Methods of Applied Mathematics for Engineers and Scientists

Based on course notes from over twenty years of teaching engineering and physical sciences at Michigan Technological University, Tomas Co's engineering mathematics textbook is rich with examples, applications and exercises. Professor Co uses analytical approaches to solve smaller problems to provide mathematical insight and understanding, and numerical methods for large and complex problems. The book emphasises applying matrices with strong attention to matrix structure and computational issues such as sparsity and efficiency. Chapters on vector calculus and integral theorems are used to build coordinate-free physical models with special emphasis on orthogonal co-ordinates. Chapters on ODEs and PDEs cover both analytical and numerical approaches. Topics on analytical solutions include similarity transform methods, direct formulas for series solutions, bifurcation analysis, Lagrange-Charpit formulas, shocks/rarefaction and others. Topics on numerical methods include stability analysis, DAEs, high-order finite-difference formulas, Delaunay meshes, and others. MATLAB(r) implementations of the methods and concepts are fully integrated.1. Matrix algebra; 2. Solution of multiple equations; 3. Matrix analysis; 4. Vectors and tensors; 5. Integral theorems; 6. Ordinary differential equations: analytical solutions; 7. Numerical solution of initial and boundary value problems; 8. Qualitative analysis of ordinary differential equations; 9. Series solutions of linear ordinary differential equations; 10. First order partial differential equations and the method of characteristics; 11. Linear partial differential equations; 12. Integral transform methods; 13. Finite difference methods; 14. Method of finite elements.