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Phil’s Math Assignments

email Scott Turner
general rules The world is understood by physics, which depends on the power of math and computers.
Math and computers relate to logic.
upcomingmatrix & vector practice
upcomingconvert a complex number to the matrix representing the same
possibilitylecture on length and perpendicularity of vectors

Past assignments:
Thursday, July 7Final exam. Problems will include
  • derivatives of basic functions
  • differentiation with the chain rule
  • related rates, i.e. 3.6
  • maxima and minima
  • Apply the definition of continuous.
  • limits
  • finding indefinite and definite integrals
  • simple differential equations
  • area in relation to the definite integral
  • derivatives of sine, cosine, exponential, and natural log
99/100 A+
Wednesday, July 6Lecture on log and exponential.
Thomas p. 441 problems 16 & 17
Study for final.
At the end of the lecture, Phil went to the whiteboard and (with a little guidance) found the derivative of the arcsin.
Tuesday, July 5Thomas 4.8 problems 12,39,45
Study for final.
Friday, July 1Lecture on the method of substitution when finding an indefinite integral.
Some reding in “A Tour of the Calculus”
Thomas, 4.7 problems 14,20,44,47,59
Thomas, 4.8: Do one substitution problem.
Wednesday, June 29
-Thursday, June 30
Read part of “A Tour of the Calculus” and discuss it with Dad.done
Tuesday, June 28Thomas, read p. 282. Read example 12 on p. 291.
Do 4.7 problem 1.
Do 4.7 problem 5 and check your answer with Dad or the back of the book before continuing.
Do 4.7 problems 11-13 and 19.
Monday, June 27Thomas Section 4.3 problems 8,9,12
Section 4.4 problem 2
lecture on definite integrals
Tuesday, June 21Thomas Section 4.2 problems 3,5,7,9,13,15,17,19,23,25,29,31,35,37,39,41,43,45,47good/excellent
Monday, June 20Read Thomas, sections 4.1 and 4.2. Do 4.2 problems 1,2,4,11,21,27,33fair
Friday, June 17Thomas Section 3.6: Read the second half of the lesson
Do problems 1,2,3,10,12,15,17,20
Wednesday, June 15Thomas Section 3.5 problems 20,40,46,47
Read the first half of Section 3.6 and do problem 7.
very good
Tuesday, June 14Thomas Section 3.4 problem 14
Section 3.5 problems 5,10,15,19,20,21
very good
Monday, June 13Thomas Section 3.4 problem 13,22,26
Section 3.5 problems 1,4
very good
Friday, June 10Thomas Section 3.4 problems 3,9,14,25good
Wednesday, May 18
-Thursday, June 4
various preparations for the Math SAT II
including Foerster 5-4 (complex numbers), 6-12 (logarithms), 10-4 (factoring, roots), 11-4 (series), 14-9 (solving trigonometric equations)
Monday, May 16Correct the spelling: assummtoat
Thomas Section 3.3 problems 7,9,13,25,26,28,33,36
Friday, May 13Thomas: Section 3.2 problems 31,35,36,42
lecture on symmetry and asymptotes
Wednesday, May 11Thomas: Read section 3.2. Do problems 3,7,12,13,15,17,21,26excellent
Tuesday, May 10Thomas Section 3.1 problems 11,18,19,21,23,26,29very good
Monday, May 9Thomas: Read Section 3.1. Do problems 1,10,17,25,31.good
Wednesday, April 27Review definition of limit and derivative.
Thomas Section 2.11 miscellaneous problems 5,12,16,19,33,41
excellent practice
preparation for the SAT reasoning testdone
Wednesday, April 13Thomas Section 2.5 Problem 25
Section 2.11 Miscellaneous Problems 4,10,27,34
very good
Friday, April 8Thomas Section 2.11 Miscellaneous Problem 104
Section 2.5 Problem 24
Section 2.11 Miscellaneous Problems 2,8,24,26
very good
Thursday, April 7Thomas Section 2.11 Miscellaneous Problem 105excellent
Wednesday, April 6Thomas Section 2.5 problems 23,29,30
Section 2.11 Miscellaneous Problems 101,102
Tuesday, April 5Thomas Section 2.11 Miscellaneous Problems 71,76,81,99,100very good
Monday, April 4Thomas Section 2.11 review questions 14,15
Section 2.11 Miscellaneous Problems 1,3,7,15,46,50,54,60
good practice
Thursday, March 31Thomas, section 2.9, Do problem 3 without a computer program.
