||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|
|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.
- finding indefinite and definite integrals
- simple differential equations
- area in relation to the definite integral
- derivatives of sine, cosine, exponential, and natural log
|Wednesday, July 6||Lecture 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 5||Thomas 4.8 problems 12,39,45|
Study for final.
|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.
|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 11-13 and 19.
|Monday, June 27||Thomas Section 4.3 problems 8,9,12|
Section 4.4 problem 2
lecture on definite integrals
|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
|Wednesday, June 15||Thomas Section 3.5 problems 20,40,46,47|
Read the first half of Section 3.6 and do problem 7.
|Tuesday, June 14||Thomas Section 3.4 problem 14|
Section 3.5 problems 5,10,15,19,20,21
|Monday, June 13||Thomas Section 3.4 problem 13,22,26|
Section 3.5 problems 1,4
|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 5-4 (complex numbers), 6-12 (logarithms), 10-4 (factoring, roots), 11-4 (series), 14-9 (solving trigonometric equations)
|Monday, May 16||Correct the spelling: assummtoat|
Thomas Section 3.3 problems 7,9,13,25,26,28,33,36
|Friday, May 13||Thomas: Section 3.2 problems 31,35,36,42|
lecture on symmetry and asymptotes
|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
|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
|Friday, April 8||Thomas Section 2.11 Miscellaneous Problem 104
Section 2.5 Problem 24
Section 2.11 Miscellaneous Problems 2,8,24,26
|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
|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
|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
|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.
|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
|Thursday, March 24|
- Suppose k'(x)=1/x.
If g(t)=k(t5), find g'(t).
- Read Thomas section 2.8.
- Thomas section 2.8, problems 21,22,23,44,53
|Wednesday, March 23|
Use the chain rule and trig identities to show that cos'(x)= -sin(x).
- Thomas 2.7 problems 29,35,39,42
|Tuesday, March 22|
- Suppose k'(x)=1/x.
If g(t)=k(t2), find g'(t).
- Suppose f'(x)=2x.
If h(y)=f(½y+3), find h'(y).
- Use the definition of derivative to find the derivative of the sine function.
|Monday, March 21||Read Thomas 2.6 on parametric equations.|
Thomas 2.6 problems 4,11,14,16,20,22
|Friday, March 18||Thomas 2.5 problems 3,27|
Lecture on chain rule
Thomas 2.6 problems 1,2,3
|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
|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
|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.
|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
|Monday, March 7||Thomas, 2.3 problems 13,46|
Read Thomas, section 2.4. Do problems 1,2,10,30
|Friday, March 4||presentation: notation and the quotient rule|
Thomas, 2.3 problems 2,15,17,29,35,37,38
|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
|Monday, February 28||Thomas, 2.2 problems 15,23,26,31|
Read part 2.3 and start on the odd-numbered problems.
|Friday, February 25||Closed book test on Thomas, Section 1 (limits and the definition of derivative)||95/100|
|Wednesday-Thursday, February 23-24||Thomas, 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 22||Thomas, Section 1 Miscellaneous problems on pp. 93-94: 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
|Thursday, February 17|
- Prove that the limit as x approaches 2 of x2 is 4.
- 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)
|Monday, February 14||
Thomas, Section 1.11 problems 8,13,15,16,24,27,38||excellent|
|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
|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.
|Tuesday, February 8||Let 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 7||Thomas, Section 1.9: do problems 65,85|
Section 1.10: do problems 9,11,13,34,39
Understand the definition of limit.
|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
|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.
|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 1-7. Also practice problems from 14-9, 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)
|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 14-9, problems 27-38||good|
|Thursday, January 20||Thomas, 1.8, Read the section and do problems 2,3,8,11,15-19,20||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 14-9||91/100|
|Monday, January 17||Foerster, Section 14-9: problems 16-26||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 14-9: Read and do problems 2-15||good|
|Wednesday, January 12|
- Lecture from Dad on "Linear Combination of Cosine and Sine"
- 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.
- Foerster, Section 14-8: problems 29a and 30a.
- Foerster, Section 14-9: problem 1
|Tuesday, January 11||Thomas, 1.6: Read. Do problems 3 and 11.||excellent|
|Monday, January 10|
- one-on-one with teacher (Dad) regarding the limit of an infinite sequence
- Foerster, section 14-3, problems 35 and 45
- Foerster, section 14-4, problems 9 and 24
- Using Foerster, section 14-5, find the exact value of cos 22.5°.
|Friday, January 7||Read about calculus.||done|
|Wednesday, January 5|
- Prove that the sum of two odd functions is odd.
