Calculus: Single Variable Part 1 – Functions Course Syllabus

Overview: This course provides a comprehensive introduction to single-variable calculus, focusing on functions, limits, derivatives, and integrals. Designed for beginners, it combines theoretical foundations with practical applications in engineering, data science, and mathematics. With approximately 14 hours of content, the course includes interactive exercises and quizzes to reinforce learning. Learners will build analytical and problem-solving skills essential for academic and professional success in quantitative fields.

Module 1: Introduction to Functions

Estimated time: 1 hour

• Definition and representation of functions
• Domain and range
• Function composition and inverses
• Real-world applications of functions

Module 2: Limits and Continuity

Estimated time: 3 hours

• Concept of a limit
• Computing limits algebraically
• One-sided limits and infinite limits
• Continuity and its implications

Module 3: Differentiation

Estimated time: 5 hours

• Definition of the derivative
• Basic differentiation rules
• Derivatives of polynomial and transcendental functions
• Applications of derivatives

Module 4: Integration

Estimated time: 5 hours

• Introduction to definite and indefinite integrals
• Fundamental Theorem of Calculus
• Basic integration techniques
• Applications in area and accumulation

Prerequisites

• Familiarity with algebra and basic trigonometry
• High school mathematics background
• Basic understanding of graphs and coordinate systems

What You'll Be Able to Do After

• Understand and analyze functions and their behavior
• Evaluate limits and determine continuity
• Compute derivatives and interpret their meaning
• Apply integration techniques to solve problems
• Use calculus concepts in real-world contexts