Matthew L. Wright
Visiting Assistant Professor, St. Olaf College

Calculus II

Math 126 ⋅ Spring 2017

Welcome to Calculus II! For course info and policies, please see the syllabus. For homework, log into WeBWork. For grades, log into Moodle.

Prof. Wright's office hours: Mon. 12:45–1:45, Wed. 9–10, Thurs. 10–11 & 1–2, Fri. 12:45–1:45, or by appointment in RMS 409

Supplemental Instruction (SI): Sun. 3:30–4:30, Tues. 7:30–8:30pm, Thurs. 8–9pm in RNS 204

Math help sessions: Sunday through Thursday, 7:30–9:00pm, in Tomson 184.

Jump to today
Monday
Feb. 6
Introduction
Derivative review
Do the following before next class:
  • Log in to WeBWork and complete the Syllabus Quiz by 8am Wednesday.
  • In the textbook, read from the beginning of Section 5.2 through Example 1 (page 374). Pay special attention to the paragraphs labeled Note 1 through Note 5.
  • Also read the subsection Properties of the Definite Integral on pages 379 and 380, paying special attention to Example 6. Come to class either understanding this example, or bring specific questions about this example.
  • Read Section 5.3, through Example 5. Pay special attention to both parts of the Fundamental Theorem of Calculus, but you may skim the proofs. Come to class with specific questions.
  • Begin Homework 1 (on WeBWork, due 8am Friday).
Wednesday
Feb. 8
Review: definite integrals and fundamental theorem of calculus
Do the following before next class:
  • Finish Homework 1 by 8am Friday.
  • Finish reading Section 5.3.
  • Read Section 5.4, up to Example 3. Pay special attention to Table 1. Also review page 401. Come to class with specific questions about anything you don't understand from this reading.
  • Begin Homework 2 (due 8am Monday).
Friday
Feb. 10
Review: indefinite integrals and fundamental theorem of calculus
Quiz today
on derivatives
Do the following before next class:
  • Finish Homework 2 by 8am Monday.
  • Read Section 5.5, through Example 3. Pay special attention to Examples 1 and 2. Come to class either understanding these examples, or bring specific questions about these examples.
  • Begin Homework 3 (due 8am Wednesday).
Monday
Feb. 13
Review: Substitution
Do the following before next class:
  • Finish Homework 3 by 8am Wednesday.
  • Read Section 6.1, through Example 3. Come to class understanding Examples 1 and 2, or bring specific questions about these examples.
  • Also read Section 6.5, through Example 1.
  • Begin Homework 4.
Wednesday
Feb. 15
Areas between curves
Average value
Do the following before next class:
  • Finish Homework 4 by 8am Friday.
  • Read pages 430 through 435 (Section 6.2). Pay special attention to Examples 1, 2, and 4. Come to class understanding these examples, or bring specific questions about these examples.
  • Begin Homework 5 (areas between curves).
Friday
Feb. 17
Volumes
Quiz today
on Chapter 5
Do the following before next class:
  • Finish Homework 5 by 8am Monday.
  • Read pages 441 through 444 (Section 6.3). Pay special attention to Examples 1 and 2. Come to class either understanding these examples, or bring specific questions about these examples.
  • Begin Homework 6 (average value and volumes).
Monday
Feb. 20
More Volumes
Do the following before next class:
Wednesday
Feb. 22
Review day
Finish Homework 7 and study for the exam.
Friday
Feb. 24
Exam 1
  • The exam will cover derivatives and integrals, from the material that we have studied so far in this course.
  • Calculators and computers will not be permitted, but the problems will be written so as to emphasize concepts and to avoid tedious arithmetic.
  • A practice exam is available here, with solutions here. (Please ignore problem 7, which requires integration by parts).
exam
No homework for next class. Have a good weekend!
Monday
Feb. 27
Integration by parts
Do the following before next class:
  • Read Section 7.1, Integration by Parts. Then begin Homework 8 (integration by parts).
  • Read Section 7.8, through Example 2. Then read page 523, starting at the Type 2: Discontinuous Integrands heading, through Example 5. Come to class knowing the two different types of improper integrals.
Wednesday
Mar. 1
Improper integrals
Do the following before next class:
  • Finish Homework 8 by 8am Friday.
  • Read the discussion about arc length, starting on page 538. Read through Example 1, which ends at the top of page 540. Take note of the Arc Length Formula and how it is used in Example 1.
  • Begin Homework 9 (improper integrals).
Friday
Mar. 3
Arc length
Quiz today
on integration by parts
Do the following before next class:
  • Finish Homework 9 by 8am Monday.
  • Read pages 554 (starting at the heading Moments and Centers of Mass) through page 558. Pay particular attention to Examples 3, 4, and 5. Bring specific questions about this reading to class on Monday.
  • Begin Homework 10 (arc length).
Monday
Mar. 6
Applications to physics
Do the following before next class:
  • Finish Homework 10 by 8am Wednesday.