- Foerster, section 14-2, problem 29
- Foerster, section 14-3, problems 28,34,53
- Foerster, section 14-4, problems 1,3,7,9,11
|Tuesday, January 4||Foerster, section 14-3, problems 1,7,11,15,27,39,52,54||excellent|
|Monday, January 3||Foerster, section 14-2, problems 1,6,17,26||excellent|
|Friday, December 31||Test|
Supertest: Simplify sin(x+4½π).
- 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.
|Wednesday, December 29||Foerster, section 12-10 numbers 8 & 11, section 13-10 problems 5 & 12 section 13-11 problem 4||excellent|
|Tuesday, December 28||Foerster, section 13-10, problems 1,2,3,11||excellent|
|Monday, December 27||Foerster, section 13-6, problems 2,9,10, section 13-7, problems 6,8, section 13-8 problem 11||very good|
|Sunday, December 26||Foerster, section 13-6, problems 3,6, section 13-7, problem 5||good|
|Thursday, December 23||Foerster, section 13-6, problems 4,8,9, section 13-7, problems 4,5,10 (some redoing)||fair|
|Wednesday, December 22||Foerster, section 13-6, problems 8&9, section 13-7, problem 4, section 13-8 choose two interesting problems||fair|
|Monday, December 20||Foerster, section 12-7, problem 18, section 13-6, problem 8, section 13-7, 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 14-3, problem 27
|Thursday, December 16||Foerster, section 12-9, Concept tests 1, 2, and 3||excellent|
|Wednesday, December 15||Foerster, section 12-8, problems 10,11,13,14||good|
|Tuesday, December 14||Foerster, section 12-8, problems 1,2,4,7,8||excellent|
|December 6 - December 13||Foerster, section 12-7, 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 12-6, all the odd-numbered 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.
|Tuesday, November 23||Prepare for tomorrow's test.||done|
|Friday, November 19
||Foerster, section 12-5, problems 30,31,33,35
|Thursday, November 18
||Explain why the sine of x in radians is close to x when x is a small angle.
|Wednesday, November 17
||Foerster, section 12-5, problems 2,4,14,25,27,29,31,33,35
|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 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
|Friday, November 5
||Foerster, section 12-4
|Thursday, November 4
||Foerster, section 11-11, Concepts Test 5
|Wednesday, November 3
- Foerster, section 11-10, problems 35,36,37,38,39,40, and...
- 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?
|Monday, November 1
||Foerster, section 11-10, problems 1,14,16,17,23,24,26,33
|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
|Wednesday, October 27
||Foerster, section 10-7, Concepts Tests 1,2,3
|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
|Wednesday, October 20
||Foerster, section 10-6, Exercise 7, including 7f
|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
|Tuesday, October 12
||Foerster, section 10-5, Exercises 1,17,20,35,44
|Monday, October 11
||Foerster, section 10-4, Exercises 1,20,35,39,53
|Thursday, October 7
||Foerster, section 10-3, Exercises 20,21,23,24
|Wednesday, October 6
||Foerster, section 10-2, Exercises 25,37,42,46,47,48
|Tuesday, October 5
||Foerster, section 9-9, tests 4, 5, & 6
|Monday, October 4
- Define “parabola”.
- Foerster, section 9-9, tests 3, 4, & 5
|Friday, October 1
- Define “circle”.
- Foerster, section 9-9, tests 1 & 2
|Thursday, September 30
- Lecture: a rigorous notation for defining “hyperbola”
- Define “line”.
- Define “ellipse”.
|Wednesday, September 29
||Foerster, section 9-9, review problems 2b, 1b, and 1c
|Tuesday, September 28
||Discuss with Dad: Supposing the graph of
xy=1 is a hyperbola, how can I find its foci?
|Monday, September 27
- Foerster, section 9-9, 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?
|Friday, September 24
||Foerster, section 9-8, Exercises 11,12,19
|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
|Monday, September 20
||Foerster, section 9-6, Exercises 11,12,16,17
|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
|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
|Tuesday, September 14
||Foerster, section 9-4. Exercises 1,3,5,7
|Thursday, September 9||
- Foerster, section 9-3. 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
9x2+25y2 = 225,
but with a different size.
|Wednesday, September 8||
- 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.
- Foerster, section 9-2. Exercises 1,3,9,11,12,13,15,19a,20
- 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.