WEEKLY BREAKDOWN: (To be updated weekly)
Week1: Introduction to Calculus, Introduction to Functions, Domain and Range.
Week2: Algebra of functions, Types of functions, Injective, Surjective, Inverses, Compositions, Cardinalities, Introduction to Limits, Epsilon Delta. (Extras: Cardinality of an infinite set)
Week3: Limit Laws, Computing Limits, Squeeze Theorem, Infinite Limits and Limits at infinity, Asymptotes, Continuous functions and their properties. (Extras: Homeomorphisms)
Week4: Intermediate Value Theorem, Location of roots theorem, Bisection method, Introduction to derivatives, Derivative by definition, Graphical analysis, Rules of Differentiation, Linear approximation, Higher order derivatives, A brief introduction to differential equations.
Week5: The Chain Rule and its applications, Implicit Differentiation and its applications, Differentials, Error Estimation, Related Rates.
Week6: Continuous functions on compact domain, Absolute and Relative Extremas, Extreme Values Theorem, Fermat's Theorem, Rolle's Thoerem and Mean Value Theorem with proof and applications.
Week7: Shape of the graph using derivatives, critical points, inflection points, intervals of increase,decrease, concavity, First and Second derivative tests for local extreme values, Speeding up/ Slowing down, Word problems on Optimization.
Week8: Taylor Series Expansion, Approximations of higher orders, Interval and radius of convergence, Differentiating and integrating Power series, Finding sums using series expansion, L'Hopital Rule and applications.
Midterm with Key
Week9: Antiderivates, Analysis of the motion given acceleration or velocity, Integration by substitution, Integration by parts, Definite integrals as "Net Area".[Fall 25 Lec17.pdf , Fall 25 Lec18.pdf ]
Week10: Properties of definite integral, Reimann sums, Definite integral as a limit of Riemann sums. [Fall 25 Lec19.pdf]
Week11: Fundamental Theorem of Calculus (with proofs) Part 1 and 2 and their applications. Applications of integration involving area between curves, Arc length and Average value of the function.[Fall 25 Lec20.pdf , Fall 25 Lec21.pdf ]
Week12: Volume of Revolution (Disk, Washer and Shell method), Introduction to ODEs, Separable ODEs, Analysis of autonomous ODEs. [Fall 25 Lec22.pdf , Fall 25 Lec23.pdf ]
Week13: Linear, Bernoulli, Substitution and Homogenous ODEs. Second order ODEs with constant coeffecients, Mass Spring System. [Fall 25 Lec24.pdf ,Fall 25 Lec25.pdf ]
