Math 1120-101 (Spring 2023) Homepage

AsULearn [eText access] Syllabus Schedule

Suggested Homework Old Exams

News & Announcements

5/05

Final grades have been posted. I sent a final email grade report.

I will keep final exams around for a while (usually a couple of years). If you want to look over your exam or have any questions about your grades, please stop by my office or email me.

Also, just because this class is over, don't feel like you can no longer ask me questions. If you ever have a question mathematical or otherwise, please stop by my office or send me an email. I'm happy to help if I can! And finally, I hope you all have a fantastic summer break!

5/02

I will hold a review session on Thursday (reading day = 5/4) at 2pm. I reserved our regular classroom (Walker 105). As requested, I will try to record the session as well.

I don't plan on doing anything structured. Mostly I just plan to go over questions and do some extra examples.

4/27

Our last quiz is Tuesday (covering 8.9). Once that is graded, I will send out a grade report that includes your overall quiz & homework average. This average will reflect a dropped quiz and curved homework grades.

Also, I will replace your lowest test score with your final exam score (if it helps).

I plan to hold a review session on reading day, Thursday, May 4^th (time TBD). Feel free to come and ask final questions...if you'd like.

You may bring one page of notes [one side of one standard size sheet of paper] to the final exam. This can be printed or handwritten. It can contain whatever you want (formulas, examples, etc.).

Studying: Please look over old quizzes, suggested homework (including chapter review problems), old tests, handouts and notes. The following sections/topics are relevant:

• 5.5 (substitution)
• 5.6 (separable DEs - not the word problems)
• 6.1 area between graphs
• 6.2 volumes of revolution: disks and washers
• 6.3 [skip]
• 6.4 volumes via slicing
• 6.5 [skip]
• 6.6 work
• 6.7 [skip]
• 6.8 [skip]
• 7.1 integration by parts
• 7.2 integrals with trig functions
• 7.3 inverse trig subs
• 7.4 [skip]
• 7.5 partial fractions
• 7.6 [skip]
• 7.7 improper integrals
• 7.8 [skip]
• 7.9 mixed practice
• 8.1-8.7 (as needed)
  • You should know how to recognize and sum geometric series.
  • You should know what absolute and conditional convergence are.
  • You may need to apply some of the convergence tests when working a power series problem - but I don't plan on asking about convergence for general series.
• 8.8 power series
• 8.9 Taylor series - skip binomial series
• 8.10 Taylor polynomials - skip error/estimation problems

You can find old tests here. The following problems are relevant:

• Fall 2021: Final Exam - all of it ← Our final should be a lot like this one.
  Test #1: 2-6, 8
  Test #2: 1-2, 4-5
  Test #3: 1, 3b, 4[as needed]
• Spring 2014: Test #1: 1-3, 4b, 5
  Test #2: 2-4, 7
  Test #3: 1[as needed], 2-3, 4ac, 5
  Final Exam: 2b, 3-9
• Fall 2010: Test #1: 4, 6
  Test #2: 1-2, 3b, 4-6
  Test #3: 1ac, 3b, 4
• Spring 2009: Test #1: 5, 7
  Test #2: 1-3, 4b, 5-6
  Test #3: 1ac, 3b, 4
  Final Exam: 2b, 3-7, 8[as needed], 9, 10

4/25

Handout from yesterday: Taylor Polynomials [Source: (.tex)] and accompanying Taylor Polynomials Sage demo.

4/14

Supplemental series convergence problems Answer Key [Source: (.tex)]

4/11

Test #3 is Tuesday, April 18^th. It will cover improper integrals, sequences, series, and series convergence tests. This amounts to sections 7.7 & 8.1-8.7 in our text. You may find the handout and examples from 4/10 and 3/29 (posted below) helpful. In addition, to notes, suggested homework, quizzes, and handouts, old tests are a good resource for studying.

Relevant problems on old exams:

• Fall 2021: Test #3 (both forms) all of it ← Our test should be a lot like this one.
  Final Exam problems 6ad
• Spring 2014: Test #2 (both forms) problem 2
  Test #3 (Sec. 101) probs. 1 and 3b & (Sec. 108) probs. 1 and 3ab
  Final Exam (both forms) problem 7
• Fall 2010: Test #3 (both forms) problems 3,4,6
• Spring 2009: Test #3 problems 3b,4,6
  Final Exam (both forms) problems 6,7ab,8

4/10

A handout summarizing series convergence tests:
Series Tests Summary [Source: (.tex)] and Stewart's Test Flowchart and Supplement Problems

3/29

Computing Series Sums in Maple:
Integral Convergence Test (.mw) [Print to pdf: (.pdf)]

3/20

After finishing up improper integrals (Section 7.7), we will discuss some software. In particular, we will use the Computer Algebra System (CAS) called Maple.

My Maple Tips & Tricks [Source: (.tex)] handout.
A companion Introduction to Maple worksheet (.mw) [Print to pdf: (.pdf)]

Maple Examples (.mw) [PDF Print: (.pdf)] from Fall 2021.

Homework #2 (.mw) [PDF Print: (.pdf)] is due Tuesday, March 28^th.

Note: With the probability examples and homework problem is there an annoying "discretization" issue that I'm glossing over. For example, if someone says they are 5 feet 10 inches tall (= 70 inches), they probably mean that their height is between about 69.5 and 70.5 inches. We will ignore this issue.

3/03

Since I didn't quite finish this derivation today...
Solving the Logistic Equation [Source: (.tex)]

2/28

Test #2 is Tuesday (March 7^th). It covers Sections 7.1-7.5 in our text.
[Checking out suggested homework from 7.9 and the chapter 7 review is a good idea too.]

