Studying Differential Equations Bernd Schr oder logo1 Bernd Schr - PowerPoint PPT Presentation

The Why and the How The Future What is Different With This Book? Studying Differential Equations Bernd Schr¨ oder logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Studying Differential Equations

The Why and the How The Future What is Different With This Book? That Guy in the Videos logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Studying Differential Equations

The Why and the How The Future What is Different With This Book? That Guy in the Videos 1. I’m a geek. logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Studying Differential Equations

The Why and the How The Future What is Different With This Book? An Overview of the Course – Motivation logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Studying Differential Equations

The Why and the How The Future What is Different With This Book? An Overview of the Course – Motivation 1. Ordinary differential equations arise throughout engineering and science. logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Studying Differential Equations

The Why and the How The Future What is Different With This Book? An Overview of the Course – Motivation 1. Ordinary differential equations arise throughout engineering and science. 2. They can arise directly in a model, such as in spring mass systems logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Studying Differential Equations

The Why and the How The Future What is Different With This Book? An Overview of the Course – Motivation logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Studying Differential Equations

The Why and the How The Future What is Different With This Book? An Overview of the Course – Motivation 1. Ordinary differential equations arise throughout engineering and science. 2. They can arise directly in a model, such as in mixing problems, spring mass systems logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Studying Differential Equations

The Why and the How The Future What is Different With This Book? An Overview of the Course – Motivation 1. Ordinary differential equations arise throughout engineering and science. 2. They can arise directly in a model, such as in mixing problems, spring mass systems or circuits. logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Studying Differential Equations

The Why and the How The Future What is Different With This Book? An Overview of the Course – Motivation ✂❇ ✂ ❇ ✂ ❇ ✂ ❇ ✂ ✂ ✂ ✂ ❇ ❇ ❇ ❇ ✂ ❇✂ ❇ ✂ ❇ ✂ ❇ ✲ RI LdI ❞ E ( t ) ∼ dt ❞ q C ❄ ✛ E ( t ) = LdI dt + RI + q C logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Studying Differential Equations

The Why and the How The Future What is Different With This Book? An Overview of the Course – Motivation 1. Ordinary differential equations arise throughout engineering and science. 2. They can arise directly in a model, such as in mixing problems, spring mass systems or circuits. logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Studying Differential Equations

The Why and the How The Future What is Different With This Book? An Overview of the Course – Motivation 1. Ordinary differential equations arise throughout engineering and science. 2. They can arise directly in a model, such as in mixing problems, spring mass systems or circuits. 3. They can arise during the solution of a partial differential equation, such as the heat equation, logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Studying Differential Equations

The Why and the How The Future What is Different With This Book? An Overview of the Course – Motivation logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Studying Differential Equations

The Why and the How The Future What is Different With This Book? An Overview of the Course – Motivation 1. Ordinary differential equations arise throughout engineering and science. 2. They can arise directly in a model, such as in mixing problems, spring mass systems or circuits. 3. They can arise during the solution of a partial differential equation, such as the heat equation, logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Studying Differential Equations

The Why and the How The Future What is Different With This Book? An Overview of the Course – Motivation 1. Ordinary differential equations arise throughout engineering and science. 2. They can arise directly in a model, such as in mixing problems, spring mass systems or circuits. 3. They can arise during the solution of a partial differential equation, such as the heat equation, the wave equation logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Studying Differential Equations

The Why and the How The Future What is Different With This Book? An Overview of the Course – Motivation Image courtesy of Loren M. Winters, used with permission. logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Studying Differential Equations

The Why and the How The Future What is Different With This Book? An Overview of the Course – Motivation 1. Ordinary differential equations arise throughout engineering and science. 2. They can arise directly in a model, such as in mixing problems, spring mass systems or circuits. 3. They can arise during the solution of a partial differential equation, such as the heat equation, the wave equation logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Studying Differential Equations

The Why and the How The Future What is Different With This Book? An Overview of the Course – Motivation 1. Ordinary differential equations arise throughout engineering and science. 2. They can arise directly in a model, such as in mixing problems, spring mass systems or circuits. 3. They can arise during the solution of a partial differential equation, such as the heat equation, the wave equation or the Schr¨ odinger equation. logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Studying Differential Equations

The Why and the How The Future What is Different With This Book? An Overview of the Course – Motivation logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Studying Differential Equations

The Why and the How The Future What is Different With This Book? An Overview of the Course – Motivation 1. Ordinary differential equations arise throughout engineering and science. 2. They can arise directly in a model, such as in mixing problems, spring mass systems or circuits. 3. They can arise during the solution of a partial differential equation, such as the heat equation, the wave equation or the Schr¨ odinger equation. logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Studying Differential Equations

The Why and the How The Future What is Different With This Book? An Overview of the Course – Motivation 1. Ordinary differential equations arise throughout engineering and science. 2. They can arise directly in a model, such as in mixing problems, spring mass systems or circuits. 3. They can arise during the solution of a partial differential equation, such as the heat equation, the wave equation or the Schr¨ odinger equation. 4. Solutions of differential equations can be compared with the actual behavior of a system to determine if the theoretical description of the system is accurate. logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Studying Differential Equations

The Why and the How The Future What is Different With This Book? An Overview of the Course – Motivation 1. Ordinary differential equations arise throughout engineering and science. 2. They can arise directly in a model, such as in mixing problems, spring mass systems or circuits. 3. They can arise during the solution of a partial differential equation, such as the heat equation, the wave equation or the Schr¨ odinger equation. 4. Solutions of differential equations can be compared with the actual behavior of a system to determine if the theoretical description of the system is accurate. This is interesting in the sciences. logo1 Bernd Schr¨ oder Louisiana Tech University, College of Engineering and Science Studying Differential Equations