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• Week 1: Definition and existence of integrals
• Week 2: properties of Integrals
• Week 3: Fundamental theorem of calculus and it's applications
• Week 4: Change of Variable theorem & Integration by parts
• Week 5: Functions of bounded variation definition and examples
• Week 6: properties of functions of bounded variation
• Week 7: Introduction of Improper integrals & Improper integrals of first kind
• Week 8: Tests for convergence of Improper integrals
• Week 9: mid term exam
• Week 10: Improper integrals of 2nd kind
• Week 11: Beta and Gamma functions
• Week 12: Absolute and conditional convergence of Improper integrals & more examples of Improper integrals
• Week 13: Introduction of sequence and series of functions & definition of pointwise convergence
• Week 14: Definition of uniform convergence & it's examples
• Week 15: Uniform convergence and continuity
• Week 16: Uniform convergence and Differentiation
• Week 17: Power series
• Week 18: Final Exam