Assignment 1
Least Square Regression
1. What is Least Square Regression method?
2. Let's assume that our objective is to figure out how many topics are covered by a student per
hour of learning. Each pair (X, Y) will represent a student. Since we all have different rates of
learning, the number of topics solved can be higher or lower for the same time invested.
Quiz 1
Interpolation
1.
2.
3.
4.
Assignment 2
Numerical Integration Techniques
1. What are Numerical Integration Techniques?
2. Use the trapezoidal rule to numerically integrate
f(x) = 0.2 + 25x
3. Use the trapezoidal rule to numerically integrate rule to numerically integrate
f(x) = 0.2 + 25x + 3x²
4. Use the 2-segment trapezoidal rule to numerically integrate f(x) = 0.2 + 25x + 3x² from a = 0
to b = 2.
5. Use Simpson’s 1/3 rule to integrate f(x) = 0.2 + 25x + 3x² + 8x³ from a = 0 to b = 2.
Quiz 2
Numerical Differentiation
1. Estimate the first derivative of f(x) = −0.1x⁴ − 0.15x³ − 0.5x² − 0.25x + 1.2 at x = 0.5 using a
step size h = 0.5. Repeat the computation using h = 0.25.
2.
3. f(x) = −0.1x⁴ − 0.15x³ − 0.5x² − 0.25x + 1.2, xi = 0.5, h1 = 0.5, h2 = 0.25.
4. Estimate the first derivative of f(x) = −0.3x⁴ − 0.17x³ − 0.5x² − 0.25x + 1.2 at x = 0.5 using a
step size h = 0.5
Assignment 3
Ordinary Differential Equations
1. What are the different methods of ODE in numerical methods?
2. Give 3 examples of ODE
3. Find the differential equation y¹ = f(y) satisfied by y(t) = 4e^(2t) + 3.
Quiz 3
1. y¹= 1/(e^y)
2. dy/dx = x(y²+1)
3. dP/dt = kP
4. y¹ = y²