Chapter 1: Functions and Limits

1.1: Introduction

1. Introduction to Function
2. More on Introduction to Functions
3. Problem3-Introduction to Function
4. Problem4-Introduction to Function
5. Domain & Range of Binary Relation
6. Graphs of Algebraic Functions
7. Graph of Functions Defined Piece-wise

1.2: Types of Functions

1. Algebraic Functions
2. Trigonometric Functions
3. Introduction to Binary Operations
4. More on Inverse Trigonometric Functions
5. Further to Inverse Trignometric Functions
6. Operations on Residue Classes Modulo n
7. Properties of Binary Operations
8. More on Logarithmic Functions
9. Theorems on Binary Operation
10. Inverse Hyperbolic Functions
11. Explicit and Implicit Functions
12. Parametric Functions
13. Even and Odd Functions
14. Problem-Even and Odd Functions

1.3: Composition of Function and Inverse of a Function

1. Composition of a Functions
2. Problem-Composition of Functions
3. Inverse of a Function
4. More on Inverse of a Functions
5. Problem-Inverse of a Function
6. Algebraic Method to find the Inverse Function
7. Problem-Algebraic Method to find the Inverse Function

1.4: Limit of a Function and Theorems on Limits

1. Meaning of the Phrase 'x' Approaches zero, Infinity
2. Problem-Meaning of the Phrase 'x' Approaches zero, Infinity
3. Concept of a Limit of a Function
4. Problem-Concept of Limit of a Function

1.5: Limits of Important Functions

1. Limit at Infinity
2. Method for Evaluating the Limits at Infinity
3. Problem-Method for Evaluating the Limits at Infinity
4. Deducting Formulae at Limit Approaches to 0 and infinity
5. Problem-Deducting Formulae at Limit Approaches to 0 and infinity
6. The Sandwitch Theorem

1.6: Continous and Discontinuous Functions

1. One-Sided Limits
2. Criterion for Existence of Limit of a Function
3. Problem1-Criterion for Existence of Limit of a Function
4. Continuity of a Function at a Number

1.7: Graphs

1. Graph of the Exponential Function
2. Problem1-Graph of the Exponential Function
3. More on Graph of Exponential Function
4. Problem1-More on Graph of Exponential Function
5. Graph of Common Logarithmic Function
6. Problem1-Graph of Common Logarithmic Function
7. Graph of Natural Logarithmic Function
8. Problem1-Graph of Natural Logarithmic Function
9. Graphs of Implicit Functions-Circle
10. Problem1-Graphs of Implicit Functions-Circle
11. Graphs of Implicit Functions-Ellipse
12. Graph of Parametric Equations
13. Problem1-Graph of Parametric Equations
14. Graphs of Discontinuous Functions
15. Problem1-Graphs of Discontinuous Functions
16. Graphical Solution of the Equation