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Web Programming Projects at LCSR (HTML, PHP, MySQL)

Introduction to Computer Science (JAVA Language)

Data Structures Projects (JAVA Language)

Computer Architecture Projects (C Language)

Systems Programming (C language)

Principles of Programming Languages (Scheme, Prolog, Python)

Numerical Analysis (MATLAB Language)

Calculus - Multivariable and Differential Equations (Maple Language)

Multivariable Calculus

  • Vector Computation - For this lab, the data will consist of coordinates for three points p, q, and r, in R^3. This program computes the vectors pq, pr, and v. Vector v is determined by the cross product of pq x pr.

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  • Vector-valued function - The components of the vector function will be various combinations of sine and cosine. This could be the theoretical description of the backbone of a large molecule. This program computes the length and curvature of the vector function.

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  • Curves and Surface- This program determines whether F(x,y)=0 is a hyperbola, a parabola, or an ellipse and finds the values for which y is (A,y) on the curve F(x,y)=0. It also determines what kind of surface G(x,y,z) is. The possible surfaces are a paraboloid, an ellipsoid, or a hyperboloid and finds the values for which z is (B,C,z) on the curve G(x,y,z) = 0.

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  • Region in Plane - This program finds the center of gravity(centroid) of the region, the area of the region , the volume of the region, and the total mass of the material filling region. It also displays the region in space and in the plane graphically.

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Differential Equations

  • Exact and Approximate Solutions of Differential Equations The program finds exact and approximate solutions of differential equations and initial value problems, finding both solutions in the form of explicit functions, solutions defined only implicitly, and graphic representations of approximate solutions.

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  • Numerical Methods This program approximate the solution of differential equations by numerical methods and superimpose these solutions on the direction fields. This allows us to extend our understanding of the solutions of differential equations for which a closed form solution is not available.

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  • The Pendulum This program examines differential equations modeling free oscillations. The effect of damping in the linear model and in the nonlinear model are compared with each other.

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  • Linear Systems - This program finds eigenvalues and eigenvectors of matrices, and solve systems of linear algebraic equations as well as systems of first-order linear differential equations.

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  • A Nonlinear System - This program examines the phase plane of an autonomous nonlinear system of two differential equations of the form x'(t) = F(x,y) and y'(t) = G(x,y).

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Projects