Calculus 1 (EN)

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