Numerical Methods for Engineers , primarily taught by Jeffrey Chasnov of the Hong Kong University of Science and Technology
: The standard systematic method for solving linear systems. Coursera assignments often require you to program partial pivoting to prevent division by zero or severe round-off errors.
Coursera employs plagiarism detection algorithms for code submissions. Flagged accounts risk certificate revocation or account suspension. numerical methods for engineers coursera answers
: These methods approximate the area under a curve using straight lines or parabolas. You will often be asked to calculate the global truncation error for these methods.
In the world of engineering, many real-world problems—like predicting heat transfer in a skyscraper or modeling airflow over a wing—result in differential equations that are impossible to solve "exactly" with pen and paper. This course follows a structured 6-week journey to teach students how to approximate these solutions using algorithms and Scientific Computing (Week 1): Numerical Methods for Engineers , primarily taught by
One of the strengths of this course is the emphasis on applying numerical methods to real-world engineering problems. The instructor provides many examples and case studies that illustrate how numerical methods can be used to solve practical problems in fields such as mechanical engineering, electrical engineering, and civil engineering.
The course covers the fundamental concepts of numerical methods, including: In the world of engineering, many real-world problems—like
| Week | Topic | Key Concepts | 💻 Programming Project | | :--- | :--- | :--- | :--- | | | Scientific Computing | MATLAB basics (scripts, functions, vectors, matrices, loops, plots) and double-precision numbers. | Create a bifurcation diagram for the logistic map. | | 2 | Root Finding | The bisection method, Newton's method, and the secant method for finding the zeros of a function. | Use Newton's method to compute the Feigenbaum delta from a logistic map bifurcation diagram. | | 3 | Matrix Algebra | Numerical linear algebra concepts: Gaussian elimination with partial pivoting, LU decomposition, operation counts, and the power method for eigenvalues. | Apply Newton's method to solve the Lorenz equations. | | 4 | Quadrature and Interpolation | Numerical integration (quadrature): trapezoidal rule, Simpson's rule, Gaussian quadrature, and adaptive routines. Interpolation: linear and cubic spline interpolation. | Write a MATLAB code combining quadrature and root-finding to find the zeros of a Bessel function. | | 5 | Ordinary Differential Equations (ODEs) | Initial value problems (IVPs) for solving ODEs, with methods such as Euler's method, Heun's method, and the Runge-Kutta (RK4) method. | Solve the Two-Body Problem. | | 6 | Partial Differential Equations (PDEs) | Boundary value problems (BVPs) for solving PDEs, including the two-dimensional diffusion equation and methods to classify and solve PDEs numerically. | Write a code to solve the Two-Dimensional Diffusion Equation. |