# MATH-1700-ES31

Welcome to the permanent home page for Section ES31 of MATH-1700 (Calculus 2) at Southeast Community College in the Spring term of 2020. I am Toby Bartels, the instructor.

• Canvas page (where you must log in for full access, available while the course is in session).
• Help with DjVu (if you have trouble reading the files below).
• Course policies (DjVu).
• Class hours: Mondays through Fridays from 11:00 to 11:50 in ESQ 100D.
Information to contact me:
• Name: Toby Bartels, PhD;
• Canvas messages.
• Email: TBartels@Southeast.edu.
• Voice mail: 1-402-323-3452.
• Text messages: 1-402-805-3021.
• Office hours:
• Mondays and Wednesdays from 9:30 to 10:30,
• Tuesdays and Thursdays from 2:30 PM to 4:00, and
• by appointment,
in ESQ 112 and online. (I am often available outside of those times; feel free to send a message any time and to check for me in the office whenever it's open.)

The official textbook for the course is the 4th Edition of University Calculus: Early Transcendentals by Hass et al published by Addison Wesley (Pearson). There are also two packets of course notes (DjVu):
• The first set, on single-variable Calculus (including material from Calculus 1);
• The second set (TBA), on multivariable Calculus (including material for Calculus 3).
1. General review:
• Date due: January 14 Tuesday.
• Reading from my notes (first set): Review at least Chapter 4 through Section 4.3 (pages 39–42).
• Reading from the textbook: Review at least Sections 5.4 and 5.5.
• Exercises due:
1. If F′(x) = f(x) for all x, then what is ∫ f(x) dx, that is the indefinite integral of f(x) with respect to x?
2. If ∫ f(x) dx = F(x) + C, then what is ∫bx=af(x) dx, that is the definite integral of f(x) with respect to x as x runs from a to b?
2. Work:
• Date due: January 15 Wednesday.
• Reading from the textbook: Section 6.5 (pages 386–389).
• Exercises due:
1. Suppose that a variable force is applied on object moving from a to b along the x-axis, such that the amount of the force in the direction of the positive x-axis is a function F of the object's position along the x-axis. Write down an integral for the work done on the object by that force.
2. Suppose that a spring with a (positive) spring constant k is stretched or compressed a (signed) distance x from its equilibrium length. Write down a formula for the force needed to hold the spring in that position.
3. Moments:
• Date due: January 16 Thursday.
• Reading from the textbook: Section 6.6 (pages 392–400).
• Exercises due:
1. If you wish to find the total mass of the plate described in Exercise 6.6.24 on page 400 of the textbook, will you do an integral with respect to x or an integral with respect to y?
2. Give the formula for the centre of mass (, ȳ) in terms of the total mass M and the moments Mx and My.
4. Differential equations:
• Date due: January 17 Friday.
• Reading from my notes (first set):
• Section 4.4 (page 42);
• Chapter 5 through Section 5.2 (pages 45–47);
• Optional: The rest of Chapter 5 (pages 47&48).
• Reading from the textbook: Section 7.2 "Separable Differential Equations" (pages 416–418).
• Exercises due: Fill in the blanks with vocabulary words:
1. An equation with differentials or derivatives in it is a(n) _____ equation.
2. A differential equation of the form dy/dx = g(x) h(y) is called _____.
5. Exponential growth:
• Date due: January 21 Tuesday.
• Section 7.2 through "Exponential Change" (pages 415&416);
• The rest of Section 7.2 (pages 418–422).
• Exercises due:
1. Fill in the blanks with a vocabulary word: A quantity is growing _____ if it is growing in such a way that its rate of growth is proportional to its size.
2. Suppose that a quantity y undergoes exponential growth with a relative growth rate constant of k and an initial value of y0 at time t = 0. Write down a formula for the value of y as a function of the time t.
6. Integration by parts:
• Date due: January 22 Wednesday.
• Reading from my notes (first set): Section 4.5 (pages 42&43).
• Reading from the textbook: Chapter 8 through Section 8.1 (pages 436–442).
• Exercises due: Use the formula ∫ u dv = uv − ∫ v du for integration by parts.
1. To find ∫ x ex dx, what should be u and what should be dv?
2. To find ∫ x ln x dx, what should be u and what should be dv?
7. Partial fractions:
• Date due: January 23 Thursday.
• Reading from the textbook: Section 8.4 (pages 456–461).
• Exercises due: Suppose that a rational expression has the denominator (x2 + 3)(x + 3)2.
1. What are the denominators of its partial fractions?
2. For each of these, indicate the maximum degree of the numerator. (If you wish, you may do this by writing a general form for each numerator, such as A or Ax + B.)
8. Trigonometric integration:
• Date due: January 24 Friday.
• Reading from the textbook: Section 8.2 through "Eliminating Square Roots" (pages 445–447).
• Exercises due:
1. To find ∫ sin2x dx, what trigonometric identity would you use? That is, sin2x = _____?
2. For which (if any) of the following other integrals would you also need to use the identity from the previous exercise? (Say Yes or No for each one.)
1. ∫ sin2x cos2x dx,
2. ∫ sin2x cos3x dx,
3. ∫ sin3x cos2x dx,
4. ∫ sin3x cos3x dx.
9. Tricky trigonometric integration:
• Date due: January 27 Monday.
• Reading from the textbook: The rest of Section 8.2 (pages 447–449).
• Exercises due: Rewrite the following expressions using only powers of sin x and/or cos x (and possibly multiplication):
1. sec2x,
2. sec x tan x,
3. csc2x,
4. csc x cot x.
10. Trigonometric substitution:
• Date due: January 28 Tuesday.
• Reading from the textbook: Section 8.3 (pages 451–454).
• Exercise due: For each of the following expressions, give a trigonometric substitution that would tend to help when finding integrals containing that expression:
1. (x2 + 25), the square root of x2 + 25;
2. (x2 − 25), the square root of x2 − 25;
3. (25 − x2), the square root of 25 − x2.
11. Integration using computers and tables:
• Date due: January 29 Wednesday.
• Section 8.5 (pages 463–467);
• Skim "A Brief Table of Integrals" (pages T1–T6).
• Optional: Look at these some or all of these computer algebra systems that will do integrals (as well as much more):
• Sage (free to download, free for most uses online, \$14.00 per month or more to make intensive computations online);
The permanent URI of this web page is `http://tobybartels.name/MATH-1700/2020SP/`.