Practice Problems

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These represent problems that emphasize topics that we believe are important and that may be similar to problems that you will see on tests.

Matlab Examples and Problems

• MacLaurin Series example: maclaurin.m, maclaurin2.m
• Bisection algorithm: find_root_bisection.m
• False position algorithm: find_root_false_position.m
• Newton Raphson algorithm: find_root_newtonraphson.m
• Polynomial regression: polynomial_fit.m
• Motion of a Projectile: Problem (Solution; trajectory.m)
• Exponential Growth and Decay: Problem (Solution; expGD.m)
• Golden Section Search Optimization Algorithm: gold_section_search.m

Floating Point Numbers

• Addition, Subtraction, Multiplication: Problem (Solution)

Taylor Series and Error

• Taylor Series Function Approximation: Problem (Solution)

Root Finding Algorithms

• Graphical Root Finding (Bisection, False-Position, and Newton-Raphson): Problem (Solution)
• Numerical Root Finding Problem 1 (False-Position and Newton-Raphson): Problem (Solution)
• Numerical Root Finding Problem 2 (False-Position and Newton-Raphson): Problem (Solution)
• More problems and information about root finding can be found in the section on interactive learning tools for numerical methods.

Curve Fitting and Interpolation

• Linearization of Coefficients: Problem (Solution)
• Fitting a Curve through a Model and Interpolation: Problem (Solution)
• Fitting a Curve through Log Data: Problem (Solution)
• Fitting a Curve and Examining Data: Problem (Solution)
• Derivation of straight line equations: Problem (Solution)
• Gain a better insight into straight-line curve fitting, correlation, and polynomial curve fitting using the interactive learning tools for numerical methods.

Numerical Integration

• Multiple Trapezoidal Rule: Problem (Solution)

• Mass of a Variable Density Rod: Problem (Solution)

• Work in Thermodynamics: Problem (Solution)

ODE Solving

• Euler and RK4 Methods with Falling Object: Problem (Solution)

• Heun's Method in Launching of Projectile: Problem (Solution)
  

Optimization

• Optimization using Golden Section Search: Problem (Solution;  Excel)
• Optimization using Steepedst Descent: Problem (Solution)