home
math


general rules 
The world is understood by physics,
which depends on the power of math and computers. 
Math and computers relate to logic. 
upcoming  matrix & vector practice 
upcoming  convert a complex number to the matrix representing the same 
possibility  lecture on length and perpendicularity of vectors 
Past assignments:
Thursday, July 7  Final 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 6  Lecture on log and exponential. Thomas p. 441 problems 16 & 17 Study for final.  done At the end of the lecture, Phil went to the whiteboard and (with a little guidance) found the derivative of the arcsin. 
Tuesday, July 5  Thomas 4.8 problems 12,39,45 Study for final.  done 
Friday, July 1  Lecture 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.  excellent 
Wednesday, June 29 Thursday, June 30  Read part of “A Tour of the Calculus” and discuss it with Dad.  done 
Tuesday, June 28  Thomas, 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 1113 and 19.  excellent 
Monday, June 27  Thomas Section 4.3 problems 8,9,12 Section 4.4 problem 2 lecture on definite integrals  excellent 
Tuesday, June 21  Thomas Section 4.2 problems 3,5,7,9,13,15,17,19,23,25,29,31,35,37,39,41,43,45,47  good/excellent 
Monday, June 20  Read Thomas, sections 4.1 and 4.2. Do 4.2 problems 1,2,4,11,21,27,33  fair 
Friday, June 17  Thomas Section 3.6: Read the second half of the lesson Do problems 1,2,3,10,12,15,17,20  excellent 
Wednesday, June 15  Thomas Section 3.5 problems 20,40,46,47 Read the first half of Section 3.6 and do problem 7.  very good 
Tuesday, June 14  Thomas Section 3.4 problem 14 Section 3.5 problems 5,10,15,19,20,21  very good 
Monday, June 13  Thomas Section 3.4 problem 13,22,26 Section 3.5 problems 1,4  very good 
Friday, June 10  Thomas Section 3.4 problems 3,9,14,25  good 
Wednesday, May 18 Thursday, June 4  various preparations for the Math SAT II including Foerster 54 (complex numbers), 612 (logarithms), 104 (factoring, roots), 114 (series), 149 (solving trigonometric equations)  done 
Monday, May 16  Correct the spelling: assummtoat Thomas Section 3.3 problems 7,9,13,25,26,28,33,36  done 
Friday, May 13  Thomas: Section 3.2 problems 31,35,36,42 lecture on symmetry and asymptotes  excellent 
Wednesday, May 11  Thomas: Read section 3.2. Do problems 3,7,12,13,15,17,21,26  excellent 
Tuesday, May 10  Thomas Section 3.1 problems 11,18,19,21,23,26,29  very good 
Monday, May 9  Thomas: Read Section 3.1. Do problems 1,10,17,25,31.  good 
Wednesday, April 27  Review definition of limit and derivative. Thomas Section 2.11 miscellaneous problems 5,12,16,19,33,41  excellent practice 
 preparation for the SAT reasoning test  done 
Wednesday, April 13  Thomas Section 2.5 Problem 25
Section 2.11 Miscellaneous Problems 4,10,27,34  very good 
Friday, April 8  Thomas Section 2.11 Miscellaneous Problem 104
Section 2.5 Problem 24
Section 2.11 Miscellaneous Problems 2,8,24,26  very good 
Thursday, April 7  Thomas Section 2.11 Miscellaneous Problem 105  excellent 
Wednesday, April 6  Thomas Section 2.5 problems 23,29,30 Section 2.11 Miscellaneous Problems 101,102  good 
Tuesday, April 5  Thomas Section 2.11 Miscellaneous Problems 71,76,81,99,100  very good 
Monday, April 4  Thomas Section 2.11 review questions 14,15
Section 2.11 Miscellaneous Problems 1,3,7,15,46,50,54,60  good practice 
Thursday, March 31  Thomas, 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
 good 
Wednesday, March 30  review 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.  excellent 
Tuesday, March 29  Thomas section 2.9, problems 1,7,12,14,15  excellent 
Monday, March 28  reading from Feynmann, QED  done 
Friday, March 25 
Thomas section 2.8, problems 56b,56h,57,58,59,64
 good 
Thursday, March 24   Suppose k'(x)=1/x.
If g(t)=k(t^{5}), find g'(t).
 Read Thomas section 2.8.
 Thomas section 2.8, problems 21,22,23,44,53
 very good 
Wednesday, March 23   cos(x)=sin((π/2)x).
Use the chain rule and trig identities to show that cos'(x)= sin(x).
 Thomas 2.7 problems 29,35,39,42
 excellent 
Tuesday, March 22   Suppose k'(x)=1/x.
If g(t)=k(t^{2}), find g'(t).
 Suppose f'(x)=2^{x}.
If h(y)=f(½y+3), find h'(y).
 Use the definition of derivative to find the derivative of the sine function.
 done 
Monday, March 21  Read Thomas 2.6 on parametric equations. Thomas 2.6 problems 4,11,14,16,20,22  excellent 
Friday, March 18  Thomas 2.5 problems 3,27 Lecture on chain rule Thomas 2.6 problems 1,2,3  very good 
Thursday, March 17  Lesson on using the standard deviation in a physics lab  done 
Wednesday, March 16  Thomas 2.4 problem 56 Thomas 2.5 problems 2,7,15,22,44  excellent 
Tuesday, March 15  Lecture on standard deviation  done 
Monday, March 14  Thomas 2.4 problem 50  very good 
Friday, March 11  Read Thomas 2.5 and do problems 1 and 43. Thomas, 2.4 problems 21,27,49  excellent 
Thursday, March 10  Thomas, 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 9  Thomas, 2.4 problems 3,14,17,19,29,32,36,41  good practice 
Tuesday, March 8  Lesson 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
 done 
Monday, March 7  Thomas, 2.3 problems 13,46 Read Thomas, section 2.4. Do problems 1,2,10,30  very good 
Friday, March 4  presentation: notation and the quotient rule Thomas, 2.3 problems 2,15,17,29,35,37,38  excellent 
Thursday, March 3  practice problems from Thomas 2.3  good 
Wednesday, March 2  discussion of pitfalls in applying the rules of differentiation  done 
Tuesday, March 1  Thomas, 2.2 problem 27
2.3 problems 5,7,9,11,13,19,25,33  fair 
Monday, February 28  Thomas, 2.2 problems 15,23,26,31
Read part 2.3 and start on the oddnumbered problems.  very good 
Friday, February 25  Closed book test on Thomas, Section 1 (limits and the definition of derivative)  95/100 
WednesdayThursday, February 2324  Thomas, Section 1 Miscellaneous problems on pp. 9394: 64,65,70(d) Also, read parts 2.1 and 2.2 and practice some problems.  good 
