A short course in mathematical methods with Maple
This unique book provides a streamlined, self-contained and modern text for a one-semester mathematical methods course with an emphasis on concepts important from the application point of view. Part I of this book follows the ?paper and pencil? presentation of mathematical methods that emphasizes fundamental understanding and geometrical intuition. In addition to a complete list of standard subjects, it introduces important, contemporary topics like nonlinear differential equations, chaos and solitons. Part II employs the Maple software to cover the same topics as in Part I in a computer oriented approach to instruction. Using Maple liberates students from laborious tasks while helping them to concentrate entirely on concepts and on better visualizing the mathematical content. The focus of the text is on key ideas and basic technical and geometric insights presented in a way that closely reflects how physicists and engineers actually think about mathematics.
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Vectors and Vector Calculus
Matrices and Rotations
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algebraic angle arbitrary axis basis vectors Bessel functions calculate coefficients column vectors command constant convergence coordinate system corresponding cos(u critical point curve defined derivative determinant diagonal divergence dsolve eigenvalue problem eigenvalues eigenvectors end proc equal equilibrium Example exponential expression Find formula Fourier series given gradient Hermitian homogeneous identity initial conditions inner product interval inverse KdV equation Legendre polynomials Let us consider Liapunov function line integral linear combination linear system linearly independent Maple multiplication nonlinear obtain operator orthonormal parameter particular solution permutation plane plot power series relation restart result rewrite right hand side rotation matrix satisfy scalar series expansion series solution Show shown in Figure soliton solve special orthogonal matrix spherical stable Sturm-Liouville surface system of differential theorem thickness=2 trajectories unit vector unstable vanishes variable Vector Calculus vector field vector space Wronskian yields zero