What you will learn
- Master limits, continuity, and the formal definition of derivatives
- Learn differentiation rules (power, product, quotient, chain)
- Apply derivatives to solve optimization and related rates problems
- Understand the Fundamental Theorem of Calculus
- Develop problem-solving skills through practical applications
- Build a strong mathematical foundation for advanced study
Program Overview
Functions and Limits
⏱️ 2-3 weeks
- Review algebraic and transcendental functions
- Explore limits graphically and analytically
- Learn continuity and the Intermediate Value Theorem
Derivatives
⏱️ 3-4 weeks
- Understand the derivative as instantaneous rate of change
- Master differentiation techniques
- Apply derivatives to tangent lines and velocity problems
Applications of Derivatives
⏱️ 3-4 weeks
- Solve optimization problems
- Analyze curve sketching (increasing/decreasing, concavity)
- Learn related rates and L’Hôpital’s Rule
Integration
⏱️ 4-5 weeks
- Understand Riemann sums and definite integrals
- Learn antiderivatives and integration techniques
- Apply the Fundamental Theorem of Calculus
Get certificate
Job Outlook
- Calculus is fundamental for careers in:
- Engineering (average salary: 70K−120K)
- Data Science (90K−150K)
- Physics Research (60K−110K)
- Economics (65K−130K)
- 28% projected growth for math-intensive jobs (BLS 2022)
- Essential for graduate studies in STEM fields
Specification: Introduction to Calculus
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