Joanna Bieri

Applied Math Professor

Department of Economics

University of Redlands

Calculus II

BOOK: Active Calculus (Free Online) We will start in chapter 5.
You can also use the Hughes-Hallett book from Calculus I - it is a great additional reference!

• Important Course Documents and Information
  
  Course Syllabus
  
  Most of our DAILY HOMEWORK will be done through: WeBWork
  NOTE: Your username is First_Last (notice the capital letters!) and your password is your student ID number. (If you have more than one last name then your username is First_Last-Last.)
  
  You can check your GRADES and hand in WRITEN WORK on Moodle
  
  
  Virtual class meetings, office hours, announcements, and recordings of from our in person classes will be on Teams
  
  
  Here is the Schedule of Topics - Updated 3/9
  NOTE: as the semester progresses we may change up the schedule a bit to suit our class pace and interests.
  
  
  
• Daily Assignments - Class Prep Videos - Reading - Handouts
  
  You will see a link for each day of class that contains four sections:
  1. Pre Class - these are the videos and assignments that you should complete before class starts.
  2. Class Time - information, handouts, and worksheets that we will do together in class.
  3. After Class - assignments that you should complete after class.
  4. Extras - anything extra that might help your learning but is completely optional.
  
  
  • DAY 1 - Click Here
    
    Monday January 10th
    To be successful in higher level math you need to keep practicing and often relearning the basics.
    Really try to work this semester to become the boss of basic algebra, trigonometric functions, derivatives, and graphing/answer checking!
    
    PRE CLASS:

    Take the Pre-Class Survey

    CLASS TIME:

    Welcome to Calculus!
    Course Syllabus

    AFTER CLASS:

    Homework Day 1

    EXTRAS:

    Set yourself up for success. Schedule times where you promise yourself you will study calculus.
    

    
    
  • DAY 2 - Click Here
    
    Wednesday January 12th
    
    PRE CLASS:

    Video: Review of Calculus I - General
    Video: Review of Calculus I - Important Integration Topics
    Extra Review as Needed:
    *** Joanna's Calculus I Website
    *** Book Chapters 1-5.2
    
    WeBWorK: Review of Calculus I
    Make a list of questions for class.
    Take the daily survey.
    

    CLASS TIME:

    Review of Calculus I

    AFTER CLASS:

    Homework Day 2

    EXTRAS:

    
    

    
    
  • DAY 3 - Click Here
    
    Friday January 14th
    
    PRE CLASS:

    Video: Integration by Substitution - Intro
    Video: Integration by Substitution - Examples
    Read: Book Chapter 5.3 - Intro - Activity 5.3.3
    
    Try examples: Activity 5.3.2
    Make a list of questions for class.
    Take the daily survey.
    

    CLASS TIME:

    Examples 5.3.3
    Start on Homework Problems

    AFTER CLASS:

    Homework Day 3

    EXTRAS:

    Derivatives Shortcut Rules
    Video: Explaining Homework Problems
    

    
    
  • DAY 4 - Click Here
    
    Wednesday January 19th
    
    PRE CLASS:

    Video: Integration by Substitution - Definite Integrals
    Video: Integration by Substitution - Harder Examples
    Read: Book Chapter 5.3 - Evaluating Definite Integrals - Activity 5.3.4 + Summary
    
    Try examples: Activity 5.3.4
    Make a list of questions for class.
    Take the daily survey.
    

    CLASS TIME:

    More examples of substitution
    Start on Homework Problems

    AFTER CLASS:

    Homework Day 4

    EXTRAS:

    Video: Explaining Day 2 WeBWorK Problems
    
    

    
    
  • DAY 5 - Click Here
    
    Friday January 21st
    
    PRE CLASS:

    Video: Integration by Parts - Intro
    Video: Integration by Parts - Examples
    Read: Book Chapter 5.4 - Intro - Activity 5.4.2
    
    Try examples: Preview Activity 5.4.1
    Activity 5.4.2
    Make a list of questions for class.
    Take the daily survey.
    

