Here is material about the administration of the course:

- 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.

- 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,

- The first set, on single-variable Calculus (including material from Calculus 1);
- The second set (TBA), on multivariable Calculus (including material for Calculus 3).

- 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:
- If
*F*′(*x*) =*f*(*x*) for all*x*, then what is ∫*f*(*x*) d*x*, that is the indefinite integral of*f*(*x*) with respect to*x*? - If ∫
*f*(*x*) d*x*=*F*(*x*) +*C*, then what is ∫^{b}_{x=a}*f*(*x*) d*x*, that is the definite integral of*f*(*x*) with respect to*x*as*x*runs from*a*to*b*?

- If

- Work:
- Date due: January 15 Wednesday.
- Reading from the textbook: Section 6.5 (pages 386–389).
- Exercises due:
- 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. - 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.

- Suppose that a variable force is applied
on object moving from

- Moments:
- Date due: January 16 Thursday.
- Reading from the textbook: Section 6.6 (pages 392–400).
- Exercises due:
- 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*? - Give the formula for the centre of mass
(
*x̄*,*ȳ*) in terms of the total mass*M*and the moments*M*_{x}and*M*_{y}.

- 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

- 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:
- An equation with differentials or derivatives in it is a(n) _____ equation.
- A differential equation of the form
d
*y*/d*x*=*g*(*x*)*h*(*y*) is called _____.

- Exponential growth:
- Date due: January 21 Tuesday.
- Reading from the textbook:
- Section 7.2 through "Exponential Change" (pages 415&416);
- The rest of Section 7.2 (pages 418–422).

- Exercises due:
- 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.
- Suppose that a quantity
*y*undergoes exponential growth with a relative growth rate constant of*k*and an initial value of*y*_{0}at time*t*= 0. Write down a formula for the value of*y*as a function of the time*t*.

- 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*d*v*=*u**v*− ∫*v*d*u*for integration by parts.- To find
∫
*x*e^{x}d*x*, what should be*u*and what should be d*v*? - To find ∫
*x*ln*x*d*x*, what should be*u*and what should be d*v*?

- To find
∫

- 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
(
*x*^{2}+ 3)(*x*+ 3)^{2}.- What are the denominators of its partial fractions?
- 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*A**x*+*B*.)

- Trigonometric integration:
- Date due: January 24 Friday.
- Reading from the textbook: Section 8.2 through "Eliminating Square Roots" (pages 445–447).
- Exercises due:
- To find ∫ sin
^{2}*x*d*x*, what trigonometric identity would you use? That is, sin^{2}*x*= _____? - 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.)
- ∫ sin
^{2}*x*cos^{2}*x*d*x*, - ∫ sin
^{2}*x*cos^{3}*x*d*x*, - ∫ sin
^{3}*x*cos^{2}*x*d*x*, - ∫ sin
^{3}*x*cos^{3}*x*d*x*.

- ∫ sin

- To find ∫ sin

- 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):- sec
^{2}*x*, - sec
*x*tan*x*, - csc
^{2}*x*, - csc
*x*cot*x*.

- sec

- 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:
- √(
*x*^{2}+ 25), the square root of*x*^{2}+ 25; - √(
*x*^{2}− 25), the square root of*x*^{2}− 25; - √(25 −
*x*^{2}), the square root of 25 −*x*^{2}.

- √(

- Integration using computers and tables:
- Date due: January 29 Wednesday.
- Reading from the textbook:
- 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);
- Maxima (free to download);
- Maple ($99.00 to download);
- Wolfram Mathematica ($160.00 to download, $80.00 per year online, free 15-day trial);
- Wolfram Alpha (free for some uses online, $4.75 per month for advanced features, $2.99 for a smartphone app with intermediate features).

- Exercise due:
Which entry
in the table of integrals in the back of the textbook (pages T1–T6)
tells you how to integrate
∫ (
*x*^{2}+ 3)^{−1/2}d*x**without*using hyperbolic functions (sinh, cosh, etc) or their inverses? (Hints: That table doesn't use negative exponents; it uses fractions instead. And it doesn't use fractional exponents; it uses roots instead.)

- More to come!

This web page and the files linked from it were written by Toby Bartels, last edited on 2020 January 23. Toby reserves no legal rights to them.

The permanent URI of this web page
is
`http://tobybartels.name/MATH-1700/2020SP/`

.