List of topics |

**Chapter 9.***Vector Differential Calculus:*
Vector Algebra in R^{2} an R^{3}. Inner Product (Dot
Product).
Vector Product (Cross Product)
Vector and Scalar Functions and Fields. Derivatives.
Curves. Tangents. Arc Length.
Curves in mechanics. Velocity and Acceleration. Gradient of a Scalar
Field. Directional Derivative. Divergence of a Vector Field. Curl of a
Vector Field.

**Chapter 10.***Vector Integral Calculus:* Line
Integrals. Line Integrals Independent of Path.
Double Integrals. Green's Theorem in the Plane.
Surfaces for Surface Integrals.
Surface Integrals. Triple Integrals. Divergence Theorem of Gauss.
Applications of the Divergence Theorem.
Stokes's Theorem.

**Chapter 13.***Complex numbers and functions:* Complex
Numbers. Complex Plane. Polar Form of Complex Numbers.
Powers and Roots. Derivative. Analytic Function. Cauchy-Riemann
Equations. Laplace's Equation. Geometry of Analytic Functions:
Conformal Mapping. Exponential Function. Trigonometric Functions,
Hyperbolic Functions. Logarithm. General Power. Linear Fractional
Transformations.

**Chapter14.***Complex Integration:* Line Integral in
the Complex Plane. Cauchy's Integral Theorem. Cauchy's Integral
Formula. Derivatives of Analytic Functions.

**Chapter 15.***Power Series, Taylor Series:*
Sequences, Series, Convergence Tests. Power Series. Functions Given by
Power Series.
Taylor Series and Maclaurin Series.

**Chapter 16.***Laurent Series, Residue Integration:*
Laurent Series. Singularities and Zeros. Infinity. Residue Integration
Method. Evaluation of Real Integrals.

**Chapter 17.**Conformal
Mappings:
Geometry of analytical functions. Linear Fractional

**Chapter 18.***Applications to Potential Theory:*
Electrostatic Fields. Use of Conformal Mapping. Heat Problems. Fluid
Flow. Poisson's Integral Formula. General Properties of Harmonic
Functions.