Tuesday, February 22  Thomas, Section 1 Miscellaneous problems on pp. 9394: 24,27,28,59,61  excellent 
Monday, February 21   Prove that the limit as x approaches 0 of the square root of x is 0.
 Discuss proof of the intermediate value theorem with Dad.
 Thomas, Section 1 Review questions and exercises on p. 91: 7,9,12,16
 good 
Thursday, February 17   Prove that the limit as x approaches 2 of x^{2} is 4.
 Thomas, Section 1.11 problems 17,19,25,29,31,33,34,44
 excellent 
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 8,13,15,16,24,27,38  excellent 
Friday, February 11 
Thomas, Section 1.11 problems 17,12,14,23,35,36,37
 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 9  Thomas, 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 8  Let f(x) = 2x if 0 < x < 2, and x^{13} 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 7  Thomas, 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 4  Thomas, 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 3  Thomas, section 1.9: do problems 23,28,44,52,56,58,72,73,74,75,91(e)  very good 
Wednesday, February 2  quiz on the fundamental theorem of algebra  excellent 
Tuesday, February 1  Thomas, Section 1.9: do problems 14,28,33,34,35,39,47,50,51,91(c)  very good 
Monday, January 31  Lecture on limit involving factoring a square root.  done 
Friday, January 28  Test on trigonometric functions, concluded.
 Simplify 1+(tan θ)^{2} using one other trigonometric function.
 Solve sin(2x+90°)=sin x
for x in the domain [180°,+180°).
 Express tan(x+y) in terms of tan x and tan y.
 92/100 
Thursday, January 27  Study 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 17. Also practice problems from 149, identifying all of the solutions in the specified domain. 
Tuesday, January 25  Thomas, Section 1.8, problems 22 and 26. Thomas, Section 1.9: do problems 11,62,15,17,27,31,32,34,91(b)  excellent 
Monday, January 24  Thomas, Section 1.9: read the section and do problems 1,3,5,13,53, 91(a).  very good 
Friday, January 21  Foerster, Section 149, problems 2738  good 
Thursday, January 20  Thomas, 1.8, Read the section and do problems 2,3,8,11,1519,20  excellent 
Wednesday, January 19  Thomas, 1.7, noting that the hint to problem 28 may be relevant to problem 15, do problems 15,16,22,23,24,25  good practice 
Tuesday, January 18  quiz on 1.7 and 149  91/100 
Monday, January 17  Foerster, Section 149: problems 1626  fair 
Friday, January 14  Thomas, 1.7: Read the section and do problems 6,8,9,11, and 12.  good 
Thursday, January 13  Foerster, Section 149: Read and do problems 215  good 
Wednesday, January 12   Lecture from Dad on "Linear Combination of Cosine and Sine"
 Foerster, Section 148: 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.
 Foerster, Section 148: problems 29a and 30a.
 Foerster, Section 149: problem 1
 good 
Tuesday, January 11  Thomas, 1.6: Read. Do problems 3 and 11.  excellent 
Monday, January 10 
 oneonone with teacher (Dad) regarding the limit of an infinite sequence
 Foerster, section 143, problems 35 and 45
 Foerster, section 144, problems 9 and 24
 Using Foerster, section 145, find the exact value of cos 22.5°.
 very good 
Friday, January 7  Read about calculus.  done 
Wednesday, January 5 
 Prove that the sum of two odd functions is odd.
 Foerster, section 142, problem 29
 Foerster, section 143, problems 28,34,53
 Foerster, section 144, problems 1,3,7,9,11
 excellent 
Tuesday, January 4  Foerster, section 143, problems 1,7,11,15,27,39,52,54  excellent 
Monday, January 3  Foerster, section 142, problems 1,6,17,26  excellent 
Friday, December 31  Test
 What is the inverse cosecant of the square root of 2?
 What is the period of f(x) = tan(2x+π)?
 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 29  Foerster, section 1210 numbers 8 & 11, section 1310 problems 5 & 12 section 1311 problem 4  excellent 
Tuesday, December 28  Foerster, section 1310, problems 1,2,3,11  excellent 
Monday, December 27  Foerster, section 136, problems 2,9,10, section 137, problems 6,8, section 138 problem 11  very good 
Sunday, December 26  Foerster, section 136, problems 3,6, section 137, problem 5  good 
Thursday, December 23  Foerster, section 136, problems 4,8,9, section 137, problems 4,5,10 (some redoing)  fair 
Wednesday, December 22  Foerster, section 136, problems 8&9, section 137, problem 4, section 138 choose two interesting problems  fair 
Monday, December 20  Foerster, section 127, problem 18, section 136, problem 8, section 137, problems 1,2,3  very good 
Friday, December 17  Lesson on trigonometric identities including the sum of angles formulas for sine and cosine. Foerster, section 143, problem 27  excellent 
Thursday, December 16  Foerster, section 129, Concept tests 1, 2, and 3  excellent 
Wednesday, December 15  Foerster, section 128, problems 10,11,13,14  good 
Tuesday, December 14  Foerster, section 128, problems 1,2,4,7,8  excellent 
December 6  December 13  Foerster, section 127, problems 1,3,5,7,9,11  excellent 
Friday, December 3  retest on the material covered by last week's test  90%, very good 
Wednesday, December 1  Foerster, section 126, all the oddnumbered problems  excellent 
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 23  Prepare for tomorrow's test.  done 
Friday, November 19 
Foerster, section 125, 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 125, problems 2,4,14,25,27,29,31,33,35 
good 
Wednesday, November 10 
 Explain why the sine of x in radians is close to x when x is a small angle.
 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 124, problems 13,15
Foerster, section 125, problems 1,3,5,7,9,11,13,15,17,19,21,23 
good 
Monday, November 8 
quickie review of Friday's solutions 
done 
Friday, November 5 
Foerster, section 124 
good 
Thursday, November 4 
Foerster, section 1111, Concepts Test 5 
very good 
Wednesday, November 3 
 Foerster, section 1110, problems 35,36,37,38,39,40, and...
 In problem 55, can you explain why the easy way works?

