Differential Equations for Engineering Systems is a research-grade digital textbook developed for electrical and computer engineers who require a system-oriented and mathematically rigorous approach to ordinary differential equations.

Rather than treating differential equations as isolated solution techniques, this book presents them as models of physical, electrical, and computational systems, emphasizing structure, interpretation, and transform-based reasoning.

The text is designed to bridge foundational theory with engineering application, supporting both advanced coursework and independent professional study.

What This Book Focuses On

This book emphasizes the role of differential equations as the mathematical backbone of:

• dynamic system modeling

• signal and system behavior

• electrical and mechanical system response

• stability and transient analysis

The treatment prioritizes clarity of formulation, correctness of interpretation, and efficiency of solution, particularly in contexts relevant to ECE.

Core Topics Covered

The material develops a coherent progression through:

• first- and higher-order ordinary differential equations

• linear systems with constant coefficients

• homogeneous and non-homogeneous equations

• impulse, step, and exponential inputs

• Laplace-transform-based solution methods

• initial-value problems and system response

• engineering interpretation of solutions

Worked examples are fully developed, and problem sets are aligned with advanced engineering expectations.

Key Features

• System-driven approach to differential equations

• Transform methods integrated naturally into solution workflows

• Emphasis on physical and engineering interpretation

• Fully worked examples and solved problem sets

• Consistent notation and mathematical typography

• Designed for advanced undergraduate and graduate ECE

Format

• Digital textbook (PDF)

• High-resolution mathematical typesetting

• Optimized for screen reading and printing

Pricing

Digital Edition (PDF):
💲 $11.99 USD

Academic and institutional licensing available upon request.

Intended Audience

• Electrical and computer engineering students

• Graduate-level engineering candidates

• Practicing engineers working with dynamic systems

• Researchers seeking a compact, rigorous ODE reference

About the Author

Mahdi Haghzadeh, PhD, is an engineer and researcher at Maxdi Research, working on mathematical systems theory, signal analysis, and advanced computational methods for engineering and physics.

Advanced Engineering Mathematics is a comprehensive, research-grade textbook developed for electrical and computer engineers who require a unified and operational understanding of mathematics.

The book emphasizes transform methods, complex analysis, and system theory as they are actually used in engineering practice—bridging coursework, research, and competitive examinations.

This is not a formula collection. It is a coherent mathematical system designed for engineers who work with signals, systems, and dynamic models.

What This Book Is For

• Senior undergraduate and graduate ECE students

• Engineers working in signal processing, control, and systems

• Candidates preparing for advanced engineering entrance or qualification exams

• Researchers seeking a compact but rigorous mathematical reference

Key Features

• Unified coverage of Fourier, Laplace, and complex analysis methods

• System-level interpretation of mathematical tools

• Fully worked examples and exam-style problems with solutions

• Consistent notation and typography, enforced by a custom LaTeX class

• One-page A4 exam formula sheet for rapid review

• MATLAB/Octave code appendix for computational reinforcement

Contents Overview

• Fourier Series and Spectral Representation

• Fourier Transform and LTI Systems

• Laplace Transform and Differential Equation Solving

• Convolution, Stability, and System Response

• Complex Analysis and Residue Methods

• Real Integrals and Conformal Mapping

• Mixed Advanced Problems and Exam Strategies

Format

• Digital textbook (PDF)

• High-resolution mathematical typesetting

• Optimized for screen and print

Licensing & Use

This product is licensed for individual academic and professional use.
For institutional licensing or course adoption, please contact Maxdi Research.

About the Author

Mahdi Haghzadeh, PhD, is a researcher and engineer working at the intersection of mathematics, systems theory, and advanced computation. His work spans engineering mathematics, signal analysis, and quantum analog computing.

OGN-MXD₁ (Venezuela) is an institutional coherence-engineering assessment produced by applying the MXD-COGN analytical engine to the Venezuela URC. The report compiles Venezuela-specific modules on sanctions dynamics, oil-sector control and interdiction (including tanker seizure patterns), external–internal coupling signals, elite coherence/fragmentation stressors, civilian welfare implications, and stability/escalation pathway families. A Phase II extension integrates local game-theoretic primitives (commitments, signaling, equilibrium families) into the MXD-COGN interface-first workflow. This publication is strictly analytical and non-prescriptive: it does not advocate political action or policy outcomes, and is designed for strategic research, institutional monitoring, and scenario conditioning under contested information.

What’s inside (bullets):

• Venezuela module pack: sanctions, oil interdiction, coupling signals, elite coherence, welfare, pathways

• Phase II: game-theoretic overlay integrated with MXD-COGN interfaces

• Institutional watchlist: high-signal indicators for update cycles

• Glossary: players, symbols, interface brittleness κ, and product architecture

Format: PDF (institutional master)
Publisher: Maxdi Global Strategic Stability Studies Group (MGSSSG)
Series: COGN-MXD products (MXD-COGN engine outputs)

This Institutional Master Package is a comprehensive, non-prescriptive analytical dossier examining the January 2026 crisis in the Islamic Republic of Iran through the Mixed-Domain, Mixed-Depth Coherence Engineering (MXD-COGN) framework.

The package integrates internal dynamics (protests, coercion, information control, elite cohesion, economic throughput) with external pressures (sanctions, tariffs, diplomatic isolation, and regional signaling) to assess systemic stability, brittleness, and escalation risk over short- and medium-term horizons.

Unlike conventional policy briefs or forecasting reports, this work does not advocate actions or outcomes. It provides a formal structural diagnosis of regime behavior under stress, identifying regime basins of attraction, interface-level failure points, and conditions under which discontinuity becomes plausible.

