BOOK OVERVIEW

"Calculus 101: A Practical Approach for Beginners" is your essential guide to mastering calculus with ease. From laying down the basic foundation to delving into advanced concepts, this book is meticulously crafted for a clear and straightforward learning experience. The book is divided into four sections to aid easy learning and retention.

Below are the sections and topics:

SECTION I: PRE-CALCULUS

Realation

Types of Relation

Domain and Range

Mapping and Image of a Relation

Functions

Function Notation

Graphs of Functions

Types of Functions

Linear Function

Quadratic Function

Polynomial Function

Exponential Function

Logarithmic Function

Rational Function

Inverse Function

Composite of Functions

limit and continuity

Introduction to Limit

Properties of Limits

Solving Undefined Limit

Evaluating Limit at Infinity

L'Hôpital's Rule on Limit

Continuous Functions

Trigonometry

Trigonometric Functions

Trigonometric Identities

Pythagorean identities

Reciprocal identities

complementary identities

Sum and difference identities

Sum to product identities

Product to sum identities

Double angle identities

Special angles identities

SECTION II: DIFFERENTIAL CALCULUS

Derivative using tangent line

Derivative using first principle

Power Rule

Constant Rule

Sum and Difference Rule

Product Rule

Quotient Rule

Chain Rule

Derivative of Trigonometric Functions

Inverse Trigonometric Functions

Derivative of Hyperbolic Functions

Inverse Hyperbolic Functions

Derivative of Exponential Function

Derivative of Logarithm Functions

Higher-Order Derivative

First Derivative

Second Derivative

Third Derivative

Application of Integration

Velocity and Acceleration

Maximum and Minimum Values

SECTION III: INTEGRATION CALCULUS

Integration using Power Rule

Constant Rule

Sum and Difference Rule

Integration by Partial Fraction

Integration by Substitution

Integration by Parts

Integration of Logarithm Functions

Integration of Inverse Trigonometric Functions

Integration of Exponential Functions

Integration of Inverse Hyperbolic Functions

Application of integration

Application to Parametric Equation

Application to Mean Value of a Function

Application to Area Between Two Curves

SECTION IV: ADVANCED CALCULUS

Partial Derivative

Implicit Derivative

Procedure for Implicit Differentiation