What you will learn
- Master limits, continuity, and the formal definition of derivatives
- Learn differentiation rules (power, product, quotient, chain)
- Apply derivatives to optimization and related rates problems
- Understand the Fundamental Theorem of Calculus
- Develop problem-solving skills through practical applications
- Build a strong base for advanced mathematics and engineering courses
Program Overview
Limits and Continuity
⏱️ 3-4 weeks
- Limit definitions and evaluation techniques
- One-sided and infinite limits
- Continuity and Intermediate Value Theorem
- Limits at infinity
Derivatives
⏱️ 4-5 weeks
- Definition of derivative as limit
- Differentiation rules
- Implicit differentiation
- Higher order derivatives
Applications of Derivatives
⏱️ 4-5 weeks
- Mean Value Theorem
- Curve sketching (increasing/decreasing, concavity)
- Optimization problems
- Related rates
Introduction to Integration
⏱️ 3-4 weeks
- Antiderivatives
- Definite integrals and Riemann sums
- Fundamental Theorem of Calculus
- Basic integration techniques
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Job Outlook
- Critical for:
- Engineering students (all disciplines)
- Computer Science fundamentals
- Economics and Business Analytics
- Physics and Applied Mathematics
- Career Impact:
- 85% of engineering jobs require calculus understanding
- Foundation for data science and machine learning
- Higher GPA correlation in technical programs
Specification: KALKÜLÜS II: TEMEL KAVRAMLAR / CALCULUS II: BASIC CONCEPTS
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