  • Do problem #3 from the Centers of Mass handout from Monday; bring questions to class on Wednesday.
  • Read Section 8.4 (pages 563 to 566). Take note of how integrals are used to compute quantities in economics and biology.
  • Begin Homework 11 (centroids).
Wednesday
Mar. 8
Applications to economics and biology
Do the following before next class:
  • Finish Homework 11 by 8am Friday.
  • Read Section 9.1, pages 580 to 583. Take note of what is a differential equation and what it means for a function to be a solution of a differential equation. Bring questions about this reading to class on Friday.
  • Begin Homework 12 (applications to economics and biology).
Friday
Mar. 10
Direction fields and differential equations
Quiz today
on improper integrals and arc length
Do the following before next class:
  • Finish Homework 12 by 8am Monday.
  • Watch this 3-minute video: What are differential equations?
  • Read Section 9.2. Focus on how Euler's Method allows you to trace the solution to a differential equation through a direction field. Also read Section 9.3 through Example 2. Bring specific questions about this reading to class on Monday.
  • Begin Homework 13 (differential equations and direction fields).
Monday
Mar. 13
Separable differential equations
Do the following before next class:
  • Finish Homework 13 by 8am Wednesday.
  • Read Section 9.4, through Example 2. Also skim over the "Other Models of Population Growth" section on page 612.
  • Begin Homework 14 (separation of variables).
Wednesday
Mar. 15
Models for population growth
Do the following before next class:
  • Finish Homework 14 by 8am Friday.
  • Watch this 10-minute video: The Integrating Factor Method.
  • Read Section 9.5, through Example 2. Pay particular attention to how the integrating factor is computed.
  • Begin Homework 15 (models of population growth and linear differential equations; due Tuesday, March 28).
Friday
Mar. 17
Linear differential equations
Quiz today
on differential equations (sections 9.1–9.3)
Have a great spring break! No class March 20 – 24.
It is recommended that you spend some time over the break working on Homework 15 and studying for the exam.
Monday
Mar. 27
Review day
Homework 15 due 8am Tuesday. Study for the exam.
Wednesday
Mar. 29
Exam 2
  • The exam will cover the material that we have studied from Chapters 7, 8, and 9 in the Stewart textbook.
  • Calculators and computers will not be permitted, but the problems will be written so as to emphasize concepts and to avoid tedious arithmetic.
  • A set of review problems is available here, with solutions here.
exam
No homework for next class.
Friday
Mar. 31
Taylor series
Do the following before next class:
  • Read pages 426 to 439 from this text (Moodle login required). Take note of how Taylor polynomials approximate functions, and how the coefficients of the polynomials are found.
  • Watch these three videos about Taylor series: exponentials, Taylor polynomials, Taylor series.
  • Begin Homework 16 (Taylor series; due Wednesday, April 5).
Monday
Apr. 3
More Taylor series
Do the following before next class:.
  • Finish Homework 16 by 8am Wednesday.
  • Read pages 464 to 468 of this text (Moodle login required). Take note of the definition of a geometric series and the formulas for the sums of both finite and infinite geometric series.
Wednesday
Apr. 5
Convergence of Taylor series
  • Read pages 470 to 477 of this text (Moodle login required). Take note of the applications of geometric series to economics and science.
  • Begin Homework 17 (convergence intervals of Taylor series; due Monday, April 10).
  • Friday
    Apr. 7
    Geometric series and applications
    Quiz today on Taylor series
    Do the following before next class:.
    • Finish Homework 17 by 8am Monday.
    • Read Section 12.1; note the three-dimensional distance formula and the equation of a sphere. Then read from the beginning of Section 12.2 through Example 2; pay special attention to the definitions of vector addition and scalar multiplication.
    • Begin Homework 18 (geometric series, due Wednesday, April 12).
    Monday
    Apr. 10
    Three-dimensional coordinates and vectors
    Do the following before next class:.
    • Finish Homework 18 by 8am Wednesday.
    • Finish reading Section 12.2; pay special attention to the properties of vectors on page 795. Then read from the beginning of Section 12.3 through Example 4. Come to class knowing the definition of the dot product and how it relates to the angle between two vectors.
    • Begin Homework 19 (3-D coordinates and vectors, due Wednesday, April 19).
    Wednesday
    Apr. 12
    Dot products
    Easter break! No class April 14 or 17.
    Do the following before next class:
    • Finish Homework 19 by 8am Wednesday.
    • Read about projections of vectors on pages 804 and 805.
    • Read from the beginning of Section 12.5, through Example 2. Pay special attention to the 3 different forms of an equation of a line in space (formulas 1, 2 and 3). Also read the section on planes, from the bottom of page 819 through Example 4, and familiarize yourself with the different forms of an equation of a plane.
