References are to the textbook: Apostol,
Calculus, Vol. I, Second Edition (1967); Readings are from the
Course Notes by Prof. J. Munkres.
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SES # |
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TOPICS |
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REFERENCES |
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READINGS |
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1 |
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Vectors in n Dimensions |
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I 12.1-12.7 |
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Chapter A.1 - A.6 (PDF - 2.7 MB) |
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2 |
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Linear Spaces, Projections |
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I 15.2-15.6, 12.9-12.10 |
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3 |
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Linear Independence |
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I 12.12-12.13 |
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Chapter A.7 - A.16 (PDF - 2.7 MB) |
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4 |
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Bases, Gauss-Jordan Reduction |
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I 12.14, 16.18 |
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Chapter A.17 - A.24 (PDF - 2.7 MB) |
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5 |
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Lines and Planes in n-space |
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I 13.2-13.6 |
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Chapter A.25 - A.33 (PDF - 2.7 MB) |
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6 |
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Linear Transformations and Matrices |
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I 16.1-16.15 |
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Chapter B.1 - B.5 (PDF - 2.1 MB) |
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7 |
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Systems of Linear Equations, Cartesian Equations of Planes |
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I 16.17-16.18, 13.16 |
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Chapter B.6 - B.24 (PDF - 2.1 MB) |
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8 |
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Inverse of a Matrix, Determinants |
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I 13.13, 16.19 |
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Chapter B.25 - B.52 (PDF - 1.1 MB) |
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9 |
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Cross Product as a Determinant |
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I 13.9-13.10 |
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Chapter B.53 - B.56 (PDF - 1.1 MB) |
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10 |
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Vector Functions of a Single Variable |
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I 14.1-14.6 |
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11 |
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Arc Length |
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I 14.10-14.12 |
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12 |
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Tangent, Normal, Curvature |
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I 14.8, 14.14 |
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13 |
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Quiz |
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14 |
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Polar Coordinates |
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I 14.16 |
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15 |
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Scalar and Vector Fields |
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II 8.1-8.8 |
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16 |
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Total Derivative, Gradients |
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II 8.10-8.13 |
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17 |
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Tangent Plane, Extreme Values |
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II 8.15-8.16, 9.9 |
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18 |
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Chain Rule |
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II 8.20-8.21 |
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Chapter C.1 - C.13 (PDF - 2.4 MB) |
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19 |
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Implicit Differentiation |
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II 9.6-9.7 |
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Chapter C.14 - C.21 (PDF - 2.4 MB) |
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20 |
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Mixed Partial Derivatives, Second Derivative Test |
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II 8.23, 9.12 |
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Chapter C.22 - C.27 (PDF - 2.4 MB) |
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21 |
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Line Integrals |
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II 10.1-10.7 |
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22 |
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The Integral of a Gradient |
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II 10.8-10.12 |
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23 |
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The Gradient of an Integral |
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II 10.14-10.16 |
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24 |
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Construction of Potential Functions |
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II 10.17, 10.21 |
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25 |
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Double Integrals Over Rectangles |
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II 11.1-11.8 |
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Chapter C.28 - C.33 (PDF - 2.4 MB) |
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26 |
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Double Integrals Over Regions |
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II 11.10-11.14 |
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Chapter D.1 - D.8 (PDF - 1.9 MB) |
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27 |
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Applications; Triple Integrals |
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II 11.16, 11.31 |
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28 |
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Existence of Double Integrals |
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11.12 |
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Chapter D.9 - D.27 (PDF - 1.9 MB) |
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29 |
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Green's Theorem in the Plane |
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II 11.19-11.20, 11.23 |
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Chapter E.1 - E.7 (PDF - 2.6 MB) |
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30 |
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Quiz |
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31 |
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Application - Conservative Fields |
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II 11.21 |
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Chapter E.8 - E.22 (PDF - 2.6 MB) |
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32 |
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Change of Variables |
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II 11.26-11.27 |
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Chapter E.23 - E.35 (PDF - 2.6 MB) |
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33 |
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Cylindrical and Spherical Coordinates |
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II 11.32-11.33 |
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34 |
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Surfaces |
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II 12.1-12.5 |
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35 |
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Surface Integrals |
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II 12.7-12.9 |
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36 |
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Stokes' Theorem |
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II 12.11, 12.18 |
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Chapter F.1 - F.5 (PDF - 1.1 MB) |
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37 |
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Gauss' Theorem |
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II 12.19 |
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38 |
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Grad, Curl, Div and All That |
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II 12.12-12.14, 12.16, 12.20 |
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Chapter F.7 - F.16 (PDF - 1.1 MB) |
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39 |
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Review |
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