Math 1510 Analysis 2

Lectures: Tuesdays 18:55 - 20:35 in B-4 / 2.39.

Summer 2024 office hours (konsultacje): Room C-19 / A.3.6, Wednesdays 13:00 - 15:00 and Thursdays 14:00 - 16:00 when the University is open. Last day: Monday 24.6 at 14:00 (a "Thursday" class schedule). 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 and 10 April). Double (iterated) integrals.
• Lecture 7 (16 April). Potential (direct PDE), review for Test 1.
• Lecture 8 (24 April). Differential equations vocabulary.
• Lecture 9 (30 April). Autonomous.
• Lecture 10 (7 May). Separable.
• Lecture 11 (14 May). First-order linear (VoP and Laplace).
• Lecture 12 (21 May). First-order linear (IF and big formula).
• Lecture 13 (4 June). Higher-order homogeneous linear.
• Lecture 14 (6 or 10 June). Higher-order non-homogeneous linear.
• Lecture 15 (11 June). Resonance and systems of linear 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 Test 1. Answers.
• List 6. Differential equations vocabulary, direct diff. eqs. Answers.
• List 7. Slope fields, autonomous ODEs, separable ODEs. Answers.
• List 8. Linear ODEs, Laplace transformations. Answers.
• List 9. Higher-order linear ODEs. Answers.
• List 10. Systems of linear ODEs, Review for Test 2. Answers.