Tracks/Civil Engineering Math — Graduate (MS/PhD)

Civil Engineering Math — Graduate (MS/PhD)

graduate

Beyond the undergraduate core: the advanced mathematics for structural dynamics, finite element analysis, computational fluid dynamics, geotechnical modeling, and reliability-based design — partial differential equations, advanced linear algebra, vector calculus, and probabilistic risk analysis.

concepts

18h

estimated

sections

Advanced Calculus & Analysis (rigorous foundations for numerical methods)

1Sequences and Their Limits
50 min
2Convergence of Series
35 min
3Taylor Series
50 min
4The Riemann Integral
35 min

Series & Transforms (vibration analysis, PDE solutions, signal processing)

1Series Convergence Tests
50 min
2Power Series
35 min
3Fourier Series
55 min
4Laplace Transform
20 min

Vector Calculus for Continuum Mechanics (stress/strain fields, fluid flow)

1Vector Fields
35 min
2Line Integrals
35 min
3Divergence and Curl
35 min
4Green's Theorem
35 min
5Surface Integrals
25 min
6Stokes' Theorem
25 min
7Divergence Theorem
25 min

Advanced Linear Algebra (finite element method, modal & buckling eigenvalue analysis)

1Linear Transformations
30 min
2Vector Space
40 min
3Determinant
30 min
4Eigenvalues and Eigenvectors
45 min

Differential Equations & PDEs (structural dynamics, heat conduction, groundwater flow)

1Second-Order Differential Equations
30 min
2Separation of Variables
30 min
3Laplace Transform
20 min
4Partial Differential Equations
45 min
5Numerical Methods
40 min
6Finite Element Method
50 min

Advanced Probability, Statistics & Reliability (risk analysis, structural reliability, geostatistics)

1Random Variables
30 min
2Expected Value
30 min
3Normal Distribution
40 min
4Hypothesis Testing
30 min
5Linear Regression
30 min
6Confidence Intervals
20 min