excellent 
Tuesday, November 2 
Foerster, section 1110, problems 27,29,34,5155
In problem 55, can you explain why the easy way works? 
very good 
Monday, November 1 
Foerster, section 1110, problems 1,14,16,17,23,24,26,33 
excellent 
Friday, October 29 
Foerster, section 119 This should be somewhat familiar, so do all of the exercises. 
excellent 
Thursday, October 28 
Foerster, section 107, Concepts Test 4 
very good 
Wednesday, October 27 
Foerster, section 107, Concepts Tests 1,2,3 
excellent 
Monday, October 25 
Foerster, section 107, review problem 2, second half
Foerster, section 107, review problem 3 
excellent 
Friday, October 22 
Foerster, section 102, Exercises 3,914,31,34,35,46
Foerster, section 107, review problem 2, first half 
excellent 
Thursday, October 21 
Foerster, section 106, Exercise 3
Foerster, section 107, review problem 1 
very good 
Wednesday, October 20 
Foerster, section 106, Exercise 7, including 7f 
good 
Monday, October 18 
Foerster, section 106, Exercise 6
Lesson with Dad 
excellent 
Friday, October 15 
Foerster, section 105, Exercises 42,43
Foerster, section 106, Exercises 1 
fair 
Wednesday, October 13 – Thursday, October 14 
Foerster, section 105, Exercises 3,5,23,29,37,38–41 
excellent 
Tuesday, October 12 
Foerster, section 105, Exercises 1,17,20,35,44 
excellent 
Monday, October 11 
Foerster, section 104, Exercises 1,20,35,39,53 
excellent 
Thursday, October 7 
Foerster, section 103, Exercises 20,21,23,24 
excellent 
Wednesday, October 6 
Foerster, section 102, Exercises 25,37,42,46,47,48 
excellent 
Tuesday, October 5 
Foerster, section 99, tests 4, 5, & 6 
excellent 
Monday, October 4 
 Define “parabola”.
 Foerster, section 99, tests 3, 4, & 5

