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{\bf Math 165: Honors Calculus \hfill Syllabus \hfill Fall 1994}
\halign{\strut\hfil #\ &#\quad\hfil&#\hfil\cr
\week
Aug. 31 & I2, I3.2--4 Axioms for real numbers & \#1,p.19:4,5,8,9,10, p.22:2,4,5,9,10\cr
Sep.  1 & I3.6--7 Inductive sets, Integers, Rationals\cr
      2 & I4.1--2 Induction & \#2,p.35:1--6,9,12\cr
\week
      5 & I4.6 Summation notation & \#3,p.40:3,4,5,6,8,11\cr
      7 & I4.8 Absolute value and triangle inequality & \#4,p.43:1,2 + suppl.\cr
      8 & Quiz 1\cr
      9 & I4.10 Pascal's triangle, binomial theorem\cr
\week
     12 & 1.1--4 Functions & \#5,p.56:5,6,8,10,11\cr
     14 & 1.4,1.8 Polynomials, ordinate sets & \#6,p.63:1--4\cr
     15 & Quiz 2\cr
     16 & 1.9--10 Partitions and step functions & \#7,p.70:1,2,3,4,6a,11\cr
\week
     19 & 1.12--13 Integrals for step functions & \#8, read I3.8--11 + suppl.\cr
     21 & Sup and inf\cr
     22 & Quiz 3\cr
     23 & 1.16--17 Upper \& lower integrals\cr
\week
     26 &1.20-1.21 Monotonic functions and integrability & \#9,p.83:1-4,10,16,20,21--23,25\cr
     28 &1.22--23 Calculation of integrals, $\int x^p dx$\cr
     29 &Quiz 4\cr
     30 &1.24-25 Properties of integrals, polynomials & \#10,p,94:1--7,11,15,17\cr
\week
Oct.  3 &2.2 Area between curves\cr
      5 &2.2 More area & \#11,p.104:1--5,8,9,14,15\cr
      6 &Quiz 5\cr
      7 &2.5--7 Trig functions\cr
\week
     10 &2.16 Average value of a function & \#12,p.119:1--4,11,18,19+20 =`a' only\cr
     12 &2.18 Integral as function & \#13,p.124:1,3,5,7\cr
     13 &Exam 1\cr
     14 &Go over Exam\cr
\week
     17 &3.1 Limits & \#14, suppl.\cr
     19 &3.2 More limits \cr
     20 &Quiz 6, 3.3 Continuity\cr
     21 &3.4 Continuity & \#15,p.138:1--5,8--12,15,20--23,32\cr
\week
 22--30 &{\bf Midsemester Break}\cr
\week
     31 &3.4 More continuity\cr
Nov.  2 &3.5 Basic Limit Theorems & \#16,p.142:1--21 (ans. to 20 is 2)\cr
      3 &Quiz 7, 3.7 Composite functions\cr
      4 &3.9 Bolzano's Theorem & \#17,p.145:1--6 (omit 2bc)\cr
\week
      7 &3.10 Intermediate Value Theorem\cr
      9 &3.12 Inverse functions & \#18,p.149: 1--5 + suppl.\cr
     10 &Quiz 8\cr
     11 &3.13--14 Properties of inverses \cr
\week
     14 &3.16 Boundedness Theorem, Extreme Value Theorem & \#19 suppl.\cr
     16 &3.17--18 Small Span Thm, Integrability of cont. fns.& \#20,p.155:1--3,6--8\cr
     17 &Quiz 9\cr
     18 &3.19 Mean Value Theorem, Derivatives \cr
\week
     21 &4.1--4 Derivatives & \#21, suppl. (p.105 in notes)\cr
     23 &4.5 Power rule, higher derivatives &\#22,p.167:3--12,16--23,25--38\cr
     24 & Thanksgiving\cr
\week
     28 &4.6--10 Tangent line, chain rule & \#23,p.173: 1--5,7,9,14,15\cr
     30 &4.11 Implicit derivatives & \#24,p. 179:1--19odd\cr
Dec.  1 &Exam 2\cr
      2 &4.11 Related rates & \#25,p.180:20--24,30--34\cr
\week
      5 &4.13 Extreme values & \#26,p.186:1--9 \cr
      7 &4.14Mean Value Theorem for Derivatives & \#27,p.191:1--14\cr
      8 &Quiz 10, 4.17 2nd derivative test\cr
      9 &4.17 Convexity &(\#28,p.194:1--19odd)\cr
\week
     12 &Extrema problems, review, student evaluations\cr
     14 &Study Day\cr
\week
Mon. 19 &Final Exam, 1:45--3:45\cr
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