The textbook "Calculus" by Gilbert Strang, is a modern calculus text written in a human-friendly style. Published in 1991 and still in print from Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor's Manual and a student Study Guide.
This digital textbook was reviewed for its alignment with California content standards.
Introduction to computational techniques arising in aerospace engineering. Applications drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.
Modeling a Changing World written by mathematics professor Tim Chartier and his student Nick Dovidio presents curricular material in an OSP Launcher package to motivate the need for numerically solving ordinary differential equations. The package discusses such applications as a mass-spring system and its connection to computer simulation for movies. An interactive model that simulates a two-body gravitational model of the moon and earth allows for exploring the topic of numerical error. Other models explore topics that include slope fields, numerical integration and numerical solvers for ordinary differential equations.
This course introduces students to MATLAB. Numerical methods include number representation and errors, interpolation, differentiation, integration, systems of linear equations, and Fourier interpolation and transforms. Students will study partial and ordinary differential equations as well as elliptic and parabolic differential equations, and solutions by numerical integration, finite difference methods, finite element methods, boundary element methods, and panel methods.
Introduction to numerical methods: interpolation, differentiation, integration, systems of linear equations. Solution of differential equations by numerical integration, partial differential equations of inviscid hydrodynamics: finite difference methods, panel methods. Fast Fourier Transforms. Numerical representation of sea waves. Computation of the motions of ships in waves. Integral boundary layer equations and numerical solutions.
Introduction to numerical methods: interpolation, differentiation, integration, systems of linear equations. Solution of differential equations by numerical integration, partial differential equations of inviscid hydrodynamics: finite difference methods, panel methods. Fast Fourier Transforms. Numerical representation of sea waves. Computation of the motions of ships in waves. Integral boundary layer equations and numerical solutions.
The deceptively simple problem of numerically solving for a charged particle moving in a static magnetic field is analyzed and solved. One does not need to "take small steps" to accurately simulate motion in interesting non-uniform fields (illustrated for a dipole).
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