First semester of a year course covering sequences and series of numbers, continuity and differentiability of real valued functions of one variable, the Riemann integral, sequences of functions and power series, functions of several variables including partial derivatives, multiple integrals, and line and surface integrals, the implicit function theorem. The first semester deals with the rigorous analysis of functions of one variable.
Instructor : J. Osborn
Prerequisite: MATH 240 and MATH 241, with grade of C or better. Not open to students who have completed MATH 350.
Text: Advanced Calculus, P. M. Fitzpatrick, PWS Publishing Company, 1996.
Topics| Chapter 1. The Real Numbers |
| Chapter 2. Sequences of Real Numbers |
| Chapter 3. Continuous Functions and Limits |
| Chapter 4. Differentiation |
| Chapter 5. Elementary Functions as Solutions of Differential Equations |
| Chapter 6. Integration |
| Chapter 7. The Second Fundamental Theorem and Its Consequences |
| Chapter 8. Approximation by Taylor Polynomials |
| Chapter 9. The Convergence of Sequences and Series of Functions |
Grading Policy: Grades will be based on two hour exams (25% each), homework (10%), and the final exam (40%).
Homework Assignments:
| Sect 1.1: | 1,2,3,4,5,7,8 |
| Sect. 1.2: | 1,2,3,4,5,8,9 |
| Sect. 1.3: | 1,4,5,8,9,10,14,15,18,23,24 |
| Sect. 2.1: | 1,2,3,5,6,7,8,9,13,14 |
| Sect. 2.2: | 1,2,3,5,6,8,9 |
| Sect. 3.1: | 1,2,3,4,5,7 |
| Sect. 3.2: | 1,2,7 |
| Sect. 3.3: | 1,2,3,6,8,9 |
| Sect. 3.4: | 1,2,3,4,5 |
| Sect. 3.5: | 1,2,3,4,5,6,8,9,10 |
| Sect. 3.6: | 1,2,3,4,10,12 |
| Sect. 4.1: | 1(a),2,4,6,7,10,11 |
| Sect. 4.2: | 2,4,5,6,10 |
| Sect. 4.3: | 1,2,3,5,9,12,14 |
| Sect. 4.4: | 1(a), 1(d), 6,8 |
| Sect. 5.1: | 1,2,3,5,10,11 |
| Sect. 5.2: | 1,3,6,7,15 |
| Sect. 5.3: | 1,2,5 |
| Sect. 6.2: | 1,2,4,6,7 |
| Sect. 6.3: | 1,2,3(a), 3(d) |
| Sect. 6.4: | 3,4,6,8 |
| Sect. 6.5: | 3,4,5,7 |
| Sect. 7.1: | 1,2(a),2(b),3,4,6 |
| Sect. 7.2: | 1,2,3,4,5 |
| Sect. 7.3: | 1,2,3,4,5 |
| Sect. 8.1: | 1(a),1(b),2,3 |
| Sect. 8.2: | 1,2,3,7,8,9 |
| Sect. 8.3: | 1,2,3 |
| Sect. 8.4: | 1,2 |
| Sect. 8.5: | 6 |
| Sect. 9.1: | 1,2,3,4,8 |
| Sect. 9.2: | 1,,2,3,4,5 |
| Sect. 9.3: | 1,2 |
| Sect. 9.4: | 1,2,3,4,5,6,7 |
Hand-in Assignment Policy Starting with Chapter 3 homework, you are to hand in the entire assignment. A selection of these problems will be graded. Each problem will be worth five points. Let me expalin one aspect of the grading system by considering an example. Suppose seven problems are graded. The grader then will look over your entire paper, and, if most of the problems have been done, will add 15 additional points, i.e., three problems worth of points. So, of the total grade, 30% would be for turning in the problems. To help the grader identiy the problems, please use a marker to highlight the section and problem numbers.
Hand-in Assignments:
| Chapter 1, due 9/15: | ||
| page A6: | 1,4 | |
| Sect 1.1: | 4,5,7 | |
| Sect. 1.2: | 3,5 | |
| Sect. 1.3: | 1,3,9,10,15,17 | |
| Chapter 2, due 9-24: | ||
| Sect 2.1: | 1,2,5,8,13,14 | |
| Sect 2.2: | 1,3,6,8 | |
| Chapter 3, due 10-04 | <\tr>||
| Graded Problems: | ||
| Sect. 3.1: | 2,5 | |
| Sect. 3.2: | 1(a), 2 | <\tr>|
| Sect. 3.3: | 2,3 | |
| Sect. 3.4: | 1,2 | |
| Sect. 5.5: | 2,8 | |
| Sect. 3.6: | 4,12 | |
| Chapter 4, due 10-15 | ||
| Graded Problems: | ||
| Sect. 4.1: | 1(a),7 | |
| Sect. 4.2: | 2,6 | |
| Sect. 4.3: | 5,9 | |
| Sect. 4.4: | 1(d),8 | |
| Sect. 4.5: | 3,10 | |
| Chapter 5, due 10-29 | ||
| Graded Problems: | ||
| Sect. 5.1: | 3,10,11 | |
| Sect. 5.2: | 6,15 | |
| Sect. 5.3: | 1,2 | |
| Chapter 6, due 11-8 | ||
| Graded Problems: | ||
| Sect. 6.2: | 1,2 | |
| Sect. 6.3: | 1,3(a) | |
| Sect. 6.4: | 6,8 | |
| Sect. 6.5: | 4,5 | |
| Chapter 7, due 11-19 | ||
| Graded Problems: | ||
| Sect. 7.1: | 1(a),1(c),2(a) | |
| Sect. 7.2: | 1(a),4,5 | |
| Sect. 7.3: | 1(a),2(b),5 | |
| Chapter 8, due 11-29 | ||
| Graded Problems: | ||
| Sect. 8.1: | 1(a), 2 | |
| Sect. 8.2: | 1,2 | |
| Sect. 8.3: | 1(a),2 | |
| Sect. 8.4: | 1 | |
| Sect. 8.5: | 6 | |
| Chapter 9, due 12-10 | Graded Problems: | |
| Sect. 9.1: | 1(a), 1(c),1(g),3,8 | |
| Sect. 9.2: | 2,3 | |
| Sect. 9.3: | 2 | |
| Sect. 9.4: | 1(a),2,5 |
Honor Pledge: Students are asked to write and sign the Campus Honor Pledge, "I pledge on my honor that I have not given or received any unauthorized assistance on this assignment/examination", on each hour exam and the final exam.
Make-up Policy: Make-up examinations will be given only in the case of an absence caused by illness, religious observance, participation in a University activity at the request of University authorities, or compelling circumstances beyond the student's control. If you miss an exam, please present convincing reasons for your absence (doctor's note,...) as soon as possible. If possible, an absence should be arranged before the exam.
Students With Disabilities: If you have a documented disability and wish to discuss academic accommodations with me, please contact me as soon as possible.
First Midterm Exam: Friday, October 29.
Second Midterm Exam: Friday, December 3.
Final Exam: Tuesday, December 14, 1:30--3:30.