**ERROR ANALYSIS**

Maclaurin series of the exponential function: File_1_1

Round-off error: File_1_2

Taylor series expansion of cos(x): File_2_1

**ROOTS OF EQUATIONS**

Graphical method: File_3_1

Bisection method: File_3_2

Root of sin(x) = x^2: File_3_3

Fixed-point iteration: File_4_1

Root of sin(sqrt(x)) – x = 0: File_4_2

Newton-Raphson method for a single equation: File_4_3

Newton-Raphson method for a system of two equations: File_4_4

Roots of the system: (x=y+x^2-0.5; y=x^2-5xy): File_4_5

**LINEAR ALGEBRAIC EQUATIONS**

Naive Gauss elimination: File_5_1

Gauss-Seidel iterative solver: File_6_1

**OPTIMIZATION**

Golden-section search for maximum of a function: File_7_1

**CURVE FITTING**

Linear regression: File_8_1

Polynomial regression: File_8_2

Newton’s interpolating polynomials: File_9_1

Lagrange’s interpolating polynomials: File_9_2

Cubic splines: File_9_3

**NUMERICAL DIFFERENTIATION AND INTEGRATION**

Integration commands in MAPLE: File_10_1

Trapezoidal rule: File_10_2

Simpson’s 1/3 rule: File_10_3

Derivation of two-point Gauss-Legendre points and weights: File_11_1

Multiple application of three-point Gauss-Legendre quadrature: File_11_2

**ORDINARY DIFFERENTIAL EQUATIONS**

Euler’s method: File_13_1

Numerical results by Euler’s method: Euler.pdf

Heun’s method: File_13_2

Numerical results by Heun’s method: Heun.pdf

Ralston’s method: File_13_3

Numerical results by Ralston’s method: Ralston.pdf

System of ODEs: File_13_4

Numerical results for system of ODEs: System.pdf