Lecture Notes

Objectives and Outcomes

Fourier Analysis

Fourier Series Example

Fourier Series 2

Vibration

Fourier Integrals

Fourier Integral Exmaple

Fourier Transforms

Partial Differential Equations

Separation of Variables

Series Solutions of Wave Equation

MathCAD of Series Solutions

D'Alembert's Solution

Heat Diffusion Equation

Heat Equation Series Solution

Heat Equation Special Solution

2-D Steady Heat Equation

MathCAD 2-D Heat Transfer

Coordinate Transformation

2-D Wave Equation

MathCAD 2-D Wave Equation

Group-1 Presentation: Finite Difference Method (FDM)

FDM MathCAD

Finite Difference Method

Example

Nodal Equations

Special Cases

Numerical Solutions for Unsteady Heat Transfer

Group-2 Presentation: Finite Element Method (FEM)

FEM Assignment

Numerical Integration

Group-3 Presentation: FEM Applications to Heat Transfer Problems