    CLASS TIME:

    Activity 5.4.2 and Activity 5.4.3
    Start on Homework Problems

    AFTER CLASS:

    Homework Day 5

    EXTRAS:

    
    

    
    
  • DAY 6
    
    Monday January 24th
    
    PRE CLASS:

    Video: Integration by Parts - Definite and Tricks - Updated correct Table Method
    Video: Integration by Parts - Harder Examples
    Video: Integration - Powers of Sine and Cosine
    Read: Book Chapter 5.4 - Evaluating Definite Integrals Using Integration by Parts - Summary
    
    Exercises 5 and 6 at end of chapter
    Make a list of questions for class.
    Take the daily survey.
    

    CLASS TIME:

    More examples of Integration by Parts and Powers of Sine and Cosine, Activity 5.4.4
    Start on Homework Problems

    AFTER CLASS:

    Homework Day 6

    EXTRAS:

    
    

    
    
  • DAY 7
    
    Wednesday January 26th
    
    PRE CLASS:

    Video: Integration using Algebra - Intro
    Video: Integration using Algebra - Examples
    Read: Book Chapter 5.5
    
    Try the examples from the worksheet - click here
    Make a list of questions for class.
    Take the daily survey.
    

    CLASS TIME:

    More examples of using Algebra to rewrite the integrand, computer algebra systems, and table integrals.
    Start on Homework Problems

    AFTER CLASS:

    Homework Day 7

    EXTRAS:

    
    

    
    
  • DAY 8
    
    Friday January 28th
    
    PRE CLASS:

    Video: Integration with Trig Substitution - Intro
    Extra Book Read: Trigonometric Substitution - not our book!
    NOTE: Trigonometric substitutions are not covered in our book so the link above is to a different free Calculus book.
    
    Try the examples, 5.65, 5.66, and 5.67 from the extra book - click here
    Make a list of questions for class.
    Take the daily survey.
    

    CLASS TIME:

    More examples of trigonometric subs.
    Start on Homework Problems

    AFTER CLASS:

    Homework Day 8

    EXTRAS:

    List of Trigonometric Identities
    List of Rules for Natural Log and Exponential Functions
    

    
    
  • DAY 9
    
    Monday January 31st
    
    PRE CLASS:

    Video: Improper Integrals - Intro
    Keep practicing your integration techniques! The first exam is in one week. Here are a bunch of practice integrals!
    Read: Book Chapter 6.5 - I know we are skipping around a bit!
    
    Try the activity 6.5.2 and 6.5.3
    Make a list of questions for class.
    Take the daily survey.
    

    CLASS TIME:

    Activity 6.5.4 or other examples
    Start on Homework Problems

    AFTER CLASS:

    Homework Day 9

    EXTRAS:

    
    

    
    
  • DAY 10
    
    Wednesday February 2nd
    We are starting our review for the first exam.
    PRE CLASS:

    Video: Improper Integrals - More Examples
    Video: General Integrals - More Examples
    
    Read: Go back and review chapters that you had trouble with!
    
    Try to do all the examples from the lecture videos. Pause the video and do the problems before you see my solution. Remember that there is often more than one way to do an integral.
    Make a list of questions for class.
    Take the daily survey.
    

    CLASS TIME:

    In class worksheet
    Worksheet solutions
    Start on Homework Problems

    AFTER CLASS:

    Homework Day 10

    EXTRAS:

    
    

    
    
  • DAY 11 - Exam Review
    
    Friday February 4th
    
    PRE CLASS:

    Read: Go back and review chapters that you had trouble with!
    Practice Exam 1a
    Practice Exam 1b
    Practice Exam Solutions - don't look at these until you finish the practice exams. Solutions for both exams can be found here.
    
    
    Work on the practice exam
    Make a list of questions for class.
    Take the daily survey.
    