Version v1.1 incorporates a major expansion with the addition of Part IV, substantially deepening the historical–structural dimension of the analysis.

What’s Included

Part I — Core Institutional Assessment

A full MXD-COGN coherence analysis of Iran’s January 2026 crisis, including:

• Protest dynamics under near-total information blackout

• Coercive capacity and execution coherence

• Economic throughput stress and bazaar-level indicators

• Elite cohesion and patronage stability

• External pressure and tariff-driven uncertainty

• 3–6–12 month trajectory projections

• Formal brittleness (κ) metrics and regime basin classification

Part II — Game-Theoretic Addendum (v1.1)

A formal strategic layer complementing MXD-COGN, modeling:

• Deterrence–retaliation dynamics (U.S., Israel, Iran, regional actors)

• Elite–security coordination games under existential stress

• Signaling, belief formation, and commitment rigidity

• Escalation equilibria and de-escalation feasibility

Part III — Best-Case Diplomatic Off-Ramp Annex

A harm-minimization–oriented analytical annex outlining:

• Verification-based de-escalation sequencing

• Conditional, reversible sanctions relief architecture

• Amnesty and safe-exit logic to prevent fight-or-fracture equilibria

• Institutional pathways for domestic political legitimacy
  (Analytical, non-operational, non-prescriptive)

Part IV — Sanctions, Geography, Ideology, and Coherence Decay in Iran

(New in v1.1)

A standalone, long-form historical–structural assessment analyzing why sanctions and isolation have devastated civilian welfare without producing regime collapse. This section integrates:

• Four decades of sanctions and boycotts as iterated external deformations

• Civilian deprivation and food insecurity as emergent systemic outcomes

• IRGC economic capture under scarcity and sanctions evasion

• Ideological framing of deprivation (“resistance economy”) and its long-term costs

• Geography, invasion memory, and siege psychology as structural constraints

• Water scarcity, drought, and groundwater depletion as latent instability accelerators

• The Zibakalam thesis on internal causality and institutional failure

Part IV situates Iran’s crisis within a coherence-decay regime, where elite and coercive stability is preserved at the expense of societal welfare and adaptive capacity.

Methodological Distinction

The MXD-COGN framework treats geopolitical crises as emergent properties of interacting subsystems, rather than linear cause-effect chains. This allows the analysis to:

• Remain robust under censorship and limited observability

• Avoid street-size or sentiment-only forecasting

• Focus on interface-level brittleness where small perturbations can produce regime shifts

• Distinguish apparent stability from structural fragility

Who This Is For

• Government and diplomatic analysts

• Think tanks and multilateral institutions

• Academic researchers (political economy, sanctions, security studies)

• Journalists covering Iran and regional escalation risk

• Risk analysts and strategic planners

Important Notice

This document is an analytical research artifact.
It does not:

• Advocate political positions

• Recommend intervention or policy

• Provide operational or tactical guidance

Redistribution is restricted. Interpretation should preserve the document’s analytical and non-prescriptive intent

Quantum Theory Fundamentals presents a modern, coherence-engineering interpretation of quantum mechanics grounded in the MXD-COGN mixed-domain inference framework. Rather than treating quantum theory as a collection of abstract postulates, this eBook develops it as a structured inference system governed by coherence, deformation, and control constraints.

The book introduces foundational quantum concepts through the lens of MXD-COGN, unifying state evolution, measurement, interference, and reversibility within a single inference-theoretic geometry. It emphasizes operational meaning, mathematical clarity, and predictive structure, making it suitable for researchers, advanced students, and engineers working at the intersection of quantum information, control theory, and complex systems.

This volume is part of the Maxdi Research eBook series and reflects independent theoretical research conducted by Maxdi Inc.

This paper introduces \textbf{Noetic Field Dynamics (NFD)}, a novel theoretical framework that unifies consciousness studies, quantum mechanics, and performance optimization. NFD posits that consciousness operates as a fundamental field (the Noetic Field) from which cognitive excitations emerge as wave-like solutions. The theory integrates three established paradigms: Csikszentmihalyi's flow psychology, Jung's synchronicity principle, and Nelson-Isaacs' quantum resonance model. We demonstrate how NFD explains peak performance phenomena across artistic, musical, and athletic domains through mathematical formalism of coherence optimization. The framework offers testable predictions for enhancing human potential while providing a unified explanation for subjective experiences of flow, synchronicity, and optimal performance. Cross-domain applications are presented with mathematical formulations, empirical predictions, and practical implications for performance enhancement.

Recent quantum information experiments demonstrate universal protocols capable of reversing, pausing, or accelerating the evolution of isolated quantum systems. These results are frequently described as ``quantum time reversal.'' In this paper, we present a rigorous reinterpretation using the MXD--COGN mixed-domain, mixed-depth coherence engineering framework. We show that quantum rewinding corresponds to restoration of inference-loop closure under deformation rather than reversal of physical time. We introduce a global coherence order parameter $\Phi$, provide an operational estimator $\widehat{\Phi}$ from experimentally accessible observables, and derive falsifiable predictions regarding metastability, critical collapse, and scaling limits. We complement the theory with illustrative simulations of $\Phi(\lambda)$ showing metastable basins and cliff-like transitions near a critical threshold $\Phi_c$. The framework provides audit-ready metrics for quantum time-control experiments and suggests practical diagnostics for quantum technologies.

Applied Quantum Mechanics

by Dr. Sina Khorasan

Sharif University of Technology, Tehran Iran

Language: Farsi

Edits: Dr. Mahdi Haghzadeh

Audio Files | Translation | Mathematics Codes | Matlab Codes

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