# Duke Math 431, Advanced Calculus I, Spring 2015

**Instructor:** Henry Adams
**Email:** henry dot adams at colostate dot edu

**Lectures:** MWF 3:20-4:10pm in Gross Hall 304B
**Textbook:** *Fundamental Ideas of Analysis* by Michael Reed

List of typos

**Overview:** This course is a proof-based introduction to elementary mathematical analysis. Topics covered include cardinality of sets, convergence of sequences, continuous functions, the Riemann integral, differentiation, sequences of functions, metric spaces, and completeness. Students will learn how to write rigorous mathematical proofs and how to construct counterexamples.

**Syllabus:** Here is the course syllabus.

## Homework

Homework 1 is due Friday, January 16.Homework 2 is due Friday, January 23.

Homework 3 is due Friday, January 30.

Homework 4 is due Friday, February 6.

Homework 5 is due Friday, February 13.

Homework 6 is due Friday, February 27.

Homework 7 is due Friday, March 6.

Homework 8 is due Friday, March 20.

Homework 8.5 is not to be turned in or graded.

Homework 9 is due Friday, April 3.

Homework 10 is due Friday, April 10.

Homework 11 is due Friday, April 17.

Homework 12 is not to be turned in or graded.

All homework is due at the beginning of class. Solutions will be posted on Sakai.

## Exams

Here is a Practice Midterm 1, posted February 9.Here are Solutions to Practice Midterm 1, posted February 10.

Here is a Midterm 1, taken February 16.

Here are Solutions to Midterm 1, posted February 18.

Here is a Practice Midterm 2, posted March 21.

Here are Solutions to Practice Midterm 2, posted March 24.

Here is a Midterm 2, taken March 27.

Here are Solutions to Midterm 2, posted March 28.

Here is a Practice Final, posted April 19.

Here are Solutions to the Practice Final, posted April 21.

## Notes

A proof that zero is less than one, posted January 15.Why is the definition of two sets having the same cardinality symmetric?, posted January 23.

Proof of Theorem 2.2.6, posted January 31.

Proof of Corollary 3.3.6, posted February 25.

Lipschitz vs uniform continuity, posted March 24.

## Schedule

Date |
Text |
Remark |

Jan 7 | §1.1 | |

Jan 9 | §1.1, §1.2 | |

Jan 12 | §1.2 | |

Jan 14 | §1.3 | |

Jan 16 | §1.3, §1.4 | Homework 1 due |

Jan 19 | MLK Day | |

Jan 21 | §1.4 | Drop/add ends |

Jan 23 | §2.1 | Homework 2 due |

Jan 26 | §2.1, §2.2 | |

Jan 28 | §2.2 | |

Jan 30 | §2.4 | Homework 3 due |

Feb 2 | §2.4, §2.5 | |

Feb 4 | §2.5, §2.6 | |

Feb 6 | §2.6 | Homework 4 due |

Feb 9 | §3.1 and Review | |

Feb 11 | §3.1 and Review | |

Feb 13 | Review | Homework 5 due |

Feb 16 | Midterm #1 | Midterm through §2.6 |

Feb 18 | §3.1 | |

Feb 20 | §3.2 | |

Feb 23 | §3.2, §3.3 | |

Feb 25 | §3.3, §4.1 | |

Feb 27 | §4.1 | Homework 6 due |

Mar 2 | §4.2 | |

Mar 4 | §4.3 | |

Mar 6 | §4.3, §4.5 | Homework 7 due |

Spring Break, March 9-13 | ||

Mar 16 | §4.5 | |

Mar 18 | §5.1 | |

Mar 20 | §5.1, §5.2 | Homework 8 due |

Mar 23 | §5.2 | |

Mar 25 | Review | Last day to withdraw |

Mar 27 | Midterm #2 | Midterm through §4.5 |

Mar 30 | §5.3 | |

Apr 1 | §5.3, §5.6 | |

Apr 3 | §5.6 | Homework 9 due |

Apr 6 | §5.7 | |

Apr 8 | §5.7, §6.1 | |

Apr 10 | §6.1 | Homework 10 due |

Apr 13 | §6.2 | |

Apr 15 | §6.2 | |

Apr 17 | Review and class picture | Homework 11 due |

Apr 20 | Review | |

Apr 22 | Review | |

Final Exam, Thursday April 30, 2:00-5:00pm |