    CLASS TIME:

    Exam Review
    

    AFTER CLASS:

    Homework Day 11 - No new homework. Nothing to hand in. Study for the exam.

    EXTRAS:

    
    

    
    
  • DAY 12 - Exam 1 in Class
    
    Monday February 7th
    
    PRE CLASS:

    Study for the exam. Practice a little bit every day. Get a good night sleep!

    CLASS TIME:

    Exam 1 - no calculators, no books/notes, no sharing brains.
    

    AFTER CLASS:

    Homework Day 12 - No new problems to hand in, but you need to prep for Wednesday's class.

    EXTRAS:

    
    

    
    
  • DAY 13
    
    Wednesday February 9th
    
    PRE CLASS:

    Video: Approximate Integration - Intro
    Video: Approximate Integration - Error
    
    Read: Book Chapter 5.6 - We are going back to chapter 5.
    
    Try the preview activity 5.6.1
    Make a list of questions for class.
    Take the daily survey.
    

    CLASS TIME:

    Numerical Integration Worksheet
    

    AFTER CLASS:

    Homework Day 13

    EXTRAS:

    
    

    
    
  • DAY 14
    
    Friday February 11th
    
    PRE CLASS:

    Video: Approximate Integration - More examples - Error
    
    Read: Book Chapter 5.6 (review this content if needed)
    
    
    Make a list of questions for class.
    Take the daily survey.
    

    CLASS TIME:

    Numerical Integration Worksheet - Error
    Numerical Integration Spreadsheet - Excel
    Numerical Integration Code - Python
    

    AFTER CLASS:

    Homework Day 14

    EXTRAS:

    
    

    
    
  • DAY 15 - UPDATED
    
    Monday February 14th
    
    ** I decided to spend one more day on numerical integration.
    PRE CLASS:

    Review the Numerical Integration Videos from Day 14 and Day 15.
    Bring your Laptop to class with Numerical Integration Code - Full Example - Python open. You should run the cells in the notebook and see if you can figure out what is going on. No pressure! Just Explore!
    
    Read: Book Chapter 5.6 (review this content if needed)
    
    Make a list of questions for class.
    Take the daily survey.
    

    CLASS TIME:

    Numerical Integration Worksheet - Full Example
    Numerical Integration Code - Full Example - Python
    

    AFTER CLASS:

    Homework Day 15

    EXTRAS:

    Python - Help with Derivatives!
    

    
    
  • DAY 16
    
    Wednesday February 16th
    
    PRE CLASS:

    Video: Applied Integration - Area
    Video: Applied Integration - Length
    
    Read: Book Chapter 6.1
    
    
    Make a list of questions for class.
    Take the daily survey.
    Make sure to do the You Try problems from the lecture videos.

    CLASS TIME:

    Example Problems - Activity 6.1.3 and 6.1.4
    Work on homework
    

    AFTER CLASS:

    Homework Day 16

    EXTRAS:

    
    

    
    
  • DAY 17
    
    Friday February 18th
    
    PRE CLASS:

    Video: Applied Integration - Volume of Revolution
    Video: Applied Integration - Volume of Revolution - Harder Examples
    
    Read: Book Chapter 6.2
    
    
    Make a list of questions for class.
    Take the daily survey.
    Make sure to do the You Try problems from the lecture videos.

    CLASS TIME:

    Example Problems
    Work on homework
    

    AFTER CLASS:

    Homework Day 17

    EXTRAS:

    
    

    
    
  • DAY 18
    
    Monday February 21st
    
    PRE CLASS:

    Video: Applied Integration - Example + Mass
    
    Read: Book Chapter 6.2 (review if needed) and Chapter 6.3 (extra)
    
    
    Make a list of questions for class.
    Take the daily survey.
    Make sure to do the You Try problems from the lecture videos.

