MTH631 Real Analysis II Notes, MCQs & Assignments | Query Point Official

MTH631 ||| Real Analysis II

MTH631 – Real Analysis II is an advanced mathematics course that extends the concepts of Real Analysis I. It focuses on differentiation, integration, sequences and series of functions, and deeper properties of real-valued functions.

Course Introduction

Real Analysis II develops a rigorous understanding of calculus using analytical and proof-based approaches. This course strengthens students’ abilities to analyze functions, convergence, and continuity at an advanced level.

Course Learning Objectives

• Understand differentiation and integration rigorously
• Analyze sequences and series of functions
• Study uniform convergence and its consequences
• Apply theorems related to continuity and differentiability
• Develop strong proof-writing and analytical skills

Major Topics / Syllabus

• Differentiation of Real-Valued Functions
• Mean Value Theorems and Applications
• Riemann Integration
• Fundamental Theorem of Calculus
• Sequences and Series of Functions
• Pointwise and Uniform Convergence
• Continuity and Differentiability of Function Series
• Power Series and Applications

Advanced Analytical Focus

• ε-δ based proofs
• Uniform convergence criteria
• Interchange of limits, integrals, and derivatives
• Rigorous justification of calculus concepts
• Mathematical reasoning and abstraction

Practice Areas

• Concept-based MCQs
• Short theoretical questions
• Long proof-oriented questions
• Analytical and application problems

Exam Preparation Tips

• Practice proofs of major theorems
• Understand convergence types clearly
• Revise differentiation and integration theorems
• Work through examples and counterexamples
• Focus on logical structure in answers

MTH631 Real Analysis II MCQs

MTH631 MCQs (click here)

MTH631 Real Analysis II Questions

MTH631 Short & Long Questions (click here)

Assignment Questions

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