Section 2.10 problems 5,23,24
Section 2.11 review questions 4,7,11,13
Wednesday, March 30review of Newton's method
Write a program to symbolically differentiate a polynomial function.
Use the chain rule to show that the derivative of the inverse of a function is the reciprocal of the derivative.
Tuesday, March 29Thomas section 2.9, problems 1,7,12,14,15excellent
Monday, March 28reading from Feynmann, QEDdone
Friday, March 25 Thomas section 2.8, problems 56b,56h,57,58,59,64 good
Thursday, March 24
  1. Suppose k'(x)=1/x.
    If g(t)=k(t5), find g'(t).
  2. Read Thomas section 2.8.
  3. Thomas section 2.8, problems 21,22,23,44,53
very good
Wednesday, March 23
  1. cos(x)=sin((π/2)-x).
    Use the chain rule and trig identities to show that cos'(x)= -sin(x).
  2. Thomas 2.7 problems 29,35,39,42
Tuesday, March 22
  1. Suppose k'(x)=1/x.
    If g(t)=k(t2), find g'(t).
  2. Suppose f'(x)=2x.
    If h(y)=f(½y+3), find h'(y).
  3. Use the definition of derivative to find the derivative of the sine function.
Monday, March 21Read Thomas 2.6 on parametric equations.
Thomas 2.6 problems 4,11,14,16,20,22
Friday, March 18Thomas 2.5 problems 3,27
Lecture on chain rule
Thomas 2.6 problems 1,2,3
very good
Thursday, March 17Lesson on using the standard deviation in a physics labdone
Wednesday, March 16Thomas 2.4 problem 56
Thomas 2.5 problems 2,7,15,22,44
Tuesday, March 15Lecture on standard deviationdone
Monday, March 14Thomas 2.4 problem 50very good
Friday, March 11Read Thomas 2.5 and do problems 1 and 43.
Thomas, 2.4 problems 21,27,49
Thursday, March 10Thomas, 2.4 problems 12,16,34,42,45
Note that for problem 45, it is easier if you rearrange the equation algebraically before differentiating it.
very good
Wednesday, March 9Thomas, 2.4 problems 3,14,17,19,29,32,36,41good practice
Tuesday, March 8Lesson on the relationship between pairs of formulas:
  • volume and surface area of a sphere
  • area and circumference of a circle
  • volume and surface area of a cube
Monday, March 7Thomas, 2.3 problems 13,46
Read Thomas, section 2.4. Do problems 1,2,10,30
very good
Friday, March 4presentation: notation and the quotient rule
Thomas, 2.3 problems 2,15,17,29,35,37,38
Thursday, March 3practice problems from Thomas 2.3good
Wednesday, March 2discussion of pitfalls in applying the rules of differentiationdone
Tuesday, March 1Thomas, 2.2 problem 27
2.3 problems 5,7,9,11,13,19,25,33
Monday, February 28Thomas, 2.2 problems 15,23,26,31
Read part 2.3 and start on the odd-numbered problems.
very good
Friday, February 25Closed book test on Thomas, Section 1 (limits and the definition of derivative)95/100
Wednesday-Thursday, February 23-24Thomas, Section 1 Miscellaneous problems on pp. 93-94: 64,65,70(d)
Also, read parts 2.1 and 2.2 and practice some problems.
Tuesday, February 22Thomas, Section 1 Miscellaneous problems on pp. 93-94: 24,27,28,59,61excellent
Monday, February 21
  1. Prove that the limit as x approaches 0 of the square root of x is 0.
  2. Discuss proof of the intermediate value theorem with Dad.
  3. Thomas, Section 1 Review questions and exercises on p. 91: 7,9,12,16
Thursday, February 17
  1. Prove that the limit as x approaches 2 of x2 is 4.
  2. Thomas, Section 1.11 problems 17,19,25,29,31,33,34,44
Tuesday, February 15 Thomas, Section 1.11 problems 40,42
Section 1.9: problem 91(g)
very good
Monday, February 14 Thomas, Section 1.11 problems 8,13,15,16,24,27,38excellent
Friday, February 11 Thomas, Section 1.11 problems 1-7,12,14,23,35,36,37 very good practice
Thursday, February 10 Prove or show Theorem 1 part (i).
Thomas, Section 1.9: problem 67
Section 1.10 problems 2,14,41
Finish reading Section 1.11
very good
Wednesday, February 9Thomas, Section 1.9: do problems 66,87,91(f)
Learn to prove Theorem 1 part (i) in appendix A.3.
