10B Summer 2026

⚠️Syllabus⚠️ 

• Office Hours: 

  • Tuesdays (In-Person) 11:30am-12:20pm in same classroom

  • Thursdays (on Zoom) 5-6pm Link

• Exam Info:

  • Midterm (in-class): Thursday 10am-11:20am, 13th Aug

  • Final Exam (same class room): Saturday 10:30am-12:30pm, 29th Aug

• Homework List

Below is a tentative schedule.

Week 1

• Lecture 1 - 27th July: 5.1 Introduction & Cavalieri's Principle

  • Pre-class notes

  • Lecture notes

  • Desmos: https://www.desmos.com/3d/ecueta0oew, https://www.desmos.com/3d/eromxpypzn

• Lecture 2 - 28th July: 5.2 Double Integral over a Rectangle & Fubini's Theorem

  • Pre-class notes

  • Lecture notes

    • Remark - "Separation of variables" is a method for solving differential equations, so the use of this term in the notes is non-standard.

  • Desmos: Riemann Integral, Double integral examples

• Lecture 3 - 29th July: 5.3 Double Integral over other regions

  • Pre-class notes

  • Lecture notes

  • Desmos: 2D Region example, same example in 3D Region

• Lecture 4 - 30th July: 5.4 Changing order of integration and Mean Value Inequality

  • Pre-class notes

  • Lecture notes

  • Mean Value Equality with Amazon products: Single Variable, Multivariable

Week 2

• Lecture 5 - 3th Aug: 5.5 Triple Integrals

  • Pre-class notes

  • Lecture notes

• Lecture 6 - 4th Aug: 6.1 The Geometry of Maps - ONLINE CLASS

  • Pre-class notes

  • Lecture notes

• Lecture 7 - 5th Aug: 6.2 Change of Variables - Polar, Cylindrical, Spherical - SUBSTITUTE

  • Pre-class notes

  • Lecture notes

• Lecture 8 - 6th Aug: 7.1, 7.2 The Path & Line Integrals - SUBSTITUTE

  • Pre-class notes

  • Lecture notes

Week 3

• Lecture 9 - 10th Aug: 7.3 Parameterised Surfaces

  • Pre-class notes

  • Lecture notes

• Lecture 10 - 11th Aug: 7.4 Area of a Surface

  • Pre-class notes

  • Lecture notes

• Lecture 11 - 12th Aug Midterm Review

  • Some review problems relevant to our midterm:

    • Review exercises for chapter 5 (pages): 

    • Review exercises for chapter 6 (pages):  

    • Review exercises for chapter 7 (pages):  

    • This is an incomplete, non-exhaustive list in preparation for the midterm. You should also review homeworks, quizzes, and in-class examples.

• Lecture 12 - 13th Aug MIDTERM

  • Exam

  • Exam Solutions

Week 4

• Lecture 13 - 17th Aug: 7.5 Integrals of Scalar Functions Over Surfaces

  • Pre-class notes

  • Lecture notes

• Lecture 14 - 18th Aug: 7.6 Surface Integrals of Vector Fields

  • Pre-class notes

  • Lecture notes

• Lecture 15 - 19th Aug: 8.1 Green’s Theorem

  • Pre-class notes

  • Lecture notes

• Lecture 16 - 20th Aug: 8.2 Stokes' Theorem

  • Pre-class notes

  • Lecture notes

Week 5

• Lecture 17 - 24th Aug: 8.3 Conservative Vector Fields

  • Pre-class notes

  • Lecture notes

• Lecture 18 - 25th Aug: 8.4 Gauss' Theorem

  • Pre-class notes 

  • Lecture notes 

• Lecture 19 - 26th Aug: Overflow

  • Pre-class notes

  • Lecture notes

• Lecture 20 - 27th Aug Final Review

  • Some review problems relevant to our final:

    • Review exercises for chapter 7 (pages):  

    • Review exercises for chapter 8 (pages ): 

    • This is an incomplete, non-exhaustive list in preparation for the final. You should also review homeworks, quizzes, and in-class examples.

Final Exam

• Time: 10:30-12:30pm, Saturday 29th Aug

• Location: SPROUL 2355 (usual classroom)