Engineering Mathematics
Calculus to FEM, statistics, transforms and cryptography
Mathematical Foundations
- Number Systems
- Arithmetic, Units & Significant Figures
- Algebra & Equations
- Exponents, Radicals & Logarithms
Functions, Trigonometry & Geometry
Engineering Mathematics I: Calculus
- Limits
- Continuity
- Differentiation
- Applications of Derivatives
- Mean Value Theorems
- Integration
- Applications of Integration
Engineering Mathematics II: Multivariable & Vector Calculus
- Functions of Several Variables
- Partial Differentiation
- Total Differential & Error Propagation
- Jacobians & Coordinate Transformations
- Double & Triple Integrals
- Vector Algebra
- Gradient, Divergence & Curl
- Line & Surface Integrals
- Green, Gauss & Stokes Theorems
Engineering Mathematics III: Differential Equations & Transforms
- Differential Equation Fundamentals
- First-Order ODEs
- Higher-Order Linear ODEs
- Systems of ODEs & State Space
- Series Solutions & Taylor Series
- Special Differential Equations
- Laplace Transform Methods
- Fourier Series
- Fourier Transform
Engineering Mathematics IV: Complex Analysis & PDEs
- Complex Numbers
- Analytic Functions & Cauchy–Riemann
- Complex Integration & Cauchy's Theorems
- Taylor & Laurent Series, Singularities
- Residue Theorem & Applications
- Partial Differential Equations
- Separation of Variables
Linear Algebra
- Matrices & Determinants
- Linear Systems & Rank
- Vector Spaces & Linear Transformations
- Eigenvalues & Eigenvectors
- Orthogonality & Matrix Decompositions
Probability
Statistics
- Descriptive Statistics
- Correlation & Regression
- Sampling, Confidence & Hypothesis Tests
- Quality, Reliability & Design of Experiments
Numerical Methods
- Numerical Foundations & Errors
- Root Finding
- Numerical Linear Systems
- Interpolation & Splines
- Numerical Differentiation & Integration
- Numerical ODE Solvers
- Numerical PDEs (Finite Differences)
Discrete Mathematics
Optimisation & Operations Research
- Unconstrained Optimisation
- Constrained Optimisation: Lagrange & KKT
- Linear Programming
- Operations Research