Vector analysis application
• Applications of vector multiplication
• Triple products
• Differentiation of vectors
• Fields
• Directional derivative; gradient
• Some other expressions involving ?
• Line integrals
• Green’s theorem in the plane
• The divergence and the divergence theorem
• The curl and stokes’ theorem 14
Fourier series and transforms
• Simple harmonic motion and wave motion; periodic functions
• Applications of fourier series
• Average value of a function
• Fourier coefficients
• Dirichlet conditions
• Complex form of fourier series
• Other intervals
• Even and odd functions
• An application to sound
• Parseval’s theorem
• Fourier transforms 14
Integral transforms
• Development of the fourier integral
• Fourier transforms—inversion theorem
• Fourier transform of derivatives
• Convolution theorem
• Momentum representation
• Transfer functions
• Laplace transforms
• Laplace transform of derivatives
• Other properties
• Convolution (faltungs) theorem
• Inverse laplace transform 12
Ordinary differential equations
• Separable equations
• Linear first-order equations
• Other methods for first-order equations
• Second-order linear equations with constant coefficients and zero right-hand side
• Second-order linear equations with constant coefficients and right-hand side not zero
• Other second-order equations
• The laplace transform
• Solution of differential equations by laplace transforms
• Convolution
• The dirac delta function