Lecture Outlines and Class Notes
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Introduction  These are the notes for the comments I made in class concerning the Fundamental Theorem of Calculus, Green's Theorem, Stokes's Theorem, the Divergence Theorem, and the Generalized Stokes's Theorem.

Chapter 9 Vector Differential Calculus. Grad, Div, Curl
    9.1 lecture outline     Vectors in 2-space and 3-space
    9.1 classnotes 
    9.2 lecture outline    Inner Product
    9.2 classnotes 

    9.3 lecture outline    Vector Product
 

    9.3 classnotes(part 1) , 9.3 classnotes(part 2)
    9.4 lecture outline    Vector and Scalar Fields; Derivatives
    9.4 classnotes(part 1) , 9.4 classnotes(part 2)
    9.5 lecture outline
    Curves, Arc Length, Velocity, and Acceleration
    9.5 classnotes(part 1)   , 9.5 classnotes(part 2)
    9.7 lecture outline
   Gradient of a Scalar Field. Directional Derivative
    9.7 classnotes   
    9.8 lecture outline    Divergence of a Vector Field

    9.8 classnotes(part 1) , 9.8 classnotes(part 2)     
    9.9 lecture outline     Curl of a Vector Field

    9.9 classnotes

Chapter 10 Vector Integral Calculus. Integral Theorems
    10.1 lecture outline    Line Integrals

    10.1 classnotes(part 1) ,  10.1 classnotes(part 2)
    10.2 lecture outline    Path Independence of Line Integrals
    10.2 classnotes(part 1) , 10.2 classnotes(part 2)  
    10.4 lecture outline    Green's Theorem in the Plane

    10.4 classnotes(part 1)
  , 10.4 classnotes(part 2) , 10.4 classnotes(part 3)

    10.5 lecture outline     Surfaces for Surface Integrals
    10.5 classnotes(part 1) ,
10.5 classnotes(part 2)
    10.6 lecture outline (reposted 10/14 to include more detail on slide 12)  Surface Integrals
    10.6 classnotes(part 1) , 10.6 classnotes(part 2) (reposted  part 2 on 10/18 to fix a few mistakes on the last page)
    10.7 lecture outline    Triple Integrals.  The Divergence Theorem of Gauss

    10.7 classnotes(part 1) , 10.7 classnotes(part 2)
    10.8 lecture outline    Further Applications of the Divergence Theorem. Some Potential Theory

    10.8 classnotes(part 1) , 10.8 classnotes(part 2) , 10.8 classnotes(part 3)
    10.9 lecture outline    Stokes's Theorem
    10.9 classnotes(part 1) ,
10.9 classnotes(part 2)

Chapter 13 Complex Numbers and Functions.  Complex Differentiation.
    13.1 lecture outline    Complex numbers and their geometric representation
    13.1 classnotes

    13.2 lecture outline    Polar form of complex numbers. Powers and roots.
    13.2 classnotes

    13.3 lecture outline    Derivative. Analytic Function. 
    13.3 classnotes

    13.4 lecture outline    Cauchy Riemann equations.  Laplace's equation.
    13.4 classnotes

    13.5 lecture outline    Exponential Function 
    13.5 classnotes

    13.6 lecture outline    Trigonometric and Hyperbolic Functions.  Euler's Formula
    13.6 classnotes

    13.7 lecture outline    Logarithm. General Power.  Principal Value.
    13.7 classnotes(part 1) ,
13.7 classnotes(part 2)

Chapter 14 Complex Integration.
    14.1 lecture outline    (reposted 11/13 to change the exercise on slide 9)   Line Integral in the Complex Plane
    14.1 classnotes(part 1) , 14.1 classnotes(part 2)

    14.2 lecture outline    Cauchy's Integral Theorem
    14.2 classnotes

    14.3 lecture outline    Cauchy's Integral Formula 
    14.3 classnotes(part 1) , 14.3 classnotes(part 2)

    14.4 lecture outline    Cauchy's Integral Formula for Derivatives
    14.4 classnotes(part 1)

Chapter 16 Laurent Series. Residue Integration.
    16.4 lecture outline    Residue Integration of Real Integrals   In this lecture we show how to evaluate certain real integrals using Cauchy's Integral Formula.
    16.4 classnotes(part 1) ,
16.4 classnotes(part 2)

Chapter 18 Complex Analysis and Potential Theory.
    18.4 lecture outline    (reposted 12/9 to fix a typo on page 9)  Fluid Flow
    18.4 classnotes


Generalized Stokes's Theorem Revisited   We revisit here the very first lecture of the course (see the link "Introduction" above) and give a bit more detail.
generalized Stokes classnotes    These are the detailed solutions of the exercises that appear in the Lecture Outline.