Udemy - Differential Equations A-Z Solve, Analyze, Apply

Level: All | Genre: eLearning | Language: English | Duration: 29 Lectures ( 10h 51m ) | Size: 3.2 GB
Learn to Solve and Apply Differential Equations with Confidence - From First Principles to Laplace Transforms
What you'll learn
Understand what differential equations are and why they're essential in science and engineering
Solve first order differential equations using methods like separation of variables, integrating factors, and exact equations
Analyze and sketch slope fields to visualize solutions
Apply first order equations to real-life scenarios such as exponential growth, decay, and mixing problems
Solve second order linear differential equations with both constant and variable coefficients
Model and analyze mechanical systems involving harmonic motion and damping
Use differential equations to describe and solve population models, velocity-acceleration relationships, and electric circuits
Learn and apply the Laplace Transform to solve initial value problems
Use Laplace techniques including step functions and partial fractions for more complex models
Understand series solutions of differential equations near ordinary points
Build confidence in mathematical modeling and analytical thinking for technical fields
Requirements
No prior knowledge of differential equations is required - this course starts from the fundamentals
A scientific calculator or math software (e.g., Desmos, WolframAlpha, or a CAS tool) may be helpful for solving and visualizing problems
Uunderstanding of calculus, including derivatives and integrals
Familiarity with basic algebra and functions (exponential, logarithmic, trigonometric)
Some experience with graphing and interpreting mathematical models
Description
Mastering Differential Equations: A Practical IntroductionHave you ever wondered how scientists model population growth, predict radioactive decay, or understand the mechanics of a vibrating spring? Differential equations are the powerful tools behind many of these real-world phenomena. In this comprehensive course, you'll be introduced to the fundamental methods for solving differential equations and see how they apply directly to problems in science and engineering.Whether you're a student tackling this subject for the first time, or you're brushing up for advanced studies, this course offers a solid, approachable foundation rooted in practical applications. Guided by the highly respected textbook Differential Equations and Boundary Value Problems: Computing and Modeling by Edwards, Penney, and Calvis, the course breaks down complex ideas into digestible, logical steps.We begin with first order differential equations-how they are formed, what they represent, and how to solve them using techniques like separation of variables and integrating factors. You'll explore real-world applications like modeling chemical mixtures and exponential decay. From there, we dive into second order equations, essential for understanding motion, vibrations, and systems with inertia.Next, we turn toward real applications. Through population models, stability analysis, and simulations of electrical circuits and mechanical systems, you'll see how differential equations bring theoretical math to life. Finally, you'll gain fluency with Laplace transforms and series solutions-powerful tools for solving initial value problems and handling more complex differential systems.Throughout the course, the focus remains on intuitive understanding, step-by-step problem solving, and meaningful applications. By the end, you'll not only be confident in your mathematical skills but also prepared to apply them in scientific and engineering contexts.Join today and start your journey into one of the most useful branches of mathematics-where calculus meets the real world.
Who this course is for
Undergraduate students enrolled in a first course in differential equations
STEM majors (engineering, physics, biology, economics) seeking a practical grasp of differential equations
Learners preparing for advanced coursework involving dynamic systems or mathematical modeling
Self-learners looking to understand how differential equations apply to real-world scientific problems
Anyone who wants to strengthen their problem-solving skills with step-by-step mathematical reasoning
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