Leo Villani

Leo Villani

Statistics

Math 1B

Math 1B, UC Berkeley, 2023

Hi, I’m Leo Villani. Here are the resources I use / mention in discussion section this semester. :D

Logistics

  • Lecture: MoWeFr 11:00–11:59 AM — Wheeler 150
  • Discussion 1: MoWeFr 10:00–11:00 AM — Etcheverry 3119
  • Discussion 2: MoWeFr 12:00–1:00 PM — Evans 2
  • Office Hours: MoWe 1:00–2:00 PM — Evans 720
  • Midterms: 9/29, 10/27, 12/1
  • Final Exam: 12/11, 11:30 AM–2:30 PM (location TBA)

Links:

Textbook

Board Photos

Exam Resources

Weekly Schedule

Week 1: 08/23 – 08/25

Worksheets

Readings this week

  • Aug 23: Introduction. Math 1A review: indefinite/definite integrals, areas, substitution.
    Textbook: 5.3–5.5, Ch. 5 review, 6.1 (if needed)
  • Aug 25: Math 1A review continued. Integration by parts.
    Textbook: 7.1

Assignments

  • WebWork HW 0 (tutorial): Due Wed Aug 23 @ 11:59 PM
  • WebWork HW 1: Due Mon Aug 28 @ 11:59 PM

Week 2: 08/28 – 09/01

Worksheets

Readings this week

  • Aug 28: Integration by parts cont’d. Trigonometric integrals.
    Textbook: 7.2
  • Aug 30: Trig integrals continued.
    Textbook: 7.2
  • Sep 01: Trig substitution.
    Textbook: 7.3

Assignments

  • WebWork HW 2: Due Tue Sep 5 @ 11:59 PM

Week 3: 09/04 – 09/08

Worksheets

Readings this week

  • Sep 4 (Labor Day): NO CLASS
  • Sep 6: Partial Fractions. Textbook: 7.4
  • Sep 8: Recap on methods of integration. Textbook: 7.5

Assignments

  • WebWork HW 3: Due Mon Sep 11 @ 11:59 PM

Week 4: 09/11 – 09/15

Worksheets

Readings this week

  • Sep 11: Numerical (approximate) integration. Textbook: 7.7
  • Sep 13: Improper Integrals. Textbook: 7.8
  • Sep 15: Application: arc length. Textbook: 8.1

Assignments

  • WebWork HW 4: Due Mon Sep 18 @ 11:59 PM

Week 5: 09/18 – 09/22

Worksheets

Readings this week

  • Sep 18: Application: center of mass. Textbook: 8.3 (pp. 560–565)
  • Sep 20: Sequences. Limit of a sequence. Textbook: 11.1
  • Sep 22: Convergence theorem for sequences.

Assignments

  • WebWork HW 5: Due Mon Sep 25 @ 11:59 PM

Week 6: 09/25 – 09/29

Worksheets

Midterm Prep

Readings this week

  • Sep 25: Series: convergence/divergence; geometric/harmonic. Textbook: 11.2
  • Sep 27: Integral test and remainder estimate. Textbook: 11.3
  • Sep 29: Midterm 1

Assignments

  • WebWork HW 6: Due Mon Oct 2 @ 11:59 PM

Week 7: 10/02 – 10/06

Worksheets

Readings this week

  • Oct 2: Comparison tests; alternating series. Textbook: 11.4, 11.5
  • Oct 4: Absolute vs conditional convergence. Textbook: 11.6
  • Oct 6: Ratio/root tests; recap. Textbook: 11.7

Assignments

  • WebWork HW 7: Due Mon Oct 9 @ 11:59 PM

Week 8: 10/09 – 10/13

Worksheets

Readings this week

  • Oct 9: Power series; radius/interval of convergence. Textbook: 11.8
  • Oct 11: Series representation of functions; termwise differentiation/integration. Textbook: 11.9
  • Oct 13: Taylor/Maclaurin series. Textbook: 11.10

Assignments

  • WebWork HW 8: Due Mon Oct 16 @ 11:59 PM

Week 9: 10/16 – 10/20

Worksheets

Readings this week

  • Oct 16: Remainder estimate; important Taylor series examples
  • Oct 18: Approximation by Taylor polynomials. Textbook: 11.11
  • Oct 20: Newton’s binomial series; multiplying/dividing series; series limits. Textbook: 9.1

Assignments

  • WebWork HW 9: Due Mon Oct 23 @ 11:59 PM

Week 10: 10/23 – 10/27

Worksheets

Readings this week

  • Oct 23: Differential equations; mathematical models. Textbook: 9.1
  • Oct 25: Euler’s method. Textbook: 9.2
  • Oct 27: Midterm 2

Assignments

  • WebWork HW 10: Due Mon Oct 30 @ 11:59 PM

Week 11: 10/30 – 11/03

Worksheets

Readings this week

  • Oct 30: Separable D.E.’s; applications. Textbook: 9.3–9.4
  • Nov 1: Linear D.E.’s. Textbook: 9.4–9.5
  • Nov 3: Further applications and examples

Assignments

  • WebWork HW 11: Due Mon Nov 6 @ 11:59 PM

Week 12: 11/06 – 11/10

Worksheets

Readings this week

  • Nov 6: Systems of D.E.’s; Lotka–Volterra. Textbook: 9.6
  • Nov 8: Second-order linear equations. Textbook: 17.1
  • Nov 10: Veterans Day — No class

Assignments

  • WebWork HW 12: Due Mon Nov 13 @ 11:59 PM

Week 13: 11/13 – 11/17

Worksheets

Readings this week

  • Nov 13: Complex roots; boundary value problems; non-homogeneous equations
  • Nov 15: Method of undetermined coefficients. Textbook: 17.2
  • Nov 17: Variation of parameters

Assignments

  • WebWork HW 13: Due Mon Nov 20 @ 11:59 PM

Week 14: 11/20 – 11/24

Worksheets

Readings this week

  • Nov 20: Oscillating motion and damping. Textbook: 17.3
  • Nov 22: Break — No section
  • Nov 24: Break — No section

Assignments

  • WebWork HW 14: Due Mon Nov 27 @ 11:59 PM

Week 15: 11/27 – 12/01

Worksheets

Readings this week

  • Nov 27: Series solutions of differential equations. Textbook: 17.4
  • Nov 29: Series solutions continued
  • Dec 1: Midterm 3

Assignments

  • WebWork HW 15: Due Sun Dec 3 @ 11:59 PM