Math 410 Sections 0101 and 0401 Spring 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 for each star. The grader will be grading as large a subset of the assigned problems as possible within her 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 | Wed 1/25 |
| Chapter 1 - Tools for Analysis | ||
| 1.1 | The Completeness Axiom and Some of Its Consequences | Fri 1/27 |
| 1.2 | The Distribution of the Integers and the Rational Numbers | Mon 1/30 |
| 1.3 | Inequalities and Identities | Wed 2/1 |
| Chapter 2 - Convergent Sequences | ||
| 2.1 | The Convergence of Sequences | Fri 2/3, Mon 2/6 |
| 2.2 | Sequences and Sets | Mon 2/6, Wed 2/8 |
| 2.3 | The Monotone Convergence Theorem | Fri 2/10 |
| 2.4 | The Sequential Compactness Theorem | Mon 2/13 |
| Chapter 3 - Continuous Functions | ||
| 3.1 | Continuity | Wed 2/15 |
| 3.2 | The Extreme Value Theorem | Fri 2/17 |
| 3.3 | The Intermediate Values Theorem | Fri 2/17 |
| 3.4 | Uniform Continuity | Mon 2/20 |
| 3.5 | The Epsilon-Delta Criterion for Continuity | Wed 2/22 |
| 3.6 | Images and Inverses: Monotone Functions | Fri 2/24 |
| 3.7 | Limits | Mon 2/27 |
| Chapter 4 - Differentiation | ||
| 4.1 | The Algebra of Derivatives | Mon 3/5, Wed 3/7 |
| 4.2 | Differentiating Inverses and Compositions | Fri 3/9 |
| 4.3 | The Mean Value Theorem and Its Geometric Consequences | Mon 3/12 |
| 4.4 | The Cauchy Mean Value Theorem and Its Analytic Consequences | Wed 3/14 |
| 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 | |
| 8.4 | A Power Series for the Logarithm | |
| 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
Basic paper syllabus