next up previous
Next: About this document ...

Mathematics 13 - Term Syllabus
(Section numbers from Marsden, Tromba, Weinstein)

The Undergraduate Program Committee


Date: June 23, 2000

=

Lecture Topics Some Standard Examples/Concepts
Day 1 Review of algebra and geometry in Euclidean space (1.1 - 1.5) Vector notation, dot and cross products, lines, planes
Day 2 Curves in Euclidean space (1.6) Curves, tangent vector, tangent line
Day 3 Graphs, level surfaces, partial derivatives, and continuity (2.1 - 2.2)  
Day 4 Differentiability, the derivative matrix, tangent planes (2.3)  
Day 5 The Chain Rule, Gradients and Directional Derivatives (2.4 - 2.5)  
Day 6 Directional Derivatives and Implicit differentiation (2.5 - 2.6)  
Day 7 Curves and acceleration (4.1)  
Day 8 Arclength (4.2)  
Day 9 Vector Fields (4.3)  
Day 10 Divergence and Curl (4.4)  
Day 11 Divergence and Curl (4.4 / 5.1)  
Day 12 Volume and Cavalieri's Principle (5.1)  
Day 13 Double integral over a rectangle (5.2 / 5.3)  
Day 14 Double Integral over other regions (5.3)  
Day 15 Triple Integrals (5.4)  
Day 16 Change of Variables, cylindrical and spherical coordinates (5.5)  
Day 17 Change of Variables, cylindrical and spherical coordinates (5.5)  
Day 18 Applications (5.6) Center of Mass, moments of inertia
Day 19 Line Integrals (6.1)  
Day 20 Line Integrals (6.1)  
Day 21 Parametrized surfaces (6.2)  
Day 22 Area of a surface (6.3)  
Day 23 Surface Integrals (6.4)  
Day 24 Green's theorem (7.1)  
Day 25 Stokes' Theorem (7.2)  
Day 26 Stokes' Theorem (7.2)  
Day 27 Gauss' theorem (7.3)  
Day 28 Path Independence and the Fundamental Theorem of Calculus (7.4)  
     




next up previous
Next: About this document ...
root 2000-06-23