Course structure Title: Numerical Methods for Technology Professionals
Course Description: This course introduces essential numerical methods used in solving engineering and scientific problems with an emphasis on applications in technology and software development. Through lectures, hands-on labs, and projects, students will learn to implement numerical algorithms using modern programming tools and gain insights into their applications across various sectors of the tech industry.
Course Structure:
Week 1-2:
Introduction to Numerical Analysis Overview of Numerical Methods: Importance in tech, basic concepts. Errors in Numerical Computation: Sources of errors, stability, and convergence.
Week 3-4:Solving Linear Equations Direct Methods: Gaussian elimination, LU decomposition. Iterative Methods: Jacobi, Gauss-Seidel, and SOR methods. Applications: Circuit analysis, computer graphics, and other tech applications.
Week 5-6:
Nonlinear Equations and Optimization Root Finding: Bisection method, Newton-Raphson method, Secant method. Optimization Techniques: Gradient descent, Newton’s method in optimization. Applications: Machine learning parameter tuning, robotics, and game development.
Week 7-8:
Interpolation and Curve Fitting Polynomial Interpolation: Lagrange and Newton polynomials. Splines: Linear, quadratic, and cubic splines. Least Squares Regression: Linear and nonlinear regression. Applications: Data visualization, model fitting in data science, animation.
Week 9-10:
Numerical Integration and Differentiation Numerical Differentiation: Finite difference methods, error analysis. Numerical Integration: Trapezoidal rule, Simpson’s rule, Gaussian quadrature. Applications: Scientific simulations, financial modeling, and quantitative analysis.
Week 11-12:
Differential Equations Initial Value Problems: Euler’s method, Runge-Kutta methods. Boundary Value Problems: Finite difference method, shooting method. Applications: Weather forecasting, engineering simulations, population dynamics. Week 13-14: Fast Fourier Transform (FFT) and Applications Understanding FFT: Algorithms and properties. Applications: Signal processing, image processing, audio compression.
Week 15-16:
Eigenvalues and Eigenvectors Power Method: For largest eigenvalues. QR Algorithm: For full spectrum. Applications: Structural analysis, systems theory, PCA in machine learning.
Course Format:
Lectures:
Twice a week.Labs:
Weekly lab sessions applying numerical methods using Python or MATLAB.
Project:
Capstone project integrating multiple numerical methods to solve a real-world problem relevant to the tech industry. Assessment: Combination of quizzes, assignments, lab reports, and a final project.
Learning Outcomes:
Understand and apply key numerical methods to solve practical problems in technology.
Develop proficiency in a programming environment conducive to implementing numerical algorithms.
Analyze and interpret results from numerical computations relevant to tech industry applications.
Target Audience:
This course is intended for aspiring tech professionals, software engineers, data scientists, and anyone interested in applying mathematical methods to solve practical problems in technology.
By the end of this course, participants will have a solid foundation in numerical methods, enhanced programming skills, and a clear understanding of how these methods apply across different areas of technology. This comprehensive approach ensures readiness for a tech-oriented career path where analytical skills and the ability to solve complex computational problems are crucial.