Differential Equations & Advanced Applications

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Differential Equations & Advanced Applications

Instructor: Stavros Richard Christopoulos

Included with

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4 modules

Gain insight into a topic and learn the fundamentals.

Intermediate level

Recommended experience

1 week to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

Prepare for a degree

Learn more

4 modules

Gain insight into a topic and learn the fundamentals.

Intermediate level

Recommended experience

1 week to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

Prepare for a degree

Learn more

What you'll learn

Apply product, quotient, and chain rules to solve real-world rate-of-change problems in science and business.
Use derivatives for optimization, identifying maxima, minima, and inflection points in practical applications.
Perform implicit and higher-order differentiation to model interdependent variables and dynamic systems.
Apply derivatives to gradient estimation, curve analysis, and optimization in data science and engineering.

Skills you'll gain

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There are 4 modules in this course

Master the foundational principles of differential calculus and unlock analytical capabilities essential for data science, engineering, and advanced mathematics. This course provides comprehensive training in derivative calculations, optimization techniques, and real-world problem-solving applications. Through systematic exploration of differentiation rules, implicit differentiation, and critical point analysis, you will develop robust mathematical reasoning skills applicable across scientific and business domains. Learn to model dynamic systems, analyze rates of change, and apply calculus techniques to solve complex optimization challenges. Whether advancing in quantitative fields or building analytical foundations for graduate studies, this course equips you with rigorous mathematical frameworks and practical computational skills to excel in data-driven decision-making and technical problem-solving.

This week you will begin solving first-order linear ordinary differential equations using integrating factors. You can also explore how these equations model real-world systems and practice solving them step by step.

What's included

2 videos7 readings2 assignments

2 videos Total 4 minutes

Welcome 2 minutes
Instructions for the week 3 minutes

7 readings Total 70 minutes

What to expect from this course 10 minutes
Overview 10 minutes
Self-Study on the Definition of ODEs 10 minutes
Self-Study on First-Order Linear ODEs 10 minutes
Step-by-Step Examples of First order ODEs - Questions 10 minutes
Step-by-Step Examples of First order ODEs - Solutions 10 minutes
Summary 10 minutes

2 assignments Total 60 minutes

Let's Practice: First-Order Linear Ordinary Differential Equations 30 minutes
Test Yourself: First-Order Linear Ordinary Differential Equations 30 minutes

This week introduces you to second-order linear ODEs with constant coefficients. You will learn to solve them using characteristic equations and apply your understanding to model dynamic systems.

What's included

2 videos6 readings2 assignments

2 videos Total 4 minutes

Welcome 1 minute
Instructions for the week 3 minutes

6 readings Total 60 minutes

Overview 10 minutes
Self-Study on Second-Order Linear ODEs 10 minutes
Second-Order Equations with Constant Coefficients 10 minutes
Examples of Second-Order Linear ODEs - Questions 10 minutes
Examples of Second-Order Linear ODEs - Solutions 10 minutes
Summary 10 minutes

2 assignments Total 60 minutes

Let's Practice: Second-Order Linear Ordinary Differential Equations 30 minutes
Test Yourself: Second-Order Linear Ordinary Differential Equations 30 minutes

This week you will continue to explore second-order ODEs by applying initial and boundary conditions to find unique solutions. You will also explore integrating factors and real-world applications such as mechanical and electrical systems.

What's included

2 videos10 readings2 assignments

2 videos Total 5 minutes

Welcome 1 minute
Instructions for the week 4 minutes

10 readings Total 100 minutes

Overview 10 minutes
Self-Study on Initial and Boundary Conditions for Second-Order ODEs 10 minutes
Worked Examples on Applying Conditions to ODEs - Questions 10 minutes
Worked Examples on Applying Conditions to ODEs - Solutions 10 minutes
Worked Examples Using Integrating Factors - Questions 10 minutes
Worked Examples Using Integrating Factors - Solutions 10 minutes
Study of Practical Examples Involving Applications 10 minutes
Examples of Second-Order ODEs with Initial/Boundary Conditions and Integrating Factors - Questions 10 minutes
Examples of Second-Order ODEs with Initial/Boundary Conditions and Integrating Factors - Solutions 10 minutes
Summary 10 minutes

2 assignments Total 60 minutes

Let's Practice: Second-Order Linear Ordinary Differential Equations (Continuation) 30 minutes
Test Yourself: Second-Order Linear Ordinary Differential Equations (Continuation) 30 minutes

The focus in this module is moving to partial differentiation, where you will learn to compute partial derivatives for multivariable functions. You can then practice interpreting these derivatives in context and apply them to data modelling.

What's included

2 videos7 readings2 assignments1 plugin

2 videos Total 4 minutes

Welcome 1 minute
Instructions for the week 2 minutes

7 readings Total 70 minutes

Overview 10 minutes
Self-Study on Partial Differentiation Concepts 10 minutes
Worked Examples of Partial Differentiation - Questions 10 minutes
Worked Examples of Partial Differentiation - Solutions 10 minutes
Examples of Partial Differentiation - Questions 10 minutes
Examples of Partial Differentiation - Solutions 10 minutes
Summary of the course and next steps 10 minutes

2 assignments Total 60 minutes

Let's Practice: Partial Differentiation 30 minutes
Test Yourself: Partial Differentiation 30 minutes

1 plugin Total 15 minutes

Attempt-and-Check Solved Examples 15 minutes

Prepare for a degree

Taking this course by University of Huddersfield may provide you with a preview of the topics, materials and instructors in a related degree program which can help you decide if the topic or university is right for you.

Instructor

Stavros Richard Christopoulos

University of Huddersfield

2 Courses 156 learners

Offered by

University of Huddersfield

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