Math 23 Main Page

Midyear 2026. For questions, contact me via pjburgos@math.upd.edu.ph.

All relevant files and links for our course (aside from the module) are listed below.

Unit 1

• Lecture 1.1. Functions of Several Variables, Level Curves, and Level Surfaces (SW1)
• Lecture 1.2. Limits and Continuity of Functions of Several Variables
• Lecture 1.3. Partial Derivatives, Higher Order Derivatives (SW2)
• Lecture 1.4. Differentiability, Differentials, Local Linear Approximation (SW3)
• Lecture 1.5. Chain Rule and Implicit Differentiation
• Lecture 1.6. Directional Derivatives, Gradients, Tangent Planes (SW4)

Unit 2

• Lecture 2.1. Relative Extrema and Second Derivative Test
• Lecture 2.2. Absolute Extrema and Lagrange Multipliers (SW5)
• Lecture 2.3. Parametric Surfaces and Surfaces of Revolution (SW6)
• Lecture 2.4. Double Integrals, Double Integrals over General Regions (SW7)
• Lecture 2.5. Double Integrals in Polar Coordinates (SW8)
• Lecture 2.6. Applications of Double Integrals (SW9)

Unit 3

• Lecture 3.2. More on Triple Integrals (SW10)
• Lecture 3.3. Integration using Cylindrical and Spherical Coordinates (SW11)
• Lecture 3.4. Vector Fields, Curl and Divergence
• Lecture 3.5. Conservative Vector Fields (SW12)
• Lecture 3.6. Line Integrals of Scalar Fields (SW13)

Unit 4

• Lecture 4.1. Line Integrals of Vector Fields
• Lecture 4.2. Fundamental Theorem of Line Integrals, Path Independence (SW14)
• Lecture 4.3. Green's Theorem (SW15)
• Lecture 4.4. Surface Integrals of Scalar Fields
• Lecture 4.5. Surface Integrals of Vector Fields (SW16)
• Lecture 4.6. Stokes' Theorem, Gauss' Divergence Theorem (SW17)