1.Exercise13: Implement Ramanujan’s formula for pi approximation.
1.Example: Add three numbers.
2.Exercise1: Calculate
3.Exercise10: generate variety or error messages.
4.Exercise11: Output a greeting message to a person with specific name and age.
5.Exercise12: Calculate the area of a donut.
6.Exercise13: Find indexes of elements within array that satisfy:
7.Exercise14: Modify the values of an array such that they satisfy:
8.Exercise14b:Script applying [boundedA] = myBoundingArray(A, top, bottom).
9.Exercise2: Create a matrix filled with 1's in checker board pattern.
10.Exercise3: Calculate area of a triangle.
11.Exercise4: Split a matrix into two column-wise.
12.Exercise5: Calculate cylinder area and volume.
13.Exercise6: Find numbe of odd values in an array.
14.Exercise7: Create a matrix filled with 2's.
15.Exercise8: Concatenate two strings.
16.Exercise9: Create an object consisted of 3 fields.
17.TryIt1: Calculate simple trigonometric sums.
18.TryIt2: Calculate all the distances between 3 coordinates.
19.TryIt3: Add one to a function.
20.TryIt4:Script file for computing Cylinder Volume and Surface Area.
1.Exercise1: Calculate the tip based on number of people and bill.
2.Exercise2: Implement a simple calculator.
3.Exercise3: Find whether a point is inside, outside or on the boundary of a regular polygon.
4.Exercise3b:Script for testing Function [S] = myInsidePolygon(polygon, point).
5.Exercise4: Modify an array to specific length, padded with 0's at end / trimmed if necessay.
6.Exercise5: Modify an array to specific length, padded with 0's at end / trimmed if necessay. No if else statements.
7.Exercise6: Represent a grade as a letter, [A+, F], based on a given percentage [0, 100]. (Map 40 to 12.)
8.Exercise7: Verify if sensor readings are measuring same variable.
9.Exercise8: Find the roots of a quadratic equation over
10.Exercise9: Define a piecewise function according to:
11.TryIt1: Make a thermostat switch based on temperature readings.
12.TryIt2: Print the parity of a number.
13.TryIt3: Calculate area or circumference of circle based on argument value .
1.Exercise10: Find first N primes by trial division.
2.Exercise11: Find first N Fibonacci that are also Primes.
3.Exercise12: Create a matrix,
4.Exercise13: Construct a Adjacency List from Adjacency Matrix (from nodes of unidirected graph).
5.Exercise13b:Script for applying [node] = myConnectivityMat2Struct(C, names).
6.Exercise2: write custom function to find max element in array of doubles.
7.Exercise3: Find the M largest array elements.
8.Exercise4: Create a matrix,
9.Exercise5: Implement matrix multiplication.
10.Exercise5b:Script applying [M] = myMatMult(P,Q).
11.Exercise6: Years needed to achieve final balance based on initial balance and interest rate.
12.Exercise7: Find all array indexes containing specific value.
13.Exercise8: Simulate rolling two dice. (Roll again if same and sum altogether.)
14.Exercise8b:Script for testing: [roll] = myMonopolyDice().
15.Exercise9: Find if n is prime by trial division.
16.TryIt1:Script for determining the number of additions in one processor clock cycle.
1.Exercise1: Sum of array elements.
2.Exercise10: Construct NxN matrix of 0's and 1's in spiral pattern using iteration.
3.Exercise11: Demonstrate infinite recursion and reaching max depth error message.
4.Exercise13: Solve Towes of Hanoi iterarively.
5.Exercise15: Sort an integer array using iterative Quick Sort.
6.Exercise2: Obtain
7.Exercise2b: Script for ploting various orders of Chebyshev Polynomials of first kind
8.Exercise3: Obtain Ackerman function from the recurrence relation:
9.Exercise4: Calculate combinations of k elements out of set containing n from the recurrence relation:
10.Exercise5: Express amount of money in terms of the values in dollar denominations: banknotes: 100, 50, 20, 10, 5, 1; coins: 0.25, 0.10, 0.05, 0.01.
