Calculus for Engineers MATH 3495

Upon successful completion of this course, the student will be able to:

• Use matrix methods to solve systems of simultaneous linear equations, fit a polynomial curve to given data, and perform polynomial interpolations.
• Use numerical derivatives to differentiate a given function or time-series (e.g. to calculate the velocity of an object from a time-series of its displacement).
• Determine the best step-size to use in numerical differentiation, taking into account the effects of truncation error and round-off error.
• Use numerical integration techniques (including the Trapezoid Rule and Simpson's Rule) to evaluate definite integrals, such as those arising in volume, centroid or moment of inertia calculations and in problems related to work done, hydrostatic force, or beam deflections.
• Write Taylor series expansions and use them to analyze the truncation error in a numerical integration.
• Solve separable and linear first-order differential equations such as arise in problems of practical engineering interest (e.g. motion in viscous and resistive media, mixing, drainage).
• Solve single first-order differential equations, systems of first-order differential equations and single second-order differential equations using numerical techniques for initial value problems (including Euler's method and Heun's method).
• Reduce higher-order differential equations to an equivalent system of first-order differential equations.
• Solve linear second-order differential equations with constant coefficients such as arise in problems of practical engineering interest (e.g. beam deflections, mechanical vibrations, forced oscillations, resonance).

Effective as of Fall 2006