Continuous-Time Signals and Linear Differential Equations

Understanding how physical systems change over time is a foundational skill in engineering and applied mathematics. Continuous-time linear time-invariant systems form the backbone of signal processing, control theory, and system modeling. This text-based course guides you from the absolute basics of signals and system properties to solving linear constant-coefficient differential equations. You will develop a strong mathematical intuition for system behavior and learn how to analyze real-world physical models. What you'll learn: - Understand the fundamental definitions of continuous-time signals, linearity, and time-invariance. - Formulate linear constant-coefficient differential equations to represent physical systems. - Solve differential equations using classical analytical methods for natural and forced responses. - Analyze system stability, causality, and impulse response characteristics. - Practice mathematical techniques with step-by-step written numerical exercises and solutions. - Explore modern computational concepts for simulating continuous-time systems. We begin with core definitions of signals and systems, establishing a solid theoretical foundation before moving on to setting up and solving differential equations. Each concept is reinforced with detailed, written numerical examples that break down the mathematical steps. This course is designed for beginners in engineering, physics, or applied mathematics who want a clear, step-by-step introduction to system analysis. No advanced prior knowledge of differential equations is required, though basic calculus is helpful. Start reading today to master the mathematical foundations of continuous-time systems.