# e-Learning Resources

Topics

Sets and Logic

Logic
Truth Table
Equivalent Statement and Implied Statement
Contrapositive and Contradiction
Universal and Existential Quantifier
Sets
Operations on Sets
Exercises

Functions
Introduction
Injective and Surjective Functions
Even, Odd and Periodic Functions
Power Functions
Piecewise Defined Functions
Exponential and Logarithmic Functions
Exercises

Polynomial and Rational Functions
Factor and Remainder Theorem
Division Algorithm
Euclidean Algorithm
Partial Fractions
Sum and Product of Roots

Trigonometry
Preliminary
Trigonometric Functions for a General Angle
Inverse Trigonometric Functions
General Solution of Trigonometric Equations
Trigonometric Identities
Subsidiary Angle Formula
Exercises

Mathematical Induction
Binomial Theorem
Limits and Continuity
Differentiation
Introduction to Differentiation
Monotonicity and Concavity
Higher Derivatives and Leibniz's Theorem
Differentiation of Parametric Equations
Mean Value Theorem
L'Hopital Rule and Curve Sketching
Taylor Polynomials

Integration
Riemann Sum
Fundamental Theorem of Calculus
Integration by Substiution
Integration by Partial Fractions
Integration by Parts (Indefinite Integrals)
Integration by Parts (Definite Integrals)
Reduction Formula
Improper Integrals

Vectors in $\mathbb{R}^2$ and $\mathbb{R}^3$
Linear Algebra