Mathematics for Engineers Specialization Course Syllabus
Full curriculum breakdown — modules, lessons, estimated time, and outcomes.
Overview: This specialization provides a comprehensive foundation in key mathematical concepts essential for engineering disciplines. Through five core courses and a capstone project, learners will develop analytical and computational skills using MATLAB. The program spans approximately 106 hours, combining theory with practical applications in engineering contexts.
Module 1: Matrix Algebra for Engineers
Estimated time: 19 hours
- Matrix operations and properties
- Gaussian elimination and row reduction
- LU decomposition
- Eigenvalues and eigenvectors
Module 2: Differential Equations for Engineers
Estimated time: 26 hours
- First-order differential equations
- Second-order linear equations
- Laplace transforms
- Systems of differential equations
Module 3: Vector Calculus for Engineers
Estimated time: 26 hours
- Gradient, divergence, and curl
- Line and surface integrals
- Green’s theorem
- Gauss’s (Divergence) theorem
- Stokes’s theorem
Module 4: Numerical Methods for Engineers
Estimated time: 26 hours
- Numerical root finding
- Numerical integration techniques
- Numerical solutions to differential equations
- Implementation using MATLAB
Module 5: Mathematics for Engineers: The Capstone Course
Estimated time: 9 hours
- Modeling fluid flow around a cylinder
- Simulation of Kármán vortex street
- Application of vector calculus and differential equations
Module 6: Final Project
Estimated time: 9 hours
- Develop a MATLAB simulation of fluid dynamics
- Apply matrix algebra and numerical methods
- Present results with analysis and visualizations
Prerequisites
- Basic knowledge of calculus and linear algebra
- Familiarity with differential equations fundamentals
- Some exposure to programming (helpful but not required)
What You'll Be Able to Do After
- Perform advanced matrix operations and decompositions
- Solve complex differential equations using analytical and numerical methods
- Apply vector calculus to three-dimensional engineering problems
- Implement numerical algorithms in MATLAB for scientific computation
- Model and simulate real-world physical phenomena like fluid flow