Math 410 Section 0501 Fall 2012
Justin Wyss-Gallifent
Resources
Basics
Homework and Due Dates
Important notes: Each homework problem is rated as either one, two or three stars in accordance with difficulty level (as judged by me). A problem is worth 5 points per star. The grader will be grading as large a subset of the assigned problems as possible within his employment obligations!Point Total and Grading
| Homework | 200 pts |
| Quizzes | 50 pts |
| Midterm 1 | 100 pts |
| Midterm 2 | 100 pts |
| Final | 200 pts |
| Total | 650 pts |
Topics
| Preliminaries | |
| Handout | Stuff You Should Know |
| Chapter 1 - Tools for Analysis | |
| 1.2,1.3 | Preliminary Topics |
| Chapter 2 - Convergent Sequences | |
| 2.1 | The Convergence of Sequences |
| 2.2 | Sequences and Sets |
| 2.3 | The Monotone Convergence Theorem |
| 2.4 | The Sequential Compactness Theorem |
| Chapter 3 - Continuous Functions | |
| 3.1 | Continuity |
| 3.2 | The Extreme Value Theorem |
| 3.3 | The Intermediate Values Theorem |
| 3.4 | Uniform Continuity |
| 3.5 | The Epsilon-Delta Criterion for Continuity |
| 3.6 | Images and Inverses: Monotone Functions |
| 3.7 | Limits |
| Chapter 4 - Differentiation | |
| 4.1 | The Algebra of Derivatives |
| 4.2 | Differentiating Inverses and Compositions |
| 4.3 | The Mean Value Theorem and Its Geometric Consequences |
| 4.4 | The Cauchy Mean Value Theorem and Its Analytic Consequences |
| 4.5 | The Notation of Liebnitz |
| Chapter 6 - Integration: Two Fundamental Theorems | |
| 6.1 | Darboux Sums: Upper and Lower Integrals |
| 6.2 | The Archimedes-Riemann Theorem |
| 6.3 | Additivity, Monotonicity and Linearity |
| 6.4 | Continuity and Integrability |
| 6.5 | The First Fundamental Theorem: Integrating Derivatives |
| 6.6 | The Second Fundamental Theorem: Differentiating Integrals |
| Chapter 8 - Approximation by Taylor Polynomials | |
| 8.1 | Taylor Polynomials |
| 8.2 | The Lagrange Remainder Theorem |
| 8.3 | The Convergence of Taylor Polynomials |
| 8.5 | The Cauchy Integral Remainder Theorem |
| 8.7 | The Weierstrass Approximation Theorem |
| Chapter 9 - Sequences and Series of Functions | |
| 9.1 | Sequences and Series of Functions |
| 9.2 | Pointwise Convergence of Sequences of Functions |
| 9.3 | Uniform Convergence of Sequences of Functions |
| 9.4 | The Uniform Limits of Functions |
| 9.5 | Power Series |
Class Material - Syllabus, Matlab, Miscellaneous
exam1spring.pdf Exam 1 from Spring 2012. The average was 54/100. The curve was 80=A, 60=B, 40=C, 35=D.