    CLASS TIME:

    Lot's more examples!!! It really does help to practice. Make sure to learn the process.
    Work on homework
    

    AFTER CLASS:

    Homework Day 18

    EXTRAS:

    
    

    
    
  • DAY 19 - UPDATED
    
    Wednesday February 23rd
    
    PRE CLASS:

    Review - keep working on Volume of Revoliution Problems.
    Make a list of questions for class.
    Take the daily survey.
    Make sure to do the You Try problems from the lecture videos.

    CLASS TIME:

    Lot's more examples!!! It really does help to practice. Make sure to learn the process.
    Work on homework
    
    

    AFTER CLASS:

    Homework Day 19 - UPDATED

    EXTRAS:

    
    
  • DAY 20
    
    Friday February 25th
    
    PRE CLASS:

    Video: Applied Integration - Work
    Video: Applied Integration - Fluid (Hydrostatic) Pressure and Force
    
    Read: Book Chapter 6.4 - Work and Hydrostatic Pressure
    
    
    Make a list of questions for class.
    Take the daily survey.
    Make sure to do the You Try problems from the lecture videos.

    CLASS TIME:

    Dam Example - Hydrostatic Pressure
    Pyramid Example - Work
    Lot's more examples!!! It really does help to practice. Make sure to learn the process.
    Work on homework
    
    

    AFTER CLASS:

    Homework Day 20

    EXTRAS:

    More problems to try - from Pauls Oneline Notes
    

    
    
  • Spring Break Feb 28 - Mar 4
    
    Spring Break Week - Extra Credit Problems
    
    

    Spring Break Worksheet
    
    Each weekday during Spring Break you have a chance earn 2 points extra credit counted toward your Exam grade. The submissions are due by 11:59pm each day.
    
    Monday 2/28 - Hand in problems 1-3 on Moodle
    Tuesday 3/1 - Hand in problems 4 and 5 on Moodle
    Wednesday 3/2 - Hand in problems 6 and 7 on Moodle
    Thursday 3/3 - Hand in problems 8 and 9 on Moodle
    Friday 3/4 - Hand in problems 10 and 11 on Moodle
    
    

  • DAY 21
    
    Monday March 7th
    
    PRE CLASS:

    Spring Break Worksheet - Solutions
    
    Video: Review - Finding Area
    Video: Review - Work on a Rope/Chain
    Video: Review - Volume of Revolution
    Video: Review - Numerical Integration
    Video: Review - Work Pumping Water from Tank
    Video: Review - Fluid Force on a Plate
    
    
    Review!
    
    
    Make a list of questions for class.
    Take the daily survey.
    Make sure to do the You Try problems from the lecture videos.

    CLASS TIME:

    More Examples.
    

    AFTER CLASS:

    Homework Day 21

    EXTRAS:

    
    
  • DAY 22 - Exam Review
    
    Wednesday March 9th
    
    PRE CLASS:

    Read: Go back and review chapters that you had trouble with!
    Practice Exam 2a
    Practice Exam 2b
    Practice Exam 2a Solutions
    Practice Exam 2b Solutions
    
    
    Work on the practice exam
    Make a list of questions for class.
    Take the daily survey.
    

    CLASS TIME:

    Exam Review
    

    AFTER CLASS:

    Homework Day 22 - No new homework. Nothing to hand in. Study for the exam.

    EXTRAS:

    
    

    
    
  • DAY 23 - Exam 2 in Class
    
    Friday March 11th
    
    PRE CLASS:

    Study for the exam. Practice a little bit every day. Get a good night sleep!

    CLASS TIME:

    Exam 2 - no calculators, no books/notes, no sharing brains.
    YOU MAY HAVE A SHEET OF PAPER with notes, hints, and formulas on it.
    

    AFTER CLASS:

    Homework Day 23 - No new problems to hand in, but you need to prep for Monday's class.

