This is an archived course. A more recent version may be available at ocw.mit.edu.

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    Calendar

    References are to the textbook: Apostol, Calculus, Vol. I, Second Edition (1967); Readings are from the Course Notes by Prof. J. Munkres.

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