Overview
This textbook introduces differential and integral calculus through conceptualunderstanding, computational techniques, and real-world applications. Studentsdevelop the mathematical foundations necessary for advanced study in mathematics,science, engineering, economics, computer science, and related disciplines.
Table of Contents
- Chapter 1: Functions and Mathematical Models
- Chapter 2: Limits and Continuity
- Chapter 3: The Derivative
- Chapter 4: Differentiation Techniques
- Chapter 5: Applications of Derivatives
- Chapter 6: Curve Analysis and Optimization
- Chapter 7: Introduction to Integration
- Chapter 8: Techniques of Integration
- Chapter 9: Applications of Integration
- Chapter 10: Differential Equations
- Chapter 11: Infinite Sequences and Series
- Chapter 12: Parametric Equations and Polar Coordinates
- Chapter 13: Vector Calculus Foundations
- Chapter 14: Advanced Applications of Calculus
- Back Matter
Learning Outcomes
- Evaluate limits and analyze continuity.
- Compute derivatives using multiple differentiation techniques.
- Apply derivatives to optimization, rates of change, and curve analysis.
- Evaluate definite and indefinite integrals.
- Apply integration to area, volume, accumulation, and physical modeling.
- Solve and interpret basic differential equations.
- Analyze infinite sequences and series.
- Work with parametric equations, polar coordinates, and vector-valued functions.
- Use calculus to model real-world phenomena in science, engineering, economics, and technology.