Math 1510 Analysis 2

Lectures for everyone: Tuesdays 15:15 - 16:55 in C-13 / 0.38.
Exercises for "Group A": Wednesdays 15:15 - 16:55 in C-4 / 31.
Exercises for "Group B": Wednesday, 17:05 - 18:45 in C-4 / 31.

Summer 2024 office hours (konsultacje): Wednesdays 13:00 - 15:00 and Thursdays 14:00 - 16:00 in room C-19 / A.3.6. Office hours are optional; come if you want extra help. Building C-19 is new and does not appear on some campus maps, so here is a Google Maps marker.

Slides

• Problem session 1 (28 Feb). Review: algebra and analysis.
• Lecture 1 (5 March). Calculating path integrals and partial derivatives.
• Lecture 2 (12 March). Gradient, meaning of path integrals and partial derivatives.
• Lecture 3 (19 March). Directional derivatives, definition of critical point.
• Lecture 4 (26 March). Second Derivative Test.
• Lecture 5 (3 April). Calculating iterated integrals (mini-lecture during problem session).
• Lecture 6 (9 April). Double (iterated) integrals.
• Lecture 7 (16 April). Double integrals / Review for exam 1.
• Lecture 8 (24 April). Potential; differential equations vocabulary.
• Lecture 9 (30 April). Autonomous ODEs.

Other resources

• Grading policy for Summer 2024.
• Faculty subject card.
• 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 of Paul's Online Notes from Lamar University. This course "textbook" shows the order of topics compared to Paul's.
• Suggested video series. (I have only watched some of these, but I have heard from previous students that they can be helpful.)
  • Professor Leonard: multivariable functions and differential equations.
  • Khan Academy: multivariable functions and differential equations.
  • 3Blue1Brown: differential equations.

Task lists

• List 0. Previous material. Ideally, you should be able to do every task from List 0 before you start Analysis 2. Answers
• List 1. Calculating path integrals and partial derivatives. Answers.
• List 2. Path integrals, calculating gradients. Answers.
• List 3. Directional derivatives, critical points, calculating iterated integrals. Answers.
• List 4. Double integrals. Answers.
• List 5. Review for Exam 1. Answers.
• List 6. Differential equations vocabulary, direct diff. eqs.