| Professor: | Dr. Douglas Anderson |
| Ivers 234G | |
| 299-4453 | |
| andersod@cord.edu |
Office Hours: Tuesday and Thursday 1-4; other times by discovery.
Purpose: The purpose of this course is to revisit the essential issues of the calculus: sequences, limits, continuity, differentiation, integration, and series, placing them on a rigorous foundation based on definition, theorem, and proof. To accomplish this goal, every exercise will involve the method of formal mathematical proof; no computational or practical examples need be expected. Ultimately we believe the clarity and precision of rigorous, analytic proofs train and discipline our thinking in a way that leads toward a more beautiful mind.
Text: Introduction to Analysis, 5th edition, by Edward D. Gaughan
Homework: Homework will be assigned each day for your development toward mastering the material, and will be due two class periods later. Each will be worth 30 points. I will drop your four (4) lowest homework scores before calculating your overall homework grade. Homework that is turned in should be neat and organized. You will not only be graded on correct answers but also on the neatness, organization, steps used to derive your answers, and the use of correct English grammar and complete sentences.
Exams: There will be three (3) unit exams, plus the final exam.
| Grading: | Points | Scale | |||
| Homework | 200 | A 90%--100% | |||
| Exams(3) | 300 | B 80%--89% | |||
| Final Exam | 200 | C 70%--79% | |||
| D 60%--69% | |||||
| F Below 60% |
| Date | Section | Exercises |
| Sept 2 | 0.1 Sets | (27) 6,7,10,11,12 |
| 5 | 0.2 Relations/Functions | (28) 14,15,16,17,18 |
| 7 | 0.3 Induction | (28) 20,21,22,23,24; read 28 |
| 9 | 0.4 Countability | (29) 32 (n>=1),33,34,35 (n>=1),36,37 |
| 12 | Fall Symposium | No Class |
| 14 | 0.5 Real Numbers | (29) 41,43,45,46,47; read 40,44 |
| 16 | 1.1 Sequences/Convergence | (54) 2,6d,8,9,10; read 7,11 |
| 19 | 1.2 Cauchy Sequences | (55) 14,15,16,18,22,24 |
| 21 | 1.3 Limit Theorems | (56) 25,26,27,28,30,other |
| 23 | 1.4 Subsequences | (57) 35,36,40,41,43,44 |
| 26 | Project | (59) Project 1.3 |
| 28 | Review | |
| 30 | EXAM I | |
| Oct 3 | 2.1 Limits of Functions | (79) 2,4,5,6,7 |
| 5 | 2.2 Functions/Sequences | (79) 11,12,13,14,15 |
| 7 | 2.3 Limit Theorems | (80) 18,20,21,22,26 |
| 10 | 2.4 Monotone Functions | (80) 23, 24: f decreasing, 25 |
| 12 | 3.1 Continuity | (104) 4,6,8,7,10 |
| 14 | 3.2 Continuous Functions | (104) 12,13,14,15,17 |
| 17 | 3.3 Uniform Continuity | (105) 19-23 |
| 19 | 3.3 Real-line Topology | (105) 28,30,31,36,38 |
| 21 | Fall Break | No Class |
| 24 | 3.4 Continuous Functions | (106) 42-45 |
| 26 | Review | |
| 28 | EXAM II | |
| 31 | 4.1 Derivatives | (129) 3,6,7,8,9 |
| Nov 2 | 4.2 Derivative Rules | (130) 11,12,13,16,19 |
| 4 | 4.3 Mean-Value Theorem | (130) 20,22,23,25 |
| 7 | 4.4 L'Hospital's Rule | (131) 32,35,37 |
| 9 | 5.1 Riemann Integral | (165) 2,3 |
| 11 | 5.2 Integrable Functions | (166) 7,9 |
| 14 | 5.3 Riemann Sums | (166) 10,11,12 |
| 16 | 5.4, 5.5 FTC | |
| 18 | 5.5, 5.6 Integrable Functions | (167) 18,22,23 |
| 21 | 6.1 Infinite Series | Handout 1-10 |
| 23 | 6.2 Absolute Convergence | (207) 13,14,15 |
| 25 | Thanksgiving Recess | No Class |
| 28 | Review | |
| 30 | EXAM III | |
| Dec 2 | 6.3 Ratio and Root Tests | (208) 21(typo),22,23 |
| 5 | 6.4 Conditional Convergence | (208) 27 |
| 7 | 6.5 Power Series | (209) 32,33 |
| 9 | 7.1 Sequences of Functions | (232) 1,3,5 |
| 12 | Review | |
| 15 | Final Exam | Thursday 2:00~4:00 |