# Introduction to Calculus for Beginners

Instructor

#### Dr. Garcia

Reviews

## Course Overview

### Introduction to Calculus for Beginners

#### Lesson 1: Understanding Limits

**Objective:**Introduce the concept of limits, explain their significance in calculus, and demonstrate basic limit problems.**Content:**Definition of a limit, notation, finding limits from graphs and tables, basic limit laws.

#### Lesson 2: Continuity and Discontinuity

**Objective:**Explore the concept of continuity, identify types of discontinuities, and understand their impact on functions.**Content:**Definition of continuity, types of discontinuities (removable, jump, infinite), examples, and exercises.

#### Lesson 3: The Derivative – Definition and Interpretation

**Objective:**Define the derivative, interpret it geometrically as the slope of a tangent line, and understand its physical meaning.**Content:**Definition of the derivative, notation, the relationship between the derivative and the slope of a function, and basic differentiation rules.

#### Lesson 4: Techniques of Differentiation

**Objective:**Learn and apply various techniques for differentiating functions.**Content:**Power rule, product rule, quotient rule, chain rule, and examples applying these techniques.

#### Lesson 5: Applications of Derivatives

**Objective:**Apply derivatives to solve real-world problems involving rates of change and motion.**Content:**Problems involving velocity, acceleration, optimization, and related rates.

#### Lesson 6: Understanding Integrals

**Objective:**Introduce the concept of integration as the reverse process of differentiation.**Content:**Definition of an integral, antiderivatives, basic integration rules, and indefinite integrals.

#### Lesson 7: The Definite Integral and Area Under a Curve

**Objective:**Understand the definite integral and its application in finding areas under curves.**Content:**Definition of the definite integral, the Fundamental Theorem of Calculus, and calculating the area under a curve.

#### Lesson 8: Techniques of Integration

**Objective:**Learn various methods of integration to solve more complex problems.**Content:**Integration by substitution, integration by parts, and the use of partial fractions.

#### Lesson 9: Applications of Integrals

**Objective:**Apply integrals to solve practical problems involving areas, volumes, and other quantities.**Content:**Area between curves, volumes of solids of revolution (using disk and shell methods), and examples of physical applications.

#### Lesson 10: Introduction to Differential Equations

**Objective:**Introduce basic differential equations and their applications.**Content:**Definition of a differential equation, basic solution techniques, and simple real-world applications such as population growth and cooling laws.

Each lesson should include a mix of theoretical explanations, practical examples, and exercises for students to practice and consolidate their understanding of the concepts.

- Prerequisite(s): MATH 105