A. Complex Numbers
1. Argand diagram
2. Polar notation
3. Euler identity
4. Applications in circuit problems
*5. Solutions to sine and cosine orthogonality integrals
B. Determinants and Matrices
1. Cramers Rule
2. Row reduction of sets of linear equations
3. Multiplication of matrices
*4. Inverse, transpose and adjoint matrices
5. Coordinate transformations
C. Multiple Integrals
1. Double and triple integrals
2. Change of variables in integrals - Jacobians
3. Cartesian, cylindrical and spherical coordinates
*4. Applications to moments of inertia and density
D. Vector Analysis
1. Fields
2. Directional derivative
3. LaPlacian
4. Line integrals
*5. Green's theorem
6. Stokes, and Gauss' theorems
E. Fourier Series
1. Fourier sine and cosine series
2. Complex series
3. Even and odd series
*4. Applications to sound
F. Differential Equations
1. First order equations
2. Simple harmonic oscillator
3. Damped, driven harmonic oscillator
G. Eigenvalue Problem
1. Eigenvectors
2. Eigenvalues
*3. Applications using the LaGrangian Formulation
H. Orthogonal Functions and Generating Equations
1. Series solutions
2. Legendre polynomials
3. Normalization and orthogonality of polynomials
*4. Laguerre and Fourier functions
I. Partial Differential Equations
1. Solutions in cartesian coordinates to La Place, wave and heat equations
2. Solutions to La Place equation in spherical coordinates
J. Fourier Transform
1. Solutions to partial differential equations
2. Transform of a Delta function
*K. Taylor Series
*denotes optional topic
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