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Calculus with Theory II >> Content Detail


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References are to the textbook: Apostol, Calculus, Vol. I, Second Edition (1967); Readings are from the Course Notes by Prof. J. Munkres.
SES #TOPICSREFERENCESREADINGS
1Vectors in n DimensionsI 12.1-12.7Chapter A.1 - A.6 (PDF - 2.7 MB)
2Linear Spaces, ProjectionsI 15.2-15.6, 12.9-12.10
3Linear IndependenceI 12.12-12.13Chapter A.7 - A.16 (PDF - 2.7 MB)
4Bases, Gauss-Jordan ReductionI 12.14, 16.18Chapter A.17 - A.24 (PDF - 2.7 MB)
5Lines and Planes in n-spaceI 13.2-13.6Chapter A.25 - A.33 (PDF - 2.7 MB)
6Linear Transformations and MatricesI 16.1-16.15Chapter B.1 - B.5 (PDF - 2.1 MB)
7Systems of Linear Equations, Cartesian Equations of PlanesI 16.17-16.18, 13.16Chapter B.6 - B.24 (PDF - 2.1 MB)
8Inverse of a Matrix, DeterminantsI 13.13, 16.19Chapter B.25 - B.52 (PDF - 1.1 MB)
9Cross Product as a DeterminantI 13.9-13.10Chapter B.53 - B.56 (PDF - 1.1 MB)
10Vector Functions of a Single VariableI 14.1-14.6
11Arc LengthI 14.10-14.12
12Tangent, Normal, CurvatureI 14.8, 14.14
13Quiz
14Polar CoordinatesI 14.16
15Scalar and Vector FieldsII 8.1-8.8
16Total Derivative, GradientsII 8.10-8.13
17Tangent Plane, Extreme ValuesII 8.15-8.16, 9.9
18Chain RuleII 8.20-8.21Chapter C.1 - C.13 (PDF - 2.4 MB)
19Implicit DifferentiationII 9.6-9.7Chapter C.14 - C.21 (PDF - 2.4 MB)
20Mixed Partial Derivatives, Second Derivative TestII 8.23, 9.12Chapter C.22 - C.27 (PDF - 2.4 MB)
21Line IntegralsII 10.1-10.7
22The Integral of a GradientII 10.8-10.12
23The Gradient of an IntegralII 10.14-10.16
24Construction of Potential FunctionsII 10.17, 10.21
25Double Integrals Over RectanglesII 11.1-11.8Chapter C.28 - C.33 (PDF - 2.4 MB)
26Double Integrals Over RegionsII 11.10-11.14Chapter D.1 - D.8 (PDF - 1.9 MB)
27Applications; Triple IntegralsII 11.16, 11.31
28Existence of Double Integrals11.12Chapter D.9 - D.27 (PDF - 1.9 MB)
29Green's Theorem in the PlaneII 11.19-11.20, 11.23Chapter E.1 - E.7 (PDF - 2.6 MB)
30Quiz
31Application - Conservative FieldsII 11.21Chapter E.8 - E.22 (PDF - 2.6 MB)
32Change of VariablesII 11.26-11.27Chapter E.23 - E.35 (PDF - 2.6 MB)
33Cylindrical and Spherical CoordinatesII 11.32-11.33
34SurfacesII 12.1-12.5
35Surface IntegralsII 12.7-12.9
36Stokes' TheoremII 12.11, 12.18Chapter F.1 - F.5 (PDF - 1.1 MB)
37Gauss' TheoremII 12.19
38Grad, Curl, Div and All ThatII 12.12-12.14, 12.16, 12.20Chapter F.7 - F.16 (PDF - 1.1 MB)
39Review




 
 


 



 








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