 45, 50. Date: 9/14 Sections: 7.6 Log: Numerical integration. The trapezoid rule, Simpson s rule. Error estimates. Assignment: In section 7.6, read examples 3 and 4, and do problems odd, odd. Notes: Quiz 3, over 7.7, will be given on Thursday, 9/20. Date: 9/17 Sections: 7.7 Log: Improper integrals. Integrals over unbounded domains. Integrands with vertical asymptotes. The comparison and limit comparison tests. Assignment: In section 7.7, read the statement of the limit comparison test along with example 8. Do problems 1-21 odd, odd, 66. Notes: Quiz 3, over 7.7, will be given on Thursday, 9/20. Date: 9/19 Sections: 6.1, 6.2 Log: Finding the volume of a solid of revolution by slicing, and by the method of cylindrical shells. Assignment: Section 6.1, problems 25, 27, 39, 43, 49. Section 6.2, problems odd, 27, 29. Review: Section 7.7, problems odd. Date: 9/21 Sections: 6.3 Log: The length of a plane curve. Derivation of the arclength integral for parametric curves and for graphs of functions. The improper arclength integral for an infinite spiral. Assignment: Section 6.3, problems 5-13 odd, 21. Review: Section 7.r (chapter 7 review) problem, 9-27 odd, odd. Notes: The paper gateway exam will be given on Thursday, 9/27.

3 Date: 9/24 Sections: 6.5 Log: Exponential growth and decay. Differential equations, initial conditions and initial value problems. Malthus population model, radiocative decay, Newton s law of cooling. Separable differential equations. Assignment: Section 6.5, problems 1, 3, 7, 9, 19, 21, 25, 31, 35, 41. Review: Section 7.r (chapter 7 review) odd. Date: 9/26 Sections: 6.6 Log: Work integrals. Hooke s law. Pumping liquids. Assignment: In section 6.6, read example 3 and do problems 3-11, 19, 23, 35. Review: Section 7.r (chapter 7 review) odd, even. Date: 9/28 Sections: 6.7 Log: Mass, moments, center of mass. Computing the center of mass of a lamina. Assignment: Section 6.7, problems 5, 7, 11, 15, 17. Date: 10/1 Sections: 8.1 Log: Sequences. Convergent and divergent sequences. The sandwich theorem. Using L Hôpital s rule to compute sequence limtis. Recursive sequences, the Fibonacci numbers. Upper bound, least upper bound and nondecreasing sequences. Assignment: In section 8.1, read theorems 1 and 3, and examples 5, 6 and 9. Do problems odd, 97 and 99. Notes: Exam 1 will be given on Thursday, 10/4. Students may retake the Gateway exam in Avery 018 and Burnett 127. Date: 10/3 Log: Review. Date: 10/5 Sections: 8.2 Log: Infinite series. Partial sums. Convergence and divergence of series. The nth term test for divergence. Geometric series. Telescoping series. Assignment: In section 8.2, do problems 7-33 odd, 37 and 39.

4 Date: 10/8 Sections: 8.3 Log: The integral test. Divergence of the harmonic series. Convergence (divergence) of the p-series for p > 1 (p 1). Assignment: In section 8.3, do problems 1-23 odd, 39, 41. Notes: Quiz 4, over 8.2 and 8.3, will be given on Thursday, 10/11. Date: 10/10 Sections: 8.4 Log: The comparison and limit comparison tests. Assignment: In section 8.4, do problems 1-29 odd and read example 3. Notes: The project will be distributed on Thursday, 10/11. You may work alone, or in groups of at most three. Date: 10/12 Sections: 8.5 Log: Absolute and conditional convergence. The ratio and root tests. Assignment: In section 8.5, do problems 1-25 odd, 39, 41. Notes: Quiz 5, over 8.5 and 8.6, will be given on Thursday, 10/18. Date: 10/15 Sections: 8.6 Log: Alternating series. The alternating series test. The conditional convergence of the alternating p-series for 0 < p 1, of the alternating harmonic series in particular. Assignment: In section 8.6, do problems 1-23 odd. Date: 10/17 Log: Review of series. Assignment: In section 8.r, do problems 9-39 odd. Date: 10/19 Sections: 8.7 Log: Power series. Interval and radius of convergence. Term-by-term differentiation and integration of power series. Assignment: In section 8.7, read examples 4, 5 and 6, and do problems 1-15 odd and odd. Notes: There will be no quiz next week.