Start to read Section 1.11.
very good
Tuesday, February 8Let f(x) = 2x if 0 < x < 2, and x13 otherwise. Use ε and δ reasoning to show that the limit as x approaches 1 of f(x) is equal to 2.very good
Monday, February 7Thomas, Section 1.9: do problems 65,85
Section 1.10: do problems 9,11,13,34,39
Understand the definition of limit.
very good
Friday, February 4Thomas, Section 1.9: do problems 64,86
Section 1.10: read, and do problems 1,3,5,7,33,37,38
very good
Thursday, February 3Thomas, section 1.9: do problems 23,28,44,52,56,58,72,73,74,75,91(e)very good
Wednesday, February 2quiz on the fundamental theorem of algebraexcellent
Tuesday, February 1Thomas, Section 1.9: do problems 14,28,33,34,35,39,47,50,51,91(c)very good
Monday, January 31Lecture on limit involving factoring a square root.done
Friday, January 28Test on trigonometric functions, concluded.
  1. Simplify 1+(tan θ)2 using one other trigonometric function.
  2. Solve sin(2x+90°)=sin x
    for x in the domain [-180°,+180°).
  3. Express tan(x+y) in terms of tan x and tan y.
Thursday, January 27Study for test on trigonometric functions (Foerster, chapter 14. Later in the day take the first part of the test. This will be closed book and short. You must know properties 1-7. Also practice problems from 14-9, identifying all of the solutions in the specified domain.
Tuesday, January 25Thomas, Section 1.8, problems 22 and 26.
Thomas, Section 1.9: do problems 11,62,15,17,27,31,32,34,91(b)
Monday, January 24Thomas, Section 1.9: read the section and do problems 1,3,5,13,53, 91(a).very good
Friday, January 21Foerster, Section 14-9, problems 27-38good
Thursday, January 20Thomas, 1.8, Read the section and do problems 2,3,8,11,15-19,20excellent
Wednesday, January 19Thomas, 1.7, noting that the hint to problem 28 may be relevant to problem 15, do problems 15,16,22,23,24,25good practice
Tuesday, January 18quiz on 1.7 and 14-991/100
Monday, January 17Foerster, Section 14-9: problems 16-26fair
Friday, January 14Thomas, 1.7: Read the section and do problems 6,8,9,11, and 12.good
Thursday, January 13Foerster, Section 14-9: Read and do problems 2-15good
Wednesday, January 12
  1. Lecture from Dad on "Linear Combination of Cosine and Sine"
  2. Foerster, Section 14-8: Review the table of properties of trigonometric functions. You should be perfectly familiar with parts 1 through 7 of this table. You should understand 8, 9, and 10 well enough that they don't surprise you.
  3. Foerster, Section 14-8: problems 29a and 30a.
  4. Foerster, Section 14-9: problem 1
Tuesday, January 11Thomas, 1.6: Read. Do problems 3 and 11.excellent
Monday, January 10
  1. one-on-one with teacher (Dad) regarding the limit of an infinite sequence
  2. Foerster, section 14-3, problems 35 and 45
  3. Foerster, section 14-4, problems 9 and 24
  4. Using Foerster, section 14-5, find the exact value of cos 22.5°.
very good
Friday, January 7Read about calculus.done
Wednesday, January 5
  1. Prove that the sum of two odd functions is odd.
  2. Foerster, section 14-2, problem 29
  3. Foerster, section 14-3, problems 28,34,53
  4. Foerster, section 14-4, problems 1,3,7,9,11
Tuesday, January 4Foerster, section 14-3, problems 1,7,11,15,27,39,52,54excellent
Monday, January 3Foerster, section 14-2, problems 1,6,17,26excellent
Friday, December 31Test
  1. What is the inverse cosecant of the square root of 2?
  2. What is the period of f(x) = tan(2x+π)?
  3. Somewhere on earth at some time of year, the sun rises at 9 a.m. and sets at 5 p.m. The sun's highest elevation above the horizon on that day is 30°. Create a sinusoidal model of the sun's elevation as a function of the time of day. Give two examples of elevations that the model predicts. Partial credit will be given for getting the period correct, for making a correct graph, for completeness, for stating what the time of year is, etc.
Supertest: Simplify sin(x+4½π).
