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4. Body of knowledge of Engineering Science
The 21 knowledge areas in Engineering Science are:
4.1 Calculus and Analysis (CAN)
- 4.1.1 Line Integrals and Vector Fields
- 4.1.2 Multiple Integrals
- 4.1.3 Multivariable Transformations
- 4.1.4 Surface Integrals and Fundamental Theorems
- 4.1.5 Vector Functions of a Real Variable
- 4.1.6 Limits and Continuity
- 4.1.7 Differential Calculus
- 4.1.8 Integral Calculus
- 4.1.9 Improper Integrals
- 4.1.10 Sequences, Series, and Power Series
- 4.1.11 Applications of the Definite Integral
- 4.1.12 Vectors and the Geometry of Space
- 4.1.13 Quadric Surfaces
- 4.1.14 Parametric Equations and Polar Coordinates
- 4.1.15 Multivariable and Vector Calculus
- 4.1.16 Complex Analysis and Conformal Mapping
- 4.1.17 Harmonic Analysis and Fourier Series
- 4.2.1 Matrices and Systems of Linear Equations
- 4.2.2 Vector Spaces and Linear Transformations
- 4.2.3 Eigenvalues and Inner Product Spaces
- 4.3.1 First-Order Ordinary Differential Equations (ODEs)
- 4.3.2 Higher-Order Differential Equations and Systems (ODEs)
- 4.3.3 Partial Differential Equations (PDEs)
- 4.3.4 Mathematical Fluid Dynamics
- 4.3.5 Asymptotic Analysis and Perturbation Methods
- 4.3.6 Dynamical Systems and Bifurcation Theory
- 4.3.7 Control Theory and Optimal Control
- 4.4.1 Mathematical Statistics and Estimation Theory
- 4.4.2 Time Series Analysis
- 4.4.3 Probability Axioms and Random Variables
- 4.4.4 Stochastic Processes and Markov Chains
- 4.5.1 Error Analysis and Floating Point Arithmetic
- 4.5.2 Numerical Linear Algebra
- 4.5.3 Numerical Solution of Nonlinear Equations
- 4.5.4 Approximation Theory and Interpolation
- 4.5.5 Numerical Integration and Quadrature
- 4.5.6 Numerical Methods for ODEs and PDEs
- 4.5.7 Finite Element Method
- 4.5.8 Optimization Algorithms
- 4.5.9 Parallel and High-Performance Computing
- 4.10.1 Kinematics and Dynamics of Particles
- 4.10.2 Work, Energy, and Conservative Forces
- 4.10.3 Rotational Motion and Angular Momentum
- 4.10.4 Systems of Particles and Linear Momentum
- 4.10.5 Non-Inertial Reference Frames and Fictitious Forces
- 4.10.6 Lagrangian and Hamiltonian Mechanics
- 4.10.7 Continuum Mechanics Foundations
- 4.10.8 Elasticity
- 4.10.9 Fluids: Hydrostatics, Hydrodynamics, and Viscosity
- 4.10.10 Vibrations and Waves
- 4.10.11 Theory of Small Oscillations and Coupled Oscillators
- 4.10.12 Transport Phenomena
- 4.11.1 Electrostatics: Electric Field and Gauss's Law
- 4.11.2 Electric Potential and Poisson/Laplace Equations
- 4.11.3 Electrostatic Energy and Dielectrics
- 4.11.4 Magnetostatics: Biot-Savart and Ampere's Laws
- 4.11.5 Magnetic Properties of Matter
- 4.11.6 Electrodynamics: Faraday's Law and Induction
- 4.11.7 Electric Current, Circuits, and Kirchhoff's Laws
- 4.11.8 Maxwell's Equations and Gauge Transformations
- 4.11.9 Electromagnetic Waves and Propagation in Media
- 4.12.1 Laws of Thermodynamics and State Functions
- 4.12.2 Kinetic Theory of Gases
- 4.12.3 Heat Engines, Entropy, and the Second Law
- 4.13.1 Crystal Structures and Reciprocal Lattices
- 4.13.2 Free Electron Model and Band Theory of Solids
- 4.13.3 Semiconductors, Insulators, and Metals
- 4.14.1 Matter and Energy
- 4.14.2 Basic Atomic Structure
- 4.14.3 Chemical Bonding
- 4.14.4 Stoichiometry
- 4.14.5 States of Matter
- 4.14.6 Environmental and Water Chemistry
- 4.14.7 Polymers and Geosynthetics
- 4.14.8 Chemical Equilibrium
- 4.14.9 Ionic Equilibrium and Salt Hydrolysis
- 4.14.10 Salts, Solubility, and Precipitation Equilibria
- 4.14.11 Electrochemistry and Electrolysis
- 4.14.12 Cement Chemistry
- 4.17.1 Synthesis of Nanomaterials and Nanofabrication
- 4.17.2 Characterization of Materials (XRD, SEM, TEM)
- 4.17.3 Energy Storage and Conversion Materials
- 4.18.1 Sample Spaces and Events
- 4.18.2 Probability Axioms and Properties
- 4.18.3 Conditional Probability and Independence
- 4.18.4 Discrete Random Variables and Distributions
- 4.18.5 Continuous Random Variables and Distributions
- 4.18.6 Joint, Marginal, and Conditional Distributions
- 4.18.7 Limit Theorems: LLN and CLT
- 4.20.1 Point Estimation
- 4.20.2 Interval Estimation and Confidence Intervals
- 4.20.3 Hypothesis Testing Foundations
- 4.20.4 Bayesian Inference