    EXTRAS:

    
    

    
    
  *** Sunday March 13th - Daylight Savings - set your clocks forward one hour!
  *** Monday March 14th (Pi Day) - no calculus class. This will give you one extra day to get over daylight savings :)
  
  • DAY 24 - Wednesday March 16th
    
    Wednesday March 16th
    
    PRE CLASS:

    Introduction to Sequences and Convergence
    Introduction to Sequences - Bounded and Monotonic
    
    
    Read: Book Chapter 8.1 Sequences
    
    
    Make a list of questions for class.
    Take the daily survey.
    Make sure to do the You Try problems from the lecture videos.

    CLASS TIME:

    Sequences Worksheet
    
    

    AFTER CLASS:

    Homework Day 24

    EXTRAS:

    
    
  • DAY 25
    
    Friday March 18th
    
    PRE CLASS:

    Introduction to Geometric Series
    
    Read: Book Chapter 8.2 Geometric Series
    
    Make a list of questions for class.
    Take the daily survey.
    Make sure to do the You Try problems from the lecture videos.

    CLASS TIME:

    Examples of Geometric Series
    Start the homework
    

    AFTER CLASS:

    Homework Day 25

    EXTRAS:

    
    
  • Exam 2 Corrections - Due in class Friday April 1st
    
    Here is what you need to complete the corrections for Exam 2:

    Exam 2 Corrections - Info
    Exam 2 Corection Extra Problems + Self Reflection

    
    
  • DAY 26
    
    Monday March 21st
    
    PRE CLASS:

    Introduction to General Series and Convergence
    Series - The Integral Test
    Sequences - The Squeeze Theorem
    
    Read: Book Chapter 8.3 Series of Real Numbers
    
    Make a list of questions for class.
    Take the daily survey.
    Make sure to do the You Try problems from the lecture videos.

    CLASS TIME:

    You try problems
    Work on homework

    AFTER CLASS:

    Homework Day 26

    EXTRAS:

    
    
  • DAY 27
    
    Wednesday March 23rd
    
    PRE CLASS:

    Series - Comparison Tests
    Series - The Ratio Test
    
    Read: Book Chapter 8.3 Series of Real Numbers (continued)
    
    Make a list of questions for class.
    Take the daily survey.
    Make sure to do the You Try problems from the lecture videos.

    CLASS TIME:

    You try problems (there are four of them!)
    Work on homework

    AFTER CLASS:

    Homework Day 27

    EXTRAS:

    
    
  Class Canceled - no new work - Friday 3/25 and Monday 3/28
  
  • DAY 28 - Wednesday 3/30
    
    Wednesday March 30th
    
    PRE CLASS:

    Review of Convergence Tests
    Alternating Series
    
    Read: Book Chapter 8.3 Series of Real Numbers (continued)
    
    Make a list of questions for class.
    Take the daily survey.
    

    CLASS TIME:

    More Examples
    Work on homework

    AFTER CLASS:

    Homework Day 28

    EXTRAS:

    
    
  • DAY 29
    
    Friday April 1st
    
    PRE CLASS:

    Overview - Convergence of Series
    Example 1
    Example 2
    Example 3
    Example 4
    You Try
    
    Read: Review Chapters about Sequences and Series.
    Flow Chart for Series Convergence Tests
    
    Make a list of questions for class.
    Take the daily survey.
    

    CLASS TIME:

    More Examples of the Different Convergence Tests

    AFTER CLASS:

    Homework Day 29

    EXTRAS:

    
    
  • DAY 30
    
    Monday April 4th
    
    PRE CLASS:

    Introduction - Power Series
    Power Series - Examples
    
    Read: Chapter 8.6 Power Series.
    Make a list of questions for class.
    Take the daily survey.
    

    CLASS TIME:

    You Try Problems
    Worksheet - Power Series
    More Examples.