very good 
Friday, October 1 
 Define “circle”.
 Foerster, section 99, tests 1 & 2

excellent 
Thursday, September 30 
 Lecture: a rigorous notation for defining “hyperbola”
 Define “line”.
 Define “ellipse”.

good 
Wednesday, September 29 
Foerster, section 99, 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 
 Foerster, section 99, review problems 2a and 1a
 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 98, Exercises 11,12,19 
very good 
Thursday, September 23 
Foerster, section 98, Exercises 10,27 
Wednesday, September 22 
Foerster, section 98, 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. 
fair 
Tuesday, September 21 
Foerster, section 98, Exercises 1,3,4,7

excellent 
Monday, September 20 
Foerster, section 96, Exercises 11,12,16,17

very good 
Friday, September 17 
Foerster, section 93, Exercise 8
Foerster, section 94, 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 96, Exercises 6,9,18

excellent after good 
Thursday, September 16 
Foerster, section 94. Exercise 15
Foerster, section 95. Exercise 8
Foerster, section 96. Exercises 1,7,5,13,18

good 
Wednesday, September 15 
Foerster, section 94. Exercises 9,11,13,17
Foerster, section 95. Exercises 1,3 
very good 
Tuesday, September 14 
Foerster, section 94. Exercises 1,3,5,7 
very good 
Thursday, September 9 
 Foerster, section 93. Exercises 1,3,5,7,9,11
 Give an equation of an ellipse with foci at (0,0) and at (2,0).
 Give an equation of a different ellipse with the same two foci.
 Give an equation of an ellipse that is similar (in the geometric sense) to
9x^{2}+25y^{2} = 225 ,
but with a different size.

very good after poor 
Wednesday, September 8 
 Foerster, section 91, 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.
 Foerster, section 92. Exercises 1,3,9,11,12,13,15,19a,20

very good 
Course Overview
 200409 to 200506
 Described as PreCalculus
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 CurryHoward 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 CurryHoward Isomorphism as well.
 For Calculus, the prime textbook candidate is the classic, by Thomas.
 For PreCalculus, the prime textbook is Algebra and Trigonometry, by Paul A. Foerster.