97/100 A
Wednesday, December 29Foerster, section 12-10 numbers 8 & 11, section 13-10 problems 5 & 12 section 13-11 problem 4excellent
Tuesday, December 28Foerster, section 13-10, problems 1,2,3,11excellent
Monday, December 27Foerster, section 13-6, problems 2,9,10, section 13-7, problems 6,8, section 13-8 problem 11very good
Sunday, December 26Foerster, section 13-6, problems 3,6, section 13-7, problem 5good
Thursday, December 23Foerster, section 13-6, problems 4,8,9, section 13-7, problems 4,5,10 (some redoing)fair
Wednesday, December 22Foerster, section 13-6, problems 8&9, section 13-7, problem 4, section 13-8 choose two interesting problemsfair
Monday, December 20Foerster, section 12-7, problem 18, section 13-6, problem 8, section 13-7, problems 1,2,3very good
Friday, December 17Lesson on trigonometric identities including the sum of angles formulas for sine and cosine.
Foerster, section 14-3, problem 27
Thursday, December 16Foerster, section 12-9, Concept tests 1, 2, and 3excellent
Wednesday, December 15Foerster, section 12-8, problems 10,11,13,14good
Tuesday, December 14Foerster, section 12-8, problems 1,2,4,7,8excellent
December 6 - December 13Foerster, section 12-7, problems 1,3,5,7,9,11excellent
Friday, December 3retest on the material covered by last week's test90%, very good
Wednesday, December 1Foerster, section 12-6, all the odd-numbered problemsexcellent
Wednesday, November 24 Test with problems taken from the following topics:
  • From the equation of a quadratic relation (with no xy term),
    • tell which conic section the graph will be, and
    • sketch the graph quickly.
  • Derive an equation of a set of points from a geometrical definition.
  • Solve systems of quadratic equations with two variables.
  • Operate with complex numbers.
  • Graph polynomials with real coefficients.
  • Find the zeros of, and/or factor a polynomial. Recognize the relationship between these two kinds of problems.
  • Use polynomials as mathematical models.
  • Find the slope of a quadratic function at a given point.
  • Calculate the number of outcomes in an event or sample space.
  • Calculate the probability of an event.
65%, fair
Tuesday, November 23Prepare for tomorrow's test.done
Friday, November 19 Foerster, section 12-5, problems 30,31,33,35 very good/fair
Thursday, November 18 Explain why the sine of x in radians is close to x when x is a small angle. excellent
Wednesday, November 17 Foerster, section 12-5, problems 2,4,14,25,27,29,31,33,35 good
Wednesday, November 10
  1. Explain why the sine of x in radians is close to x when x is a small angle.
  2. The graph of the cosine of x is close to a parabola when x is a small angle. What is the equation of that parabola? Any method you can think of to come up with the answer is fair game.
Problem 2 done using concepts of calculus.
Tuesday, November 9 Foerster, section 12-4, problems 13,15
Foerster, section 12-5, problems 1,3,5,7,9,11,13,15,17,19,21,23
Monday, November 8 quickie review of Friday's solutions done
Friday, November 5 Foerster, section 12-4 good
Thursday, November 4 Foerster, section 11-11, Concepts Test 5 very good
Wednesday, November 3
  1. Foerster, section 11-10, problems 35,36,37,38,39,40, and...
  2. In problem 55, can you explain why the easy way works?
Tuesday, November 2 Foerster, section 11-10, problems 27,29,34,51-55
In problem 55, can you explain why the easy way works?
very good
Monday, November 1 Foerster, section 11-10, problems 1,14,16,17,23,24,26,33 excellent
Friday, October 29 Foerster, section 11-9
This should be somewhat familiar, so do all of the exercises.
Thursday, October 28 Foerster, section 10-7, Concepts Test 4 very good
Wednesday, October 27 Foerster, section 10-7, Concepts Tests 1,2,3 excellent
Monday, October 25 Foerster, section 10-7, review problem 2, second half
Foerster, section 10-7, review problem 3
Friday, October 22 Foerster, section 10-2, Exercises 3,9-14,31,34,35,46
Foerster, section 10-7, review problem 2, first half
Thursday, October 21 Foerster, section 10-6, Exercise 3
Foerster, section 10-7, review problem 1
very good
Wednesday, October 20 Foerster, section 10-6, Exercise 7, including 7f good
Monday, October 18 Foerster, section 10-6, Exercise 6
Lesson with Dad
Friday, October 15 Foerster, section 10-5, Exercises 42,43
Foerster, section 10-6, Exercises 1
Wednesday, October 13 – Thursday, October 14 Foerster, section 10-5, Exercises 3,5,23,29,37,38–41 excellent
Tuesday, October 12 Foerster, section 10-5, Exercises 1,17,20,35,44 excellent
Monday, October 11 Foerster, section 10-4, Exercises 1,20,35,39,53 excellent
Thursday, October 7 Foerster, section 10-3, Exercises 20,21,23,24 excellent
Wednesday, October 6 Foerster, section 10-2, Exercises 25,37,42,46,47,48 excellent
