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Differential Equations & Advanced Applications · LearnSpace
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Differential Equations & Advanced Applications

Курс от University of Huddersfield
Средний≈ 10.3 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

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.

Навыки, которые вы освоите

Differential EquationsMathematical ModelingDerivativesModel OptimizationMathematical Theory & AnalysisApplied MathematicsEngineering AnalysisAdvanced MathematicsCalculusAnalytical Skills

Программа курса

4 модулей · 50 учебных материалов

01First-Order Linear Ordinary Differential Equations (ODEs)12 материалов

Introduction

What to expect from this courseЧтениеWelcomeВидеоOverviewЧтениеInstructions for the weekВидео

Учитесь у экспертов

Stavros Richard Christopoulos

Преподаватель курса

Differential Equations & Advanced Applications
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Обучение на Coursera

≈ 10.3 ч

4 модулей

Язык: Английский

Часть программы вашего университета
Calculus to Modeling BridgeDIALOGUE

Definition of an Ordinary Differential Equation (ODE)

Self-Study on the Definition of ODEsЧтение

First-Order Linear Ordinary Differential Equations (ODEs)

Self-Study on First-Order Linear ODEsЧтение

Examples of First-Order Linear ODEs

Step-by-Step Examples of First order ODEs - QuestionsЧтениеStep-by-Step Examples of First order ODEs - SolutionsЧтение

Summary and Assessment

SummaryЧтениеLet's Practice: First-Order Linear Ordinary Differential EquationsЗаданиеTest Yourself: First-Order Linear Ordinary Differential EquationsЗадание
02Second-Order Linear Ordinary Differential Equations11 материалов

Introduction

WelcomeВидеоOverviewЧтениеInstructions for the weekВидео

Introduction to Second-Order Linear Ordinary Differential Equations

Self-Study on Second-Order Linear ODEsЧтение

Second-Order Equations with Constant Coefficients

Second-Order Equations with Constant CoefficientsЧтение

Examples of Second-Order Linear ODEs

Examples of Second-Order Linear ODEs - QuestionsЧтениеExamples of Second-Order Linear ODEs - SolutionsЧтение

Summary and Assessment

SummaryЧтениеODE Mastery CheckpointDIALOGUELet's Practice: Second-Order Linear Ordinary Differential EquationsЗаданиеTest Yourself: Second-Order Linear Ordinary Differential EquationsЗадание
03Second-Order Linear Ordinary Differential Equations (Continuation)14 материалов

Introduction

WelcomeВидеоOverviewЧтениеInstructions for the weekВидео

Second-Order Linear Ordinary Differential Equations (Continuation)

Self-Study on Initial and Boundary Conditions for Second-Order ODEsЧтениеWorked Examples on Applying Conditions to ODEs - QuestionsЧтениеWorked Examples on Applying Conditions to ODEs - SolutionsЧтение

Integrating Factors

Worked Examples Using Integrating Factors - QuestionsЧтениеWorked Examples Using Integrating Factors - SolutionsЧтение

Applications of Differential Equations

Study of Practical Examples Involving ApplicationsЧтение

Examples of Second-Order ODEs with Initial/Boundary Conditions and Integrating Factors

Examples of Second-Order ODEs with Initial/Boundary Conditions and Integrating Factors - QuestionsЧтениеExamples of Second-Order ODEs with Initial/Boundary Conditions and Integrating Factors - SolutionsЧтение

Summary and Assessment

SummaryЧтениеLet's Practice: Second-Order Linear Ordinary Differential Equations (Continuation)ЗаданиеTest Yourself: Second-Order Linear Ordinary Differential Equations (Continuation)Задание
04Partial Differentiation13 материалов

Introduction

WelcomeВидеоOverviewЧтениеInstructions for the weekВидео

Partial Differentiation

Self-Study on Partial Differentiation ConceptsЧтениеWorked Examples of Partial Differentiation - QuestionsЧтениеWorked Examples of Partial Differentiation - SolutionsЧтение

Examples of Partial Differentiation

Examples of Partial Differentiation - QuestionsЧтениеExamples of Partial Differentiation - SolutionsЧтениеAttempt-and-Check Solved ExamplesPLUGIN

Summary and Assessment

Mathematical Modeling MasteryDIALOGUELet's Practice: Partial DifferentiationЗаданиеTest Yourself: Partial DifferentiationЗаданиеSummary of the course and next steps Чтение