Math 13
Fall 2011
Calculus of vector valued functions
Syllabus
This lecture plan is tentative and will be updated irregularly. With strong likelihood some of the topics in the end of the syllabus will not be covered. The written homework page and the WeBWorK assignment will be updated on the regular basis
Lectures 
Sections in Text 
Brief Description 
Wednesday September 21, 2010 
1.11.5 
The geometry of Euclidean space 
Friday September 23, 2010 
2.1, 2.2 
The geometry of realvalued functions. Limits and continuity 
Monday September 26 
2.3 
Limits and Continuity, Differentiation 
Wednesday September 28 
2.4 
Introduction to paths 
Friday September 30 
Section 2.5 and Derivatives as matrices 
Derivatives as matrices, properties of derivatives 
Monday October 3

2.6 
Gradients and directional derivatives. 
Wednesday October 5 Final day for electing to use the NonRecording Option. 
3.1 
Iterated partial derivatives 
Friday October 7 
3.2 
Taylor series 
Monday October 10 
3.3 
Extrema of realvalued functions 
Wednesday October 12

3.4 
Constrained extrema and Lagrange multipliers. 
Friday October 14 
3.5 
Implicit function theorem 
Monday October 17 
4.1 
Acceleration, Newton’s second law 
Tuesday October 18 No class The First Midterm Exam 68 PM in Carpenter 013 

Wednesday October 19 
4.2 
Arc Length 
Friday October 21 Homecoming weekend No class. Instead we will have an xhour on Tuesday October 25 

Monday October 24 
Read Section 4.3 
Vector fields 
Tuesday October 25 xhour instead of the class on Friday October 21 
Read Section 4.4 and start section 5.1 
Divergence and Curl 
Wednesday October 26 
5.1, 5.2 
The double integral 
Friday October 28 
5.3, 5.4 
The double integral over more general regions. Changing the order of integration. 
Monday October 31 Note that Tuesday November 1 is the final day for dropping the fourth course without the grade notation of W 
5.5 
The triple integral. 
Tuesday November 1 xhour instead of the class on Monday November 28 
6.1, 6.2 
The geometry of maps from R^{2} to R^{2 }^{ }The change of variables theorem 
Wednesday November 2 
6.2 
The change of Variables Theorem. 
Friday November 4 
6.3 

Monday November 7 
7.1 and 7.2 
The path integral and the line integral 
Tuesday November 8 xhour possibly instead of one of the coming classes 68 PM Second Midterm Exam in Carpenter 013 
7.3 
Parametrized surfaces 
Wednesday November 9 
7.4 
Area of a surface 
Friday November 11 Final day to withdraw from a course 
7.5, 7.6 
Integrals of vector fields and scalar functions over surfaces 
Monday November 14 
8.1 
Green's theorem 
Wednesday November 16 
8.2 
Stokes's theorem 
Friday November 18 Final day to alter the grade limit filed under the NRO 
8.3 
Conservative fields 
Monday November 21 
8.4 
Gauss' theorem 
Thanksgiving recess: starts at 5:50 PM on Tuesday November 22 and ends at 7:45 AM on Monday November 28 

Monday November 28 No class. Instead we will have an xhour on Tuesday November 1 

Wednesday November 30 
8.6 
Differential Forms and Stokes Theorem 
Thursday December 1Friday December 2 PreExamination Break 


Math 13 Final Exam is 36 PM Saturday December 3 in Kemeny 007 Final Examinations begin on Saturday December 3 and end on Wednesday December 7 