    • Begin Homework 20 (dot products, due Friday, April 21).
    Wednesday
    Apr. 19
    Lines and planes in space
    Do the following before next class:
    Friday
    Apr. 21
    Review day
    Do the following before next class:
    Monday
    Apr. 24
    Exam 3
    • The exam will cover the material that we have studied about Taylor and geometric series, as well as material from Chapter 12 in the Stewart textbook.
    • Calculators and computers will not be permitted, but the problems will be written so as to emphasize concepts and to avoid tedious arithmetic.
    • Practice problems: this file and this file contain lots of good problems about series; for practice with 3-D coordinates and vectors, work some problems from Sections 12.1, 12.2, 12.3, and 12.5 in the Stewart textbook.
    exam
    Do the following before next class:
    • Read Section 14.1, paying close attention to the examples. Then read Section 14.3 through Example 2, taking special note of the interpretation of partial derivatives.
    Wednesday
    Apr. 26
    Partial derivatives
    Do the following before next class:
    • Read Section 14.4, taking note of the equation of the tangent plane to a surface. In addition, carefully read Examples 2 and 3 for linear approximation. You may skip the subsection on differentials, but read the last section on functions of three or more variables.
    • Begin Homework 22 (partial derivatives, due Monday, May 1).
    Friday
    Apr. 28
    Tangent planes and linear approximations
    Do the following before next class:
    • Work on Homework 22 (partial derivatives, now due 8am Wednesday).
    • Begin Homework 23 (tangent planes and linear approximation, now due Friday, May 5).
    Monday
    May. 1
    No class — attend the events in Tomson Hall and elsewhere on campus.
    Do the following before next class:
    • Finish Homework 22 by 8am Wednesday.
    • Read from the beginning of Section 14.6 through Example 4. Take special note of Theorem 3 and Definition 8. Observe how the directional derivative is used in the examples. Then read the subsection Maximizing the Directional Derivative on pages 938 to 941.
    • Work on Homework 23 (tangent planes and linear approximation, due Friday, May 5).
    Wednesday
    May. 3
    Directional derivatives
    Do the following before next class:
    • Finish Homework 23 by 8am Friday.
    • Read Section 14.7, through Example 7. Pay close attention to Theorems 1 and 2, and Examples 1, 2 and 3.
    • Begin Homework 24 (directional derivatives, due Wednesday, May 10).
    Friday
    May. 5
    Gradient
    Intro to maximum and minimum values
    Quiz today on partial derivatives and tangent planes.
    Do the following before next class:
    • Work on Homework 24 (due Wednesday, May 10).
    • Re-read Section 14.7, through Example 7.
    Monday
    May. 8
    Maximum and minimum values
    Do the following before next class:
    • Finish Homework 24 by 8am Wednesday.
    • Read Section 15.1, and observe how the volume under a surface can be represented by a double integral and approximated by a sum of volumes of boxes. Then read Section 15.2 through Example 3, and take note of how double integrals are evaluated in the examples.
    • Begin Homework 25 (max/min values, due Friday, May 12).
    Wednesday
    May. 10
    Double integrals
    Iterated integrals
    Do the following before next class:
    • Finish Homework 25 by 8am Friday.
    • Read Section 15.3. Pay special attention to how the bounds of integration are determined in the examples.
    • Begin Homework 26 (double integrals, due Tuesday, May 15).
    Friday
    May. 12
    Double integrals over general regions
    Quiz today on directional derivatives, gradients, and max/min values
    Do the following before next class:
    • Work on Homework 26 (double integrals, due Tuesday, May 15).
    • From Section 15.5, read the subsections Density and Mass and Moments and Centers of Mass. Pay close attention to Examples 1 and 2, and to the formulas given in box 5 on page 1005.
    Monday
    May. 15
    Applications of double integrals
    Finish Homework 26 and study for the final exam!
    Prof. Pell's Q/A Session: Wednesday, May 17, 1–2pm in RNS 310
    Prof. Wright's Q/A Session: Thursday, May 18, 12:30–1:30pm in RNS 208
    Tuesday
    May. 23
    Final Exam, 2–4pm
    • The final exam will be cumulative, but will emphasize topics in Chapters 14 and 15.
    • Calculators and computers will not be permitted, but the problems will be written so as to emphasize concepts and to avoid tedious arithmetic.
    • Click here for more detailed information and practice problems. After working the problems, click here for solutions.
    • Information about review sessions will also be posted here soon.
    • Lastly, make sure you are familiar with the St. Olaf final exam policies.
    exam