11.Exercise6: Calculate the Golden Ratio from the continued fraction:
12.Exercise7: Calculate the Greatest Common Divisor of a and b from the recurrence relation:
13.Exercise8: Calculate the values in a row of the Pascal Triangle or coefficients of m-th order binomial (polynomial) equation.
14.Exercise9: Construct NxN matrix of 0's and 1's in spiral pattern using recursion.
15.TryIt1: Calculate
16.TryIt2: Calculate the n-th Fibonacci number recursively.
17.TryIt3: Calculate the n-th Fibonacci number iteratively.
18.TryIt3b:Script for testing compexity of iterative vs recursive Fibonacci functions.
19.TryIt4: Solve the Towers of Hanoi -recursive.
20.TryIt5: Sort an integer array using Quick Sort - recursive.
1.Exercise7a: Calculate n-th Fibonacci number iteratively using predefined size array.
2.Exercise7b: Calculate n-th Fibonacci number iteratively expanding an array on each iteration.
3.Exercise7c:Script testing execution time of function using predefined size of arrays (a) and expanding array on each iteration (b).
4.TryIt1: Estimate complexity of a function based on its code. Estimated complexity: profile on; ChapterTryIt1(1000); profexport('Chapter7TryIt1', 'Function Profiling');
5.TryIt2: calculate n-th Fibonacci using iterative implementation (with memoization?).
6.TryIt3: Estimate the compexity of n-th Fibonacci using recursive implementation.
7.TryIt4: Find number of possible division by 2 or n epxressed as 2^out and estimate complexity.
8.TryIt5:Script comparing implemented vs built-in sum function using profiler.
1.Exercise1: Convert a number from binary to decimal representation.
2.Exercise10: Find the number with specific gap (= 1).
3.Exercise2: Convert a number from decimal to binary representation.
4.Exercise3:Script for verifying the validity of the functions from Chapter8 Ex 1 and Ex2, based on their opposite actions.
5.Exercise4: Perform addition between binary numbers.
6.Exercise6: Convert a IEEE754 floating point to decimal.
7.Exercise7: Construct a IEEE754 binary representation from number in base10 using custom functions and the standard specifications.
8.Exercise7ver: Convert a number from decimal to IEEE754 standard binary using built-in functions.
9.Exercise8: Compare complexity (based on run time plot) of recursive and iterative implementations of functions returning Fibonacci Numbers.
10.TryIt1:Script demonstrating computer limited possibility of storing real numbers and its dependance on the value of the represented number: the larger the number, the larger the gap (space between two consecutive representable values).
11.TryIt2:Script showing IEEE754 single precision floating point representation:
12.TryIt3:Script demonstrating double precision floating point overflow and how MATLAB / Octave is handling it.
13.TryIt4:Script demonstrating underflow of double precision floating point number and how MATLAB /Octave is handling it.
1.TryIt1: Demonstrate input type checking.
1.TryIt1:Script demonstrating the save and load functions; .mat files.
2.TryIt2:Script demonstrating writing to a .txt file; using functions: fopen, fprintf, fclose.
3.TryIt3:Script demonstrating reading from a .txt file and using functions: fopen, fgetl and str2num.
4.TryIt4:Script demonstrating writing to Microsoft Excel files, .xls and the use of function: xlswrite. Error message due to bug made me add the line: r_extnd = 0; in the beginning of function: xlswwrite.m in: io package.
5.TryIt5:Script demonstrating reading a .xls file and the use of functions: xlsread().
1.Exercise1:Script drawing a 2D plot of a cycloid.
2.Exercise10: Plot vertcies of Sierpinski Triangle.
3.Exercise11: Draw Barnsley Fern.
4.Exercise12: Plot a 3D parametric curve.
5.Exercise12b:Script aplying: [ ] = myParametricPlotter(f, g, t).
6.Exercise13: Plot contour or surf.
7.Exercise13b:Script applying [] = mySurfacePlotter(F, x, y, option).
8.Exercise2:Script drawing sublots with different axis scale of the same function.
9.Exercise3:Script drawing two functions on same plot.
