Textbook in PDF format

Introduction
Physical Processes and Mathematical Models
Approximation, Error, and Convergence
Approximate Solution of Differential Equations and the Finite Element Method
Brief History of the Finite Element Method
Finite Element Software
Significance of Finite Element Analysis for Engineering
Typical Process for Obtaining a Finite Element Solution for a Physical Problem
A Note on Linearity and the Principle of Superposition
Strong and Weak Form for One-Dimensional Problems
Strong Form for One-Dimensional Elasticity Problems
General Expressions for Essential and Natural B.C. in One-Dimensional Elasticity Problems
Weak Form for One-Dimensional Elasticity Problems
Equivalence of Weak Form and Strong Form
Strong Form for One-Dimensional Heat Conduction
Weak Form for One-Dimensional Heat Conduction
Finite Element Formulation for One-Dimensional Problems
Introduction—Piecewise Approximation
Shape (Interpolation) Functions and Finite Elements
Discrete Equations for Piecewise Finite Element Approximation
Finite Element Equations for Heat Conduction
Accounting for Nodes with Prescribed Solution Value (“Fixed” Nodes)
Examples on One-Dimensional Finite Element Analysis
Numerical Integration—Gauss Quadrature
Convergence of One-Dimensional Finite Element Method
Effect of Concentrated Forces in One-Dimensional Finite Element Analysis