The quiz this Wednesday (March 1^st) will cover 7.3 & 7.4. The remaining class time this week will be devoted to discussing 7.5 (partial fraction decompositions). I plan to review for the test on Monday.

Test topics include:

• 7.1 = integration by parts
• 7.2 = integrating trig functions: powers of sine/cosine, powers of secant/tangent, and integrating stuff like sin(2x)cos(5x).
• 7.3 = inverse trig substitutions: integrals involving $a^2-x^2$, $x^2-a^2$, and $x^2+a^2$ [use a sub like $x=a \cdot \sin(\theta)$ etc., convert to a 7.2 problem, convert back using a triangle.]
• 7.4 = completing the square: integrals with a quadratic or square root of a quadratic denominator. [split into a u-sub piece and complete the square piece, do the u-sub piece, do the complete the square piece by completing the square, factoring out a number to get a "1", make a u-sub, integrate, sub back in.]
• 7.5 = partial fraction decompositions: polynomial division to make fractions proper, write down our "forms", be able to compute partial fraction decompositions and then integrate.

I will provide a bunch of trig formulas on the test. In particular, see:
A Note about Test #2 Formulas [Source: (.tex)]

Like last time, the best approximation of our upcoming test is the corresponding test from Fall 2021. Looking at other old exams is a great idea, but our current text includes some kinds of problems that did't show up in my old tests.

I highly recommend looking at notes, quizzes, examples worked out in the text, as well as suggested homework from 7.1-7.5. You might want to check out suggested homework from 7.9 ("mixed practice") and the Chapter 7 review (skip 39,41,43,45 in the review - these use stuff we haven't covered yet).

Review questions:

• CALCULUS 1 EXAMS: (some basic integral stuff)
  • Summer 2022: Final Exam problem 10
  • Summer 2017: Final Exam problems 9,10
  • Summer 2012: Final Exam problems 9,10
• CALCULUS 2 EXAMS:
  • Fall 2021: Test #2 (both forms) all of it ← Our test should be a lot like this one.
    Final Exam problems 3,5
  • Spring 2014: Test #1 (both forms) all of it
    Final Exam (both forms) problems 4-6
  • Fall 2010: Test #1 (both forms) problem 6
    Test #2 (both forms) problems 4-6
  • Spring 2009: Test #1 (both forms) problem 7
    Test #2 problems 2,5,6
    Final Exam (both forms) problems 4,5

2/20

A possibly helpful summary of Some Trig Formulas [Source: (.tex)]

2/15

A handout for tomorrow: Three ways to integrate [Source: (.tex)]

2/08

Don't forget that (Achieve) Homework #1 is due Sunday (2/12) evening. All but the last question on hydrostatic pressure are based on examples we've already covered. We'll cover hydrostatic pressure examples on Friday.

Test #1 is Tuesday, February 14^th. You are responsible for the material we covered in Section 4.8, Chapter 5, Chapter 6, and Section 7.6. Topics: Approximations (left, right, midpoint, trapezoid, Simpson's rule), the Fundamental Theorem of Calculus (both parts), Integration via substitution, Separation of variables DEs, Area between curves, Volumes via disks/washers/slices, Arc length, Work, and Hydrostatic force.

You can skip: Error estimates for approximations, volumes via shells, surface area of revolutions, work problems involving springs, and center of mass stuff (section 6.8).

To review for the test I recommend looking over Homework (suggested and assigned), Examples from class, Quizzes, and problems from Old Tests (more details below).

I plan to cover hydrostatic pressure on Friday and then use remaining time plus class on Monday to review for the test.

Old MAT 1110 (Calculus 1) exams can be found here and
Old MAT 1120 (Calculus 2) exams can be found here.

Relevant review questions:

• From CALCULUS 1 EXAMS:
  • Summer 2022: Final Exam problems 3d,8,9,10,11
  • Summer 2017: Final Exam problems 6,7,8f,9,10
  • Summer 2012: Final Exam problems 6,7,8f,9,10
• From CALCULUS 2 EXAMS:
  • Fall 2021: Test #1 (both forms) all of it ← Our test should be a lot like this one.
    Final Exam problems 1,2,4
  • Spring 2014: Test #1 (both forms) problems 1b,4a
    Test #2 (both forms) problems 1,3,4,5,7
    Final Exam (both forms) problems 2,3,4a
    
  • Fall 2010: Test #1 (both forms) problems 2-6
    Test #2 (both forms) problems 1-3
  • Spring 2009: Test #1 (both forms) problems 2-7
    Test #2 problems 1,3,4
    Final Exam (both forms) problems 1-3

1/30

Separation of Variables Examples [Source: (.tex)]

1/17

Review:
Derivatives Practice (.pdf) [Source: (.tex)] and the Sage version.

Repurposed (& somewhat revised) from the now defunct Math 1030 (Business Calculus):
Some Derivative Practice [Source: (.tex)]
Some Integral Practice [Source: (.tex)]


A few SAGE demos:
Area Approximation (simple interface).
Area Approximation++ (allows general partitions & table input).

1/16

If you are interested, there is free tutoring available. Genie Griffen (griffine@appstate.edu) is our MathSci faculty contact.

From Genie:

Hi All,
Tutoring will begin on Sunday, Jan. 22.

As of right now the drop in tutoring schedule is as follows:

Drop in tutoring for General Math/Stats:

• In person: Sunday-Thursday from 5-8 pm, D.D. Dougherty Room 208
• In Zoom: Sunday-Thursday from 8-10 pm, Zoom link: https://appstate.zoom.us/my/matstt

Tutoring by Appointment: Some courses have tutors available for individual appointments, please direct your students to the UTS website: https://studentlearningcenter.appstate.edu/students/tutoring if they are interested!

Let me know if you have any questions,
Genie

1/03

Syllabus, schedule, suggested homework, & AsULearn have been updated.