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• Syllabus: 2020Spring2321S4

Lecture Notes:

Chapter 1.
1.2 Rn as a vector space  Math2321Sec1.2 #1, 3, 5, 7, 9, 10, 13-16, 19-21, 23-24, 27, 29, 33, 36, 41-43, 45, 46
1.3 Dot product, angles, and orthogonal projection Math2321Sec1.3 #1-4, 9-12, 17-19, 22, 23, 27-30, 33-35, 45-48
1.4 Lines, planes, and hyperplanes Math2321Sec1.4  #1-4, 9-12, 13-17, 19, 21-23, 27-30
1.5 Cross product Math2321Sec1.5 #1-4, 9-12, 17-20, 27-29, 31, 35, 37, 41
1.6 Functions of a single variable  Math2321Sec1.6 #1, 4, 5, 7, 9, 10, 18, 19, 21-25, 29, 33-35
1.7 Multivariable functions Math2321Sec1.7-1.8 #1, 2, 4, 7-10, 15, 17-19, 21, 27, 28
1.8 Graphing surfaces Math2321Sec1.7-1.8#1-10, 11-15, 19, 20, 23, 25
Chapter 2.
2.0 Multi-variable functions and Limits Math2321Sec2.0 #
2.1 Partial derivatives Math2321Sec2.1 #1, 2, 5, 7, 13, 16, 18, 19, 22, 27, 29, 32, 34
2.3 Linear approximation, tangent planes, and the differential Math2321Sec2.3 #1, 3, 5, 6, 11, 12, 15, 17, 22, 23
2.4 Differentiation rules Math2321Sec2.4 #1-4, 8, 19, 20, 23, 25, 27, 31, 32
2.5 Directional derivatives Math2321Sec2.5 #1, 3, 5-7, 11-13, 19-21, 25-27, 33-35, 37
2.7 Level sets and gradient vectors Math2321Sec2.7#1-3, 7-13, 17, 18, 21, 24
2.8 Parameterizing surfaces Math2321Sec2.8 #1-3, 5, 9-11, 17-19, 21, 29, 30
2.9 Local extrema Math2321Sec2.9#1-6, 9-14, 17-20, 35
2.10 Optimization Math2321Sec2.10#1, 2, 7, 8, 9, 10, 13, 17, 19, 20
2.11 Lagrange multipliers Math2321Sec2.11 #1, 3, 12, 13, 15, 19, 23, 27, 29
Chapter 3.
3.1 Iterated integrals Math2321Sec3.1-3.2 #1, 3, 4, 5, 9, 16, 17-24, 27, 28
3.2 Integration in R^2 Math2321Sec3.1-3.2 #1-3, 6-8, 17, 18, 23, 24, 27-29, 31-33
3.3 Polar coordinates Math2321Sec3.3 #1-7, 17
3.4 Integration in R^3 and R^n Math2321Sec3.4 #1, 3, 6, 7, 9, 11, 13, 14, 16-18, 20
3.5 Volume Math2321Sec3.5 #1-3, 9-11, 17, 18
3.6 Cylindrical and spherical coordinates Math2321Sec3.6 #1-3, 7-9, 13-15, 19-21, 25-27, 31, 32, 35, 36
3.8 Density and mass Math2321Sec3.8#1, 2, 7-10
3.11 Surfaces and area Math2321Sec3.11#1-3, 9, 11-13, 15-17, 19-21
Chapter 4.  
4.1 Vector fields Math2321Sec4.1 #1, 3, 7, 8-14, 17, 18, 21, 22, 26-28
4.2 Line integrals Math2321Sec4.2 #1-3, 7, 8, 15, 16, 18-20, 23, 25, 27
4.3 Conservative vector fields Math2321Sec4.3#1-3, 7-9, 15-17, 23, 24, 27, 33, 35, 41, 43
4.4 Green’s Theorem Math2321Sec4.4#1, 3, 5, 7-9, 13, 15
4.3-4.4 continue. Math2321Sec4.3-4
4.5 Flux through a surface Math2321Sec4.5 #1, 2, 7, 9, 10, 11, 15, 19, 20
4.6 The Divergence Theorem Math2321Sec4.6 #1-4, 6-11
4.7 Stokes’ Theorem Math2321Sec4.7
Summary of Chapter 4 Math2321Sec4Summary

1. Worldwide Multivariable Calculus, by David B. Massey

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