5 Date: 10/24 Sections: 8.8 Log: Taylor series, Taylor coefficients, Taylor polynomials. Assignment: In 8.8 do 3-7 odd, 33, 35, 37. Date: 10/26 Sections: 8.8 Log: Taylor series and polynomials for exp, sin and cos. Approximation by Taylor polynomials. Assignment: In 8.8 do problems 9-27 odd. Notes: Quiz 6, over 8.8 and 8.9, will be given on Thursday, 11/1. Date: 10/29 Sections: 8.9 Log: Convergence of Taylor series and and approximation by Taylor polynomials. Estimating error in Taylor polynomial approximation. Assignment: In 8.9 do problems 9-23 odd. Date: 10/31 Sections: 8.9 Log: Applications of Taylor series: Approximating integrals, the Coates-Euler formula. Computing Taylor series for certain functions (e.g. erf, arctan, Si). Assignment: In 8.9 do problems 25, 49, 50. In 8.r, do odd. Date: 11/2 Sections: 8.10 Log: Binomial series for f(x) = (1 + x) m. Assignment: In 8.10 do problems 1-19 odd. Review: 8.r, problems 19-69, odd. Notes: Exam 2, covering sections , will be given on Thursday, 11/8. Date: 11/5 Log: Outline of exam material. Review of series. Date: 11/7 Log: Review of series.

6 Date: 11/9 Sections: 9.1 Log: Polar coordinates. Translating rectangular into polar coordinates and vice-versa. Equations in polar coordinates. Assignment: In 9.1 do problems 1-17 odd, odd and odd. Notes: Quiz 7, over sections 9.1 and 9.2, will be given on Thursday, 11/15. Date: 11/12 Sections: 9.2 Log: Graphing functions of the form r = f(θ). The slope of a polar graph. Symmetries of polar graphs. The cardioid and the lemniscate. Assignment: In 9.2 do problems 5-25 odd. Read example 2. Date: 11/14 Sections: 9.3 Log: Arclength and area in polar coordinates. Assignment: In 9.3 do problems 3-9 odd and odd. Date: 11/16 Sections: 10.1 Log: Points, distances, equations and ineqaulities in three-dimensional space. The error estimate in project problem 5. Assignment: Section 10.1, problems 1-27 odd, 31 and 35. Date: 11/19 Sections: 10.2 Log: Two and three-dimensional vectors. Scalars and vectors. The component form of a vector. The magnitude of a vector. The zero vector. Vector addition and scalar multiplication. Assignment: Section 10.2, problems 1-15 odd.

7 Date: 11/26 Sections: 10.3 Log: The standard basis vectors ı, j and k. Unit vectors. The dot product of two vectors. The geometric definition of the dot product. Using the dot product to find angles between vectors. Orthogonal vectors. Projections and components. Assignment: In 10.3 do problems 1-11 odd and 15. Notes: Quiz 8, over section 10.3, will be given on Thursday, 11/29. Date: 11/28 Sections: 10.5 Log: Lines in space. Parametric equations for the line through a point P in the direction v. Parametric equations for the line and line segment joining two points. Parametric equations for the line through a point P parallel to a given line. Assignment: In 10.5 do problems 1-7 odd, 11 and 13. Read examples 3 and 4. Date: 11/30 Sections: 11.1 Log: Two- and three-dimensional vector-valued functions. Sketching the oriented curve traced by a vector-valued function. Speed, velocity and acceleration. Assignment: In 11.1, do problems 1-13 odd. Notes: Exam 3, over sections , , 10.5, 11.1 and 11.2, will be given on 12/6. Date: 12/3 Sections: 11.2 Log: Indefinite and definite integrals of vector-valued functions. Initial value problems. The ideal projectile. Assignment: In 11.2, do problems 1-19 odd. Review: Section 9.r, problems 1-15 odd, odd. Section 10.r, problems 1-15 odd, 19, 23, 31, 32. Section 11.r, problems 3, 7, 11, 12 and 13. Date: 12/5 Log: Review. Date: 12/7 Sections: 11.3 Log: The arclength of a curve in space. The arclength parameter. Assignment: In 11.3, do problems 1-13 odd.

8 Date: 12/10 Log: Review of techniques of integration, series and power series. Notes: Copies of old 107 finals are available at the bookstore. Bring your ID to the final! Date: 12/12 Log: Review of Taylor series, applications of the integral. Notes: The final exam rooms are Dougherty: Burn 120, Kamalov: Arch 127, Stolee: Ferg 217. Date: 12/14 Log: Review. Notes: Copies of old 107 finals are available at the bookstore. Bring your ID to the final!

9 odd odd, , 27, 39, 43, odd, 27, odd, , 3, 7, 9, 19, 21, 25, 31, 35, , 19, 23, , 7, 11, 15, odd, 43, odd odd, 29, odd, 29, 35, , 9, odd, 29, 45, odd, odd odd, odd, r 9-43 odd, odd, 97, odd, 37 and odd, 39, odd odd, 39, odd odd, odd odd, 33, 35, odd, 49, odd. 8.r 9-69 odd odd, odd, odd odd odd, odd. 9.r 1-15 odd, odd odd, 31, odd odd, odd, 11, r 1-15 odd, 19, 23, 31, odd odd odd. 11.r 3, 7, 11, 12, 13. Cumulative Homework List