Advanced Calculus

Fall 2012



Week 1 (Aug 27 - Aug 31)

  • Introductory Day + Preliminaries
  • Ch 1: Completeness Axiom
  • Ch 1: Integers, Rationals
  • Ch 1: Inequalities, Identities

Week 2 (Sep 3 - Sep 7) **Events Calendar**

  • Labor Day (No Class)
  • Ch 2: Covergence of Sequences
  • Ch 2: Sequences and Sets
  • Hands On Day

Week 3 (Sep 10 - Sep 14) **Events Calendar**

  • Ch 2: Monotone Convergence Thm
  • Ch 2: Sequential Compactness
    • Skip Covering Properties
  • Hands On Day
  • Ch 3: Continuity

Week 4 (Sep 17 - Sep 21)

  • Ch 3: Extreme Value Theorem
  • Ch 3: Intermediate Value Theorem
  • Ch 3: Uniform Continuity
  • Hands On Day

Week 5 (Sep 24 - Sep 28)

  • Ch 3: ε-δ Criterion for Continuity
  • Hands On Day
  • Exam One
  • Ch 3: Images and Inverses

Week 6 (Oct 1 - Oct 5)

  • Ch 3: Limits
  • Ch 4: Algebra of Derivatives
  • Hands On Day
  • Ch 4: Differentiating Inverses/Compositions

Week 7 (Oct 8 - Oct 12) **Events Calendar**

  • Ch 4: Mean Value Theorem
  • Ch 4: Cauchy Mean Value Theorem
  • Hands On Day
  • Ch 4: Leibnix Notation

Week 8 (Oct 15 - Oct 19)

  • Fall Break
  • Fall Break
  • Ch 5: Solutions of ODE's
  • Ch 5: Logs and Exps
    • Skip Trigs, Inverse Trigs

Week 9 (Oct 22 - Oct 26)

  • Ch 6: Darboux Sums
  • Hands On Day
  • Exam Two
  • Ch 6: Archimedes-Riemann

Week 10 (Oct 29 - Nov 2)

  • Ch 6: Additivity, Montonicity, Linearlty
  • Ch 6: Continuity and Integrability
  • Ch 6: First Fundamental Theorem
  • Hands On Day

Week11 (Nov 5 - Nov 9) **Events Calendar**

  • Ch 6: Second Fundamental Theorem
  • Ch 7: Solutions of ODE's
  • Hands On Day
  • Ch 7: Integration by Parts, Substitution

Week 12 (Nov 12 - Nov 16) **Events Calendar**

  • Ch 7: Convergence of Darboux/Riemann sums
  • Hands On Day
  • Exam Three
  • Ch 7: Approximating Integrals

Week 13 (Nov 19 - Nov 23)

  • Ch 8: Taylor Polynomials
  • Ch 8: Lagrange Remainder Theorem
  • Thanksgiving
  • Thanksgiving

Week 14 (Nov 26 - Nov 30)

  • Ch 8: Convergence of Taylor Polynomials
  • Ch 8: Logarithm as Power Series
  • Hands On Day
  • Ch 8: Cauchy Integral Remainder Theorem

Week 15 (Dec 3 - Dec 7)

  • Ch 8: A Monstrous Function
  • Weierstrass Approximation Theorem
  • No Class (Reading Period)
  • No Class (Reading Period)

Notes

  1. 53 Class days
  2. 3 In class exams + Final
  3. 12 Hands On and absorb days