# Assignments Calculus B--- Math 112

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### Homework Problems

Monday, January 18 Syllabus/Course procedures
Euler's method: introducing the method
Implementing Euler's Method on a computer: Introducing Loops

Wednesday, January 20 Introducing Project and Paper #1: Euler's Method Project   Euler's Method Exercises
Friday, January 22 Introduction to Maple--or a refresher.
*
Monday, January 25 Class work on Euler's Method Project

Wednesday, January 27

Approximating sums: Left, right, midpoint and trapezoidal sums

Section 5.6

Friday, January 29

## No class---Carol Schumacher at a conference

*
Monday, February 1 Summation notation; working with sums
The definition of the integral.
Computing integrals using Riemann Sums
Section 5.7 Euler's Method Project Due
Sect 5.6:
5, 6, 9, 16, 21, 23, 24, 28, 29, 32, 33, 34. (Well-labeled diagrams are required!)
Wednesday, February 3 Approximating Integrals numerically
Comparing errors in left, right, midpoint. trapezoidal Riemann sums---Simpson's rule
Worksheet: Computing Integrals Using Riemann Sums
Friday, February 5

Group Quiz #1
Comparing errors continued.

Sect 6.1, part 1: 1, 4, 5, 11, 15-18, 19a, 26, 28, 31, 35.
*
Monday, February 8 Error Bounds for Approximating Sums: general cases: Proofs of the error estimates Section 6.2 Sect 6.1, part 2: 29, 30, 38, 40, 43, 46, 52, 54, 55, 56, 61, 62, 63, 64.
Wednesday, February 10 Back to the FTC: Integrals and antiderivatives. Review of "guess and check" methods and substitution.   Sect 6.2:
1, 2, 5, 6, 11, 13, 15, 17.
Friday, February 12 Integration by partial fractions, part I Section 8.2 Integral Worksheet #1 due----not to turn in.
*
Monday, February 15
Test #1 (through section 6.2)
Wednesday, February 17 Integration by parts Section 8.1 Integral Worksheet #2--- Partial Fractions
Friday, February 19 Integration by Partial Fractions, part II.   Integral Worksheet #3--- Integration by Parts
*
Monday, February 22 Practice: Integral Worksheet # 4--- General techniques   Sect 8.2:
2, 6cd, 7cd, 28c, 31, 33-40.
Wednesday, February 24

## Gateway exam

Friday, February 26 Areas between curves Section 7.1 (through top of page 417)
*
Monday, March 1 Finding volumes by parallel cross section
Introducing the goblet project
Sect 7.1: 13, 14, 16, 17, 19, 23.
Wednesday, March 3 Center of Mass of a solid of revolution---work on the goblet project   Sect 7.1: 39, 40, 42, 43.
Sect 7.2: 25, 26, 27, 28, 29, 31.
Friday, March 5 Work on the goblet project.

### Spring Break

Monday, March 22

Separation of variables

Section 7.4
Wednesday, March 24 Solving the logistic equation   Sect 7.4: 1, 2, 3, 4, 9, 12, 13, 18, 19, 21, 22.
Friday, March 26 Group quiz #2---techniques and applications of integration   Goblet project due
*
Monday, March 29 Approximations by polynomials: Taylor polynomials. Section 9.1
Wednesday, March 31 Taylor Polynomials and Taylor's theorem Section 9.2 Sect. 9.1: 3, 5, 7-10, 13, 16, 18, 21, 22, 25, 26, 27, 30, 31, and 32.
Friday, April 2

Geometric series---a first look.

*
Monday, April 5 L'Hopital's Rule
Introducing Improper integrals
L'Hopital's Rule handout Sect. 9.2: 5, 7, 8, 10.
Wednesday, April 7 Improper integrals Section 10.1 L'Hopital's Rule exercises (handout)
Friday, April 9 Sequences of real numbers: definitions and convergence. Section 11.1 Sect. 10.1, part I: 1, 3, 4, 5, 7, 8, 12.
*
Monday, April 12

Sequences of real numbers---getting more precise.

Geometric series---ideas to consider and write about.

Sect. 10.1, part II: 9-17 (odds only) and 33, 35, 39, 45.
Sect. 11.1:
1-17 (odds only), 18.
Wednesday, April 14 Convergence and divergence of series Section 11.2 Sect. 11.1: 19-24, 27, 31, 33, 34, 50, 51, 52, 54.
Friday, April 16
Tests for convergence of series--pt 1
Section 11.3

Sect. 11.2:
4, 7, 8, 11, 12, 13, 17, 20, 23, 24.
(Hint: on the last two. Compute a few partial sums for the series. Find a pattern so you can get a limit.)

*
Monday, April 19 Tests for convergence of series---pt 2
Wednesday, April 21 Working with the convergence tests   Geometric series paper due.
Friday, April 23

Absolute vs. conditional convergence; Alternating series

Section 11.4 Testing for convergence---worksheet
*
Monday, April 26

## Test #2

Wednesday, April 28 Power Series Section 11.5
Friday, April 30 Power Series---a work day.   Sect. 11.4: 1, 3, 4, 6, 7, 9, 11, 14, 19, 20, 21, 23, 24, 25.
*
Monday, May 3 Finish power series
Taylor and Maclaurin Series
Section 11.6 Sect. 11.5: 4-7, 9, 10 , 11, 13, 23, 25, 26, 43, 47.
Wednesday, May 5
Taylor's theorem, revisited

Course evaluations
Section 11.7 Sect. 11.6: 1-4, 5,6,7,10, 11, 20, 35, 36, 37.
Friday, May 7 Recap/review of series   Sect. 11.7: 2-5, 7, 9, 12.