Skip to content

References: Mathematical Foundations

  1. Complex number - Wikipedia - Introduces complex arithmetic, the complex plane, polar form, and Euler relationships needed to represent sinusoidal signals and phasors.

  2. Linear algebra - Wikipedia - Surveys vectors, matrices, linear transformations, eigenvalues, and inner products that underpin transform methods and multidimensional signal models.

  3. Probability theory - Wikipedia - Covers random variables, distributions, expectation, variance, and foundational probability concepts used later for noise and stochastic signals.

  4. Introduction to Linear Algebra (6th Edition) - Gilbert Strang - Wellesley-Cambridge Press - Strang popularized geometric, column-space-first explanations that make eigenvectors, orthogonality, and matrix operations intuitive for engineering students.

  5. Advanced Engineering Mathematics (10th Edition) - Erwin Kreyszig - Wiley - Kreyszig’s problem-centered integration of complex analysis, differential equations, Fourier methods, and probability has long connected mathematical tools directly to engineering applications.

  6. Linear Algebra - MIT OpenCourseWare - Gilbert Strang’s lectures, notes, exercises, and solutions develop matrix methods, eigenvalues, orthogonality, and practical engineering applications.

  7. Engineering Statistics Handbook - NIST/SEMATECH - Provides accessible explanations, worked examples, and reference tables for probability distributions, estimation, variation, and statistical analysis.

  8. Signals and Systems - MIT OpenCourseWare - Connects complex numbers, exponentials, differential equations, and linear algebra to continuous- and discrete-time signal analysis.

  9. Signals and Systems - Engineering LibreTexts - Includes open modules on linear algebra, Hilbert spaces, complex exponentials, and mathematical analysis with interactive examples.

  10. The Scientist and Engineer's Guide to DSP - Steven W. Smith - Builds the required mathematics through visual explanations and practical examples rather than relying exclusively on formal derivations.