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Table of Contents

Chapter 1: Introduction
1.1 Background of the Study
1.2 Statement of the Problem
1.3 Objectives of the Study
1.4 Research Questions
1.5 Significance of the Study
1.6 Limitations of the Study
1.7 Scope of the Study

Chapter 2: Literature Review
2.1 Overview of Differential Equations
2.2 Introduction to Liapunov Functions
2.3 Previous Studies on Stability Analysis
2.4 Applications of Liapunov Functions in Differential Equations

Chapter 3: Research Methodology
3.1 Research Design
3.2 Data Collection Methods
3.3 Data Analysis Techniques
3.4 Case Studies
3.5 Theoretical Framework

Chapter 4: Discussion of Findings
4.1 Analysis of Stability using Liapunov Functions
4.2 Comparison of Results with Previous Studies
4.3 Interpretation of Results
4.4 Implications for Future Research

Chapter 5: Conclusion and Summary
5.1 Summary of Key Findings
5.2 Contributions to the Field
5.3 Recommendations for Future Research
5.4 Conclusion

Brief Overview:

The thesis titled “Analyzing stability of differential equations using Liapunov functions” focuses on the application of Liapunov functions in analyzing the stability of differential equations. The study aims to investigate the effectiveness of Liapunov functions in determining the stability of various types of differential equations.

Chapter 1 provides an introduction to the background of the study, the objectives, limitations, and scope of the research. Chapter 2 presents a comprehensive literature review on differential equations, Liapunov functions, previous studies on stability analysis, and their applications in differential equations.

Chapter 3 outlines the research methodology, including the research design, data collection methods, data analysis techniques, case studies, and theoretical framework. Chapter 4 discusses the findings of the study, analyzing stability using Liapunov functions, comparing results with previous studies, and interpreting the implications for future research.

Finally, Chapter 5 presents the conclusion and summary of the thesis, summarizing key findings, contributions to the field, recommendations for future research, and overall conclusions drawn from the study. This thesis aims to contribute to the understanding of stability analysis in differential equations using Liapunov functions and provide valuable insights for further research in this area.

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