10.Exercise4:Script comparing hist vs bar.
11.Exercise5:Script drawing the student grade distribution as a pie chart.
12.Exercise6:Script drawing four 3D suplots of: surf, mesh, contour and contourf.
13.Exercise7: Plot a n-side regular polygon.
14.Exercise8: Use func2str to display a function formula on a plot.
15.Exercise8b:Script testing myFunPlotter(f, x).
16.Exercise9: Plot polynomials of various degrees.
17.Exercise9b:Script applying [] = myPolyPlotter(n, x).
18.TryIt1:Script showing basic data visualization via function plot().
19.TryIt10:Script showing 3D plotting and the use of function plot3().
20.TryIt11:Script showing the use of meshgrid.
21.TryIt12:Script showing 3D graphs using surf and contour.
22.TryIt13:Script showing animation of sine wave by successive redrawing of a plot; ctrl + C to quit.
23.TryIt14:Script showing animation created of successive frames and saved as movie.
24.TryIt14b:Script showing animation created of successive frames which then are converted to movie with the help of other program; Implementation using: ImageMagick/mencoder to manipulate the frames.
25.TryIt2:Script showing a generating of data and displaying it as a function graph.
26.TryIt3:Script showing a function graph with additional paramaters specifying line color and mark type.
27.TryIt4:Script showing plotting multiple data sets on same graph.
28.TryIt5:Script showing the use of graph labels and title.
29.TryIt6:Script showing the use of sprintf in title().
30.TryIt7:Script showing the use of legend().
31.TryIt8:Script showing the use of axis() and grid.
32.TryIt9:Script for generating various subplots and demonstrate the use of functions: subplot, plot, scatter, bar, loglog, semilogx, semilogy.
1.Exercise2: Find if two vectors are orthogonal up to a specific accuracy.
2.Exercise2b:Script applying myIsOrthogonal(v1, v2, tol).
3.Exercise3: Find if two string are similar (additionally showing Cosine Similarity.)
4.Exercise4: Find linear independent columns. (basis) of a matrix.
5.Exercise4b:Script tesing myMakeLinInd().
6.Exercise5: Calculate determinant of a matrix using recursive Cramer's Rule of expanding into minors.
7.Exercise5b:Script applying [D] = myRecDec(M) and comparing it to the built-in: det().
8.Exercise7: Calculate derivative of a polynomial. (differentiating / integrating of polynomials is a linear transformation.)
9.Exercise8: Solve a system of linear equations. Cover all possibilities.
10.Exercise8b:Script applying [N, x] = myNumSols (A, b).
11.Exercise9: Determine power flow along a network edges, based on power generation and demand nodes.
12.Exercise9b:Script applying [f] = myFlowCalculator(S, d).
13.TryIt1:Script showing the use of function norm().
14.TryIt10:Script showing a validation of the method for Solving a Linear System of Equations.
15.TryIt11:Script showing Method for finding Solutions of System of Linear Equations. In particular, the case of overdetermined system with existing solution.
16.TryIt12:Script showing Method for finding Solutions of System of Linear Equations. In particular, the case of infinite numer of solutions.
17.TryIt13:Script demonstrating that a linear combination of solutions of
18.TryIt2:Script calculating the angle between two vectors.
19.TryIt3:Script showing a vector expressed as a linear combination.
20.TryIt4:Script checking vector linear dependence.
21.TryIt5:Script showing matrix multiplication error due to inner-dimension mismatch.
22.TryIt6:Script showing det() and the effect of the identity matrix in multiplication.
23.TryIt7:Script showing the use of determinants for finding if matrix is singular; inverse matrices.
24.TryIt8:Script showing Method for checking if a System of Linear Equations has a solution.
25.TryIt9:Script showing Method for finding Solutions of System of Linear Equations. In particular, the case of unique solution.
1.Exercise2: Least Square Regression (as a solution of System of Linear Equations).
2.Exercise2b:Script applying [Beta] = myLSParams (f, x, y).
3.Exercise3: Least Square Regression with linearized exponential functions.
4.Exercise3b:Script applying [alpha, beta] = myExpFit (x,y).
