(Volume 2)

Applied Mathematics: Body & Soul is a mathematics education reform project developed at Chalmers University of Technology and includes a series of volumes and software. The program is motivated by the computer revolution opening new possibilities of computational mathematical modeling in mathematics, science and engineering. It consists of a synthesis of Mathematical Analysis (Soul), Numerical Computation (Body) and Application. Volumes I-III present a modern version of Calculus and Linear Algebra, including constructive/numerical techniques and applications intended for undergraduate programs in engineering and science. Further volumes present topics such as Dynamical Systems, Fluid Dynamics, Solid Mechanics and Electro-Magnetics on an advanced undergraduate/graduate level.

Volume 2.- 27 The Integral.- 28 Properties of the Integral.- 29 The Logarithm log(x).- 30 Numerical Quadrature.- 31 The Exponential Function exp(x) = ex.- 32 Trigonometric Functions.- 33 The Functions exp(z), log(z), sin(z) and cos(z) forz ? ?.- 34 Techniques of Integration.- 35 Solving Differential Equations Using the Exponential.- 36 Improper Integrals.- 37 Series.- 38 Scalar Autonomous Initial Value Problems.- 39 Separable Scalar Initial Value Problems.- 40 The General Initial Value Problem.- 41 Calculus Tool Bag I.- 42 Analytic Geometry in ?n.- 43 The Spectral Theorem.- 44 Solving Linear Algebraic Systems.- 45 Linear Algebra Tool Bag.- 46 The Matrix Exponential exp(xA).- 47 Lagrange and the Principle of Least Action*.- 48 N-Body Systems*.- 49 The Crash Model*.- 50 Electrical Circuits*.- 51 String Theory*.- 52 Piecewise Linear Approximation.- 53 FEM for Two-Point Boundary Value Problems.- References.