## Phil’s Math Assignments

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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 includederivatives of basic functionsdifferentiation with the chain rulerelated rates, i.e. 3.6maxima and minimaApply the definition of continuous.limitsfinding indefinite and definite integralssimple differential equationsarea in relation to the definite integralderivatives of sine, cosine, exponential, and natural log 99/100 A+ Wednesday, July 6 Lecture on log and exponential.Thomas p. 441 problems 16 & 17Study for final. doneAt 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 12,39,45Study 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 14,20,44,47,59Thomas, 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 11-13 and 19. excellent Monday, June 27 Thomas Section 4.3 problems 8,9,12Section 4.4 problem 2lecture 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 lessonDo problems 1,2,3,10,12,15,17,20 excellent Wednesday, June 15 Thomas Section 3.5 problems 20,40,46,47Read the first half of Section 3.6 and do problem 7. very good Tuesday, June 14 Thomas Section 3.4 problem 14Section 3.5 problems 5,10,15,19,20,21 very good Monday, June 13 Thomas Section 3.4 problem 13,22,26Section 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 IIincluding Foerster 5-4 (complex numbers), 6-12 (logarithms), 10-4 (factoring, roots), 11-4 (series), 14-9 (solving trigonometric equations) done Monday, May 16 Correct the spelling: assummtoatThomas Section 3.3 problems 7,9,13,25,26,28,33,36 done Friday, May 13 Thomas: Section 3.2 problems 31,35,36,42lecture 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 23,29,30Section 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 5,23,24Section 2.11 review questions 4,7,11,13 good Wednesday, March 30 review of Newton's methodWrite 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(t5), 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(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. 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 3,27Lecture on chain ruleThomas 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 56Thomas 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 12,16,34,42,45Note 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 13,46Read Thomas, section 2.4. Do problems 1,2,10,30 very good Friday, March 4 presentation: notation and the quotient ruleThomas, 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 odd-numbered problems. very good 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. good 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 good 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 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 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 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 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 65,85Section 1.10: do problems 9,11,13,34,39Understand the definition of limit. very good Friday, February 4 Thomas, Section 1.9: do problems 64,86Section 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 xfor 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 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) 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 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 good 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°. very good 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 excellent 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 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 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 excellent 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. 65%, fair Tuesday, November 23 Prepare 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 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 good 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 Foerster, section 11-10, 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 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 11-9This should be somewhat familiar, so do all of the exercises. excellent 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 excellent Friday, October 22 Foerster, section 10-2, Exercises 3,9-14,31,34,35,46 Foerster, section 10-7, review problem 2, first half excellent 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 excellent Friday, October 15 Foerster, section 10-5, Exercises 42,43 Foerster, section 10-6, Exercises 1 fair 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 Define “parabola”. Foerster, section 9-9, tests 3, 4, & 5 very good Friday, October 1 Define “circle”. Foerster, section 9-9, tests 1 & 2 excellent Thursday, September 30 Lecture: a rigorous notation for defining “hyperbola” Define “line”. Define “ellipse”. good 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 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? 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. fair 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 excellentafter 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 good 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 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. very goodafter poor 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 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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