    AFTER CLASS:

    Homework Day 30

    EXTRAS:

    
    
  • DAY 31
    
    Wednesday April 6th
    
    PRE CLASS:

    Power Series - Functions
    Power Series - Derivatives and Integrals
    
    Read: Chapter 8.6 Power Series.
    Make a list of questions for class.
    Take the daily survey.
    

    CLASS TIME:

    You Try Problems
    More Examples.

    AFTER CLASS:

    Homework Day 31

    EXTRAS:

    
    
  • DAY 32
    
    Friday April 8th
    
    PRE CLASS:

    Taylor Series - Introduction
    Taylor Series - Examples
    
    Read: Chapter 8.6 Power Series.
    Make a list of questions for class.
    Take the daily survey.
    

    CLASS TIME:

    You Try Problems
    More Examples.

    AFTER CLASS:

    Homework Day 32

    EXTRAS:

    
    
  • DAY 33
    
    Monday April 11th
    
    PRE CLASS:

    Taylor Series - More Complicated Functions
    Taylor Series - Applications and Error
    
    Read: Chapter 8.6 Power Series.
    Make a list of questions for class.
    Take the daily survey.
    

    CLASS TIME:

    You Try Problems
    More Examples.

    AFTER CLASS:

    Homework Day 33

    EXTRAS:

    
    
  • DAY 34
    
    Wednesday April 13th
    
    PRE CLASS:

    No New Lecture Videos -- Please do the worksheet, so we have lots of examples to talk about in class.
    Pre Class Worksheet
    
    Read: Chapter 8.6 Power Series.
    Make a list of questions for class.
    Take the daily survey.
    

    CLASS TIME:

    Lots of Examples of Taylor Series, Power Series, Sequences, and Series.

    AFTER CLASS:

    Homework Day 34 - No new homework. Nothing to hand in. Study for the exam.

    EXTRAS:

    
    
  • DAY 35 - Exam Review
    
    Friday April 15th
    
    PRE CLASS:

    Read: Go back and review chapters that you had trouble with!
    Practice Exam 3
    Practice Exam 3 - Solutions
    
    
    Work on the practice exam
    Make a list of questions for class.
    Take the daily survey.
    

    CLASS TIME:

    Exam Review
    

    AFTER CLASS:

    Homework Day 35 - No new homework. Nothing to hand in. Study for the exam.

    EXTRAS:

    Flow Chart for Series Convergence Tests
    More Practice Problems with Solutions
    

    
    
• Practice Exams and Solutions
  • Homework Solutions
    WebWork answers and solutions are available after they are handed in.
    Solutions to handwriten homework will be posted here:
    
    
    
  • Practice Exams
    
    
    
    
    
• Lecture Notes
  USE AT YOUR OWN RISK - There could be typos that are corrected in class, so please use common sense and your own notes to compare to what you see here:
  Review of Calculus I
  Integration by Substitution
  Integration by Parts
  More Integration by Parts and Tricks for Integration
  Algebraic Simplification
  Trigonometric Substitution - Plus Extra Examples and Integration Hints at the end of the notes.
  Improper Integrals.
  More Improper Integrals and Integration Review.
  Numerical Integration - Approximations
  Error in Numerical Integration
  Area and Volume by Integration.
  Volumes of Revolution.
  Integration in Polar Coordinates.
  More Examples (Complicated Regions) - Mass by Integration.
  Applications of Integration to Physics - Work.
  Applications of Integration to Physics - Pressure.
  Introduction to Sequences and Review of Limits.
  Geometric Series.
  General Series.
  Comparison and Limit Comparison Tests.
  Alternating Series and Ratio Test.
  In-Class Practice with Convergence of Series.
  Power Series and Interval of Convergence
  Functions and Power Series
  Taylor Polynomials
  Taylor Series
  Finding and Using Taylor Series
  Applications of Taylor Series
  Review - Integration Techniques and Applications
  Review - Sequences and Series
The math kitties are forming a study group but Muffin forgot about social distancing!

Photo thanks to cuteoverload.com