Introduction
Real Numbers
Operation and Properties on real numbers
Order Relation and Inequalities
Absolute value
Intervals
Coordinates System
Cartesian Coordinates
Polar Coordinates
Function
Definition
Operations
Type of Functions
Limits
Motivation
Numerical Approximations
Definitions
Algebraic Theorem of Limits
Squeeze Theorem
One sided limits
Limits Involving Trigonometric Functions
Limits at infinity
Infinite Limits
Limits of sequences
Natural number e as a limits
Limits involving e
Continuity of Functions
Derivatives
Motivations
Definition
Power Rule
Derivatives of addition and subtraction
Derivatives of multiplication and division
Derivatives of compositions and Chain Rule
Derivatives of Inverse of a Function
Derivatives of Trigonometric Function
Derivatives of Cyclometric Functions
Derivatives of Logarithmic Functions
Derivatives of Exponential Functions
Derivatives of Hyperbolic Functions (?)
Derivatives of Parametric Functions
Derivatives of Implicit Functions
Derivatives with Logarithm
Higher Derivatives
Differentials
Application of Derivatives
Geometric meaning of derivatives
Physical aspect of derivatives
Maximum and Minimum
Critical Points
Extreme values
Theorem of Extreme Values
Rolle’s Theorem
Mean Value Theorem
Convexity of a functions
Inflection Points
First Derivatives Test
Second Derivatives Test
Asimptot
Graphing Functions (using Calculus)
Practical Problems on Extreme Value
Taylor Series
MacLaurin Series
L’Hospital Rules
MacLaurin Series on Limits