5.Exercise5:Script applying [beta] = myLinRegression (f, x, y), which is same as Chapter13Exercise2(f, x, y).
6.Exercise6:Script applying [alpha, beta] = myExpRegression (x,y), same as Chapter13Exercise3(x,y).
7.TryIt1:Script demonstrating the equivalent use of x = A \ y; x = pinv(A) * y; x = inv(A' * A) * A' * y;
8.TryIt2:Script demonstrating fitting a line modeled by the estimation function
1.Exercise1: Linear Interpolation.
2.Exercise1b:Script applying [Y] = myNearestNeighbor (x, y, X).
3.Exercise2: Cubic Spline Interpolation.
4.Exercise2b:Script applying [Y] = MyCubicSpline(x, y, X).
5.Exercise3: Nearest Neighbor Interpolation.
6.Exercise3b:Script applying [Y] = myNearestNeighbor (x, y, X).
7.Exercise5: Cubic Spline (Flat) Interpolation (constraints on end points equal to 0).
8.Exercise5b:Script comparing [Y] = MyCubicSplineFlat(x, y, X) and [Y] = MyCubicSpline(x, y, X).
9.Exercise6: Quintic Spline Interpolation.
10.Exercise6b:Script applying [Y] = MyQinticSpline(x, y, X).
11.Exercise7: Plot interpolated data using method specified by argument value.
12.Exercise7: Plot interpolated data using method specified by argument value. Use built-in functions.
13.Exercise7b:Script applying [ ] = myInterpPlotter (x, y, X, option).
14.Exercise8: Cubic Spline Interpolation with slope at end points specified by argument value.
15.Exercise8b:Script applying [Y] =myDCubicSpline (x, y, X, D).
16.Exercise9: Lagrange Polynomial Interpolation.
17.Exercise9b:Script applying [Y] = myLagrange(x,y,X).
18.TryIt1:Script showing Linear Interpolation.
19.TryIt2:Script showing Cubic Spline Interpolation using built-in functions.
20.TryIt3:Script showing how to find polynomials coefficients used in Cubic Spline Interpolation.
21.TryIt4:Script showing interpolation using Lagrange Polynomials.
1.Exercise3: Function
2.Exercise3b:Script comparing the values of a function and its Taylor approximation.
3.Exercise4: Function
4.Exercise4b:Script comparing the values of a function and its Taylor approximation.
5.Exercise5b:Script comparing the errors of Taylor approximations of the function:
6.Exercise5c: Approximation of
7.Exercise5s: Approximation of
8.Exercise5sc: Approximation of
9.Exercise6:Script showing 3rd order Taylor approximation of
10.TryIt1:Script producing a graph of the Taylor expansion (till 3rd term) of the function sin(x) between
11.TryIt2:Script comparing an approximated function value using up to 7th order Taylor expansion with exact value.
12.TryIt3:Script demonstrating the use of linear approximation (1st order or till 1st term) and its range of validity around the point of expansion.
1.Exercise1: Approximate the N-th root of x using the Newton-Raphson method.
2.Exercise2: Find interval of values where
% using the Bisection Method with error metric:
3.Exercise2b:Script applying [X] = myFixedPoints (f, g, tol, maxiter).
4.Exercise4: Show root approximation and error in each successive step in finding root of
5.Exercise4b:Script applying [R, E] = myBisection (f, a, b, tol).
6.Exercise5: Store successive root approximations and errors of
7.Exercise5b:Script applying [R, E] = myNewton (f, df, x0, tol).
8.Exercise6: Minimize the cost of a pipeline (in terms of the value
9.Exercise6b:Script for applying [x] = myPipeBuilder (C_ocean, C_land, L, H); compared against built-in function.
10.Exercise7:Script finding a value for which the Newton step of a function oscillates indefinitely.
11.TryIt1:Script demonstrating function root approximation using fzero().
12.TryIt2:Script demonstrating function root approximation using fzero().
13.TryIt3: Find root of f in tol using the Bysection Method.
14.TryIt4:Script showing Function Root Finding via Bisection Method.
