Covid 2019: Notes for Class 11 & 12 PCM Students preparing for ISC/CBSE/JEE examinations.

These are physics, chemistry and mathematics notes which might be extremely useful for students who are unable to attend school because of Covid 19. 

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Phase 1: (1st April 2020) Starting with Calculus

 Quick and introductory definitions related to Funtions, Limits and Continuity - Defining the domain and range of a function, the meaning of continuity, limits, left and right hand limits, properties of limits and the "lim" operator; some common limits;  defining the L'Hospital rule, intermediate and extreme value theorems.  

Functions, Limits and Continuity - Solved Problem Set I - The Domain, Range, Plots and Graphs of Functions;  L'Hospital's Rule- -  Solved problems demonstrating how to compute the domain and range of functions, drawing the graphs of functions, the mod function, deciding if a function is invertible or not; calculating limits for some elementary examples, solving 0/0 forms, applying L'Hospital rule.

 Functions, Limits and Continuity - Solved Problem Set II - Conditions for Continuity, More Limits, Approximations for ln (1+x) and sin x for infinitesimal values of x  

More advanced cases of evaluating limits, conditions for continuity of functions, common approximations used while evaluating limits for ln ( 1 + x ), sin (x); continuity related problems for more advanced functions than the ones in the first group of problems (in the last tutorial).

 Functions, Limits and Continuity - Solved Problem Set III - Continuity and Intermediate Value Theorems - Problems related to Continuity, intermediate value theorem.

Introductory concepts and definitions related to Differentiation - Basic formulas, Successive Differentiation, Leibnitz, Rolle and Lagrange Theorems, Maxima , Minima, Convexity, Concavity, etc - Theory and definitions introducing differentiability, basic differentiation formulas of common algebraic and trigonometric functions , successive differentiation, Leibnitz Theorem, Rolle's Theorem,  Lagrange's Mean Value Theorem, Increasing and decreasing functions, Maxima and Minima; Concavity, convexity and inflexion, implicit differentiation. 

Differential Calculus - Solved Problem Set I - Common Exponential, Log , trigonometric and polynomial functions  - Examples and solved problems - differentiation of common algebraic, exponential, logarithmic, trigonometric and polynomial functions and terms; problems related to differentiability . 

Calculus: Differential Calculus: Solved Problem Set II - Derivability / Differentiability, Continuity; Changing Independent Variables; N-th derivative

Differential Calculus- Solved Problem Set III with MCQ Quiz- Increasing, Decreasing functions; maxima, minima, extreme values; Rolle's Theorem ; Inspecting Polynomials

Phase 2: (2nd April 2020) Starting with Algebra, polynomial functions and curve sketching

Phase 3 (Trigonometry)