Tuesday, October 5 Foerster, section 9-9, tests 4, 5, & 6 excellent
Monday, October 4
  1. Define “parabola”.
  2. Foerster, section 9-9, tests 3, 4, & 5
very good
Friday, October 1
  1. Define “circle”.
  2. Foerster, section 9-9, tests 1 & 2
Thursday, September 30
  1. Lecture: a rigorous notation for defining “hyperbola”
  2. Define “line”.
  3. Define “ellipse”.
Wednesday, September 29 Foerster, section 9-9, review problems 2b, 1b, and 1c excellent
Tuesday, September 28 Discuss with Dad: Supposing the graph of xy=1 is a hyperbola, how can I find its foci? done
Monday, September 27
  1. Foerster, section 9-9, review problems 2a and 1a
  2. Consider proving that the graph of xy=1 is a hyperbola. Apart from algebraic steps (e.g. distributive law, or simplifying equations) what would be essential to the proof?
very good
Friday, September 24 Foerster, section 9-8, Exercises 11,12,19 very good
Thursday, September 23 Foerster, section 9-8, Exercises 10,27
Wednesday, September 22 Foerster, section 9-8, Exercises 7,8,9,18
In problem 18, you have a somewhat simple 4th degree polynomial to factor and I don't know whether you've done that before. Ask me.
Tuesday, September 21 Foerster, section 9-8, Exercises 1,3,4,7 excellent
Monday, September 20 Foerster, section 9-6, Exercises 11,12,16,17 very good
Friday, September 17 Foerster, section 9-3, Exercise 8
Foerster, section 9-4, Exercise 8
Find a polynomial equation for the set of points equidistant from the x and the y axes. Tell whether or not the graph is a conic section.
Foerster, section 9-6, Exercises 6,9,18
after good
Thursday, September 16 Foerster, section 9-4. Exercise 15
Foerster, section 9-5. Exercise 8
Foerster, section 9-6. Exercises 1,7,5,13,18
Wednesday, September 15 Foerster, section 9-4. Exercises 9,11,13,17
Foerster, section 9-5. Exercises 1,3
very good
Tuesday, September 14 Foerster, section 9-4. Exercises 1,3,5,7 very good
Thursday, September 9
  1. Foerster, section 9-3. Exercises 1,3,5,7,9,11
  2. Give an equation of an ellipse with foci at (0,0) and at (2,0).
  3. Give an equation of a different ellipse with the same two foci.
  4. Give an equation of an ellipse that is similar (in the geometric sense) to
      9x2+25y2 = 225,
    but with a different size.
very good
after poor
Wednesday, September 8
  1. Foerster, section 9-1, including the exercise. Note that throughout chapter 9, Foerster keeps things manageable by analyzing quadratic relations which have no xy term, i.e. B=0.
  2. Foerster, section 9-2. Exercises 1,3,9,11,12,13,15,19a,20
very good

Course Overview

  • 2004-09 to 2005-06
  • Described as Pre-Calculus
    but we know better!
  • There will be more matrices and combinatorics.
  • There will be plenty of logarithms, exponentials, sines, tangents, and functions.
  • There will be complex numbers, polynomials, roots, and factoring.
  • But we've seen all of those before! So we will be doing all of these things while beginning to learn calculus.
  • Plus, there will be more programming, logic, and proofs. The presentation will be unusual, because your teacher is still trying to reinforce his weak intuition for the Curry-Howard Isomorphism and for Category Theory. So the programming language will have explicit logic, also known as static types. It could be Haskell or even Dad's own Ambidexter, if that gets off the ground. There's this nifty book, The Haskell Road to Logic, Maths and Programming, which has an introduction to many wonderful things, but unfortunately it seems to be weak on the Curry-Howard Isomorphism as well.
  • For Calculus, the prime textbook candidate is the classic, by Thomas.
  • For Pre-Calculus, the prime textbook is Algebra and Trigonometry, by Paul A. Foerster.

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