15.TryIt5: Find root of tol, using the Newton-Raphson Method.
16.TryIt5b:Script demonstrating [R] = myNewton (f, dx, x0, tol).
17.TryIt6:Script showing limitations of Newton-Raphson method. In particular derivative of a function that evaluates close to 0.
18.TryIt7:Script showing limitations of Newton-Raphson method. In particular, the instability of convergence leading to unintended root, away from the initial guess.
1.Exercise1: Implement forward, central and backward Finite Difference Method for approximating derivative of a function evaluated on 1D grid of size
2.Exercise1b:Script applying [df, X] = myDerCalc (f, a, b, N, option).
3.Exercise2b:Script applying [dy, X] = myNumDiff(f, a, b, n, option) (same as in Exercise 1).
4.Exercise3: Smooth function values from a 1D grid and use them to approximate function derivative.
5.Exercise3b:Script applying [dy, X] = myNumDiffwSmoothing (x, y, n).
6.TryIt1:Script demonstrating derivative approximation by calculating function value differences on a 1D grid.
7.TryIt2:Script showing the relation between grid spacing and the error of Finite Difference Function Derivatives Approximation.
1.Exercise1: Numerically Approximate the Integral of a function.
2.Exercise2: Implement Simpson's Method: Interpolate the input sample using Lagrange Polynomial and Return Approximation of the area under the curve in the interval
3.Exercise4: Numerically Approximate the Integral of a function.
4.Exercise4b:Script applying [I] = myNumInt(f, a, b, n, option) on few test cases.
5.Exercise5: Calculate the coefficients of the n-th term in Fourier Series.
6.Exercise5a: Apply [An, Bn] = myFourierCoeff (f, n) an plot the result along with exact function value.
7.Exercise5b: Script applying [An, Bn] = myFourierCoeff (f, n) on few test cases.
8.TryIt1: Script demonstrating Numerical Integration Methods: Riemann, Midpoint Method. Approximate the integral of
9.TryIt2: Script demonstrating integral approximation using Trapezoid Rule.
10.TryIt3: Script demonstrating Integration Approximation using Simpson's Rule.
11.TryIt4: Script comparing Built-in vs Custom Trapezoidal Rule implementation for approximating Integrals of functions.
12.TryIt5: Script demonstrating approximation of a Cumulative Integral using built-in functions.
13.TryIt6: Script demonstrating approximation of Integrals using built-in functions.
1.Exercise1: Represent Logistic Equation.
2.Exercise1b: Script comparing approximation and analytic solution to the Logistis Equation.
3.Exercise2: Represent the Lorenz Equation, which is a simplified system of equations describing the 2D flow of fluid.
4.Exercise2a: Solve the Lorenz Equation using ode45.
5.Exercise2b: Script showing a plot of a solution of the Lorenz Equation; creating a simulation (animation) of particle trajectory (Lorenz Attractor).
6.Exercise3: Represent Mass-Spring-Damper system by reducing the order of the ODE describing it.
7.Exercise3b: Script showing a plot of the solutions to the Mass-Spring-Damper system in the cases of: no damping, underdapming, critical damping and overdamping.
8.Exercise4: Implement Forward Euler method for ODE integration.
9.Exercise4b: Script applying [T, S] = myForwardEuler (dS, tSpan, S0) and comparing it to ode45 and the exact solution.
10.Exercise5: Implement fourth order Runge-Kutta method for ODE integration.
11.Exercise5b:Script applying [T, S] = myRK4(dS, tSpan, S0) and comparing it to ode45.
12.TryIt1: Script demonstrating Euler Approximation for Exponential Function.
13.TryIt2: Script demonstrating Numerical Stability of ODEs Integration schemes.
14.TryIt3: Script demonstrating built-in ODE solvers and their approximation error.
15.TryIt4: Script demonstrating built-in ODE solvers and their approximation error.
16.TryIt5: Script demonstrating built-in ODE solver: ode45.
OS: Windows 10
IDE: Octave-4.2.1
MIT License
Copyright (c) 2017 Chris B. Kirov
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.