Lecture Notes

• Lecture1: Real Number System
• Lecture2: Sequences1
• Lecture3: Sequences2
• Lecture4: Continuous function
• Lecture5: Maxima, Minima, Intermediate Value Property, Differentiability
• Lecture6: Rolle's Theorem, Mean Value Theorem
• Lecture7, 8, 9: Cauchy Mean Value Theorem, L'Hospital Rule, Local Maximum, Point of Inflection
• Lecture10: Taylor's Theorem
• Lecture11-13: Infinite Series, Convergence tests, Leibniz Theorem
• Lecture14: Power Series, Taylor's Series
• Lecture15-16: Riemann Integration
• Lecture17: Fundamental Theorems of Calculus
• Lecture18: Improper Integral
• Lecture19: Area Between Two Curves, Polar coordinates (Extra notes on polar coordinate)
• Lecture20: Area in Polar Coordinates, Volume of Solids
• Lecture21: Washer and Shell Methods, Length of a plane curve
• Lecture 22: Areas of surfaces of revolution, Pappus’s Theorems

MID-SEM EXAM, 20th September, 2017

• Lecture 23: Review of vectors, equations of lines and planes; sequences in R^3
• Lecture 24: Calculus of Vector Valued Functions
• Lecture 25: Principal Normal; Curvature
• Lecture 26-27: Functions of Several Variables : Continuity and Differentiability
• Lecture 28: Directional Derivatives, Gradient, Tangent Plane
• Lecture 29: Mixed derivative Theorem, MVT, Extended MVT
• Lecture 30: Maxima, Minima, Second Derivative Test
• Lecture 31: Lagrange Multiplier Method
• Lecture 32: Double integrals
• Lecture 33: Change of Variable in a Double Integral, Triple Integrals (Surface plots)
• Lecture 34: Change of Variables in a Triple Integral, Area of a Parametric Surface
• Lecture 35: Surface Area, Surface Integrals
• Lecture 36: Line Integrals, Green's Theorem
• Lecture 37: Green's Theorem (contd.), curl, Divergence
• Lecture 38: Stokes' Theorem
• Lecture 39: The Divergence Theorem

END-SEM EXAM, 20th November, 2017