The purpose of this task is to give students experience modeling a real-world example of exponential growth, in a context that provides a vivid illustration of the power of exponential growth, for example the cost of inaction for a year.

This class is an applications-oriented course covering the modeling of large-scale systems in decision-making domains and the optimization of such systems using state-of-the-art optimization tools. Application domains include: transportation and logistics planning, pattern classification and image processing, data mining, design of structures, scheduling in large systems, supply-chain management, financial engineering, and telecommunications systems planning. Modeling tools and techniques include linear, network, discrete and nonlinear optimization, heuristic methods, sensitivity and post-optimality analysis, decomposition methods for large-scale systems, and stochastic optimization.
This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5223 (System Optimisation: Models and Computation).

This simple conceptual problem does not require algebraic manipulation, but requires students to articulate the reasoning behind each statement.

This task provides an opportunity for students to construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

This task provides an opportunity for students to construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

This task focuses on the fact that exponential functions are characterized by equal successive quotients over equal intervals. This task can be used alongside F-LE Equal Factors over Equal Intervals.

This task focuses on the fact that linear functions are characterized by constant differences over equal intervals. It could be used alongside to F-LE Equal Differences over Equal Intervals I & II.

This course is offered to graduate students and addresses issues regarding ultrafast optics. Topics covered include: Generation, propagation and applications of ultrashort pulses (nano-, pico-, femto-, attosecond pulses); Linear and nonlinear pulse shaping processes: Optical solitons, Pulse compression; Laser principles: Single- and multi-mode laser dynamics, Q-switching, Active and passive mode-locking; Pulse characterization: Autocorrelation, FROG, SPIDER; Noise in mode-locked lasers and its limitations in measurements; Laser amplifiers, optical parametric amplifiers, and oscillators; Applications in research and industry: Pump-probe techniques, Optical imaging, Frequency metrology, Laser ablation, High harmonic generation.

These problems give students the opportunity to construct and compare linear, quadratic, and exponential models.

This worksheet guides students through the somewhat lengthy process of finding the equation of a line given two points.