Integration
Differentiation
Multiple Integrals
Partial Derivatives
Maxima and Minima
Differential Equation
Limits and Continuity
Determinants
Vector Spaces
Diagonalization
Matrix Operations
Linear Transformations
Eigenvalues & Eigenvectors
Systems of Linear Equations
Series Solutions
Laplace Transforms
Engineering Problems
First-Order Differential E.
Homogeneous & Non-Homog.
Second-Order Differential Equ.
Method – Variation of Parameters
Random Variables
Hypothesis Testing
Probability Theorems
Conditional Probability
Probability Distributions
Correlation & Regression
Expectation and Variance
Residue Theorem
Analytic Functions
Contour Integration
Conformal Mapping
Taylor and Laurent Series
Cauchy’s Integral Theorem
Cauchy-Riemann Equations
Line Integrals
Stokes’ Theorem
Surface Integrals
Green’s Theorem
Scalar and Vector Fields
Gauss’s Divergence Theorem
Gradient, Divergence, and Curl
Z-Transform
Fourier Transform
Laplace Transform
Inverse Transforms
Fast Fourier Transform
Discrete Fourier Transform
Signal & System
Numerical Integration
Root-Finding Methods
Solving Linear Systems
Numerical Differentiation
Finite Difference Methods
Euler, Runge-Kutta Methods
Interpolation & Extrapolation
Heat Equation
Wave Equation
Laplace Equation
Fourier Series Solutions
Elliptic, Parabolic, Hyperbolic
Boundary and Initial Conditions
Method of Separation of Variable