MAT 1653 Analysis 1 (Winter 2023)

Lectures for everyone: Wednesdays 11:15 - 13:00 in C-4 / 40 with dr Adam Abrams.
Exercises for “Group 1”: Tuesdays 18:55 - 20:35 in C-4 / 31 with dr Adam Abrams.
Exercises for “Group 2”: Thursdays 07:30 - 09:00 in C-4 / 31 with dr Artur Rutkowski.

Winter 2023 office hours / konsultacje (these are are optional; come if you want extra help):

Adam Abrams: Mondays 14-16 and Wednesdays 14-16 in C-19 / A.3.6. Last day: 5 February 2024.

Artur Rutkowski: Tuesdays 15-17 and Wednesdays 1-3 in C-19 / A.3.4.

Grading policy for Winter 2023. All grades will be recorded on ePortal.

Lecture slides

• Slides from 3 October. Course intro, algebra and trig review.
• Slides from 4 October. Course intro, limits of sequences.
• Slides from 18 October. Squeeze Theorem, limits of functions.
• Slides from 25 October. Continuity, tangent lines, derivate at a point.
• Slides from 8 November. Linear approximations, Power Rule, Sum Rule.
• Slides from 22 November. Increasing decreasing, absolute min/max, First Derivative Test.
• Slides from 29 November. Product Rule, Second Derivative Test, Concavity, exponentials.
• Slides from 6 December. Chain Rule, Quotient Rule, logarithms.
• Slides from Tuesday 12 December. L'Hôpital's Rule, Taylor polynomials.
• Slides from 13 December. Definite integrals as area, FTC.
• Slides from 20 December. Indefinite ∫, properties of definite ∫, intro to u-sub.
• Slides from 10 January. Integration by substitution (u-sub.), area.
• Slides from 17 January. Integration by parts, volume of revolution.
• Slides from 24 January. More integration by parts, improper integrals.
• Slides from 31 January. Review, bonus topics.

Task lists

• List 0. Algebra review, line equations. Answers.
• List 1. Limits of sequences. Answers.
• List 2. Limits of functions, discontinuities. Answers.
• List 3. Derivative at a point, tangent lines and linear approximations. Answers.
• List 4. Review for midterm exam. Answers.
• List 5. Critical points, inc/decreasing, absolute extremes. Answers.
• List 6. Local extremes, concavity. Answers.
• List 7. L'Hôpital's Rule, Taylor pn./series, simple anti-derivatives. Answers.
• List 8. Indefinite and definite integrals, u-sub. Answers.
• List 9. Integration by parts, area and volume. Answers.
• List 10. REVIEW. Answers.

All grades will be recorded on ePortal.

Suggested resources

• Speaking mathematics. Examples of how to say formulas out loud. Especially helpful if English is not your first language.
• There is no physical textbook, but we will mostly follow chapters from Paul's Online Notes, which cover several courses from Lamar University.
  • Course "textbook" showing the order of topics compared to Paul's.
  • Review chapter with pages on common functions including sin(x), e^x, and log(x).
• Videos. (I have only watched some of these, but I have heard from previous students that they can be helpful.)
  • Professor Leonard. Full video lectures from a course at Merced College.
  • Khan Academy. Hundreds of worked examples and practice problems.
  • 3Blue1Brown. Focuses on ideas and visuals, with fewer specific examples.