This text surveys the mathematical foundations of applied mechanics. The sections on engineering mathematics covers simultaneous algebraic and differential equations, matrix algebra, the theory of optimization and the calculus of variations. Considerable attention is also paid to engineering applications in theoretical thermodynamics, strength of materials ang Lagrangian-Hamiltonian dynamics. The unifying themes of the text are the mathematical foundations, work-energy principles and the Legendre transform.
The only prerequisite is the background in mathematics and physics typical of the advanced-undergraduate in engineering.
1. Theory of Equations 2. Theory of Extreme Values of Functions 3. The Calculus of Variations 4. The Extremum Principles of Thermodynamics 5. The Stationarity of Extremum Principles of Solid Mechanics 6. Equations of Motion and the Stationarity Principles of Language and Hamilton Appendix A: Matrix Algebra and the Linear Inderpendence of Vectors Appendix B: A Review of Elementary Real Analysis
Dewey Decimal Classfication (DDC)