## AboutCalculus Volume 2 - Textbook and Exercise

Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates.

✨Contents of the Application✨
1 Integration
Introduction
1.1 Approximating Areas
1.2 The Definite Integral
1.3 The Fundamental Theorem of Calculus
1.4 Integration Formulas and the Net Change Theorem
1.5 Substitution
1.6 Integrals Involving Exponential and Logarithmic Functions
1.7 Integrals Resulting in Inverse Trigonometric Functions
Key Terms
Key Equations
Key Concepts
Chapter Review Exercises
2 Applications of Integration
Introduction
2.1 Areas between Curves
2.2 Determining Volumes by Slicing
2.3 Volumes of Revolution: Cylindrical Shells
2.4 Arc Length of a Curve and Surface Area
2.5 Physical Applications
2.6 Moments and Centers of Mass
2.7 Integrals, Exponential Functions, and Logarithms
2.8 Exponential Growth and Decay
2.9 Calculus of the Hyperbolic Functions
Key Terms
Key Equations
Key Concepts
Chapter Review Exercises
3 Techniques of Integration
Introduction
3.1 Integration by Parts
3.2 Trigonometric Integrals
3.3 Trigonometric Substitution
3.4 Partial Fractions
3.5 Other Strategies for Integration
3.6 Numerical Integration
3.7 Improper Integrals
Key Terms
Key Equations
Key Concepts
Chapter Review Exercises
4 Introduction to Differential Equations
Introduction
4.1 Basics of Differential Equations
4.2 Direction Fields and Numerical Methods
4.3 Separable Equations
4.4 The Logistic Equation
4.5 First-order Linear Equations
Key Terms
Key Equations
Key Concepts
Chapter Review Exercises
5 Sequences and Series
Introduction
5.1 Sequences
5.2 Infinite Series
5.3 The Divergence and Integral Tests
5.4 Comparison Tests
5.5 Alternating Series
5.6 Ratio and Root Tests
Key Terms
Key Equations
Key Concepts
Chapter Review Exercises
6 Power Series
Introduction
6.1 Power Series and Functions
6.2 Properties of Power Series
6.3 Taylor and Maclaurin Series
6.4 Working with Taylor Series
Key Terms
Key Equations
Key Concepts
Chapter Review Exercises
7 Parametric Equations and Polar Coordinates
Introduction
7.1 Parametric Equations
7.2 Calculus of Parametric Curves
7.3 Polar Coordinates
7.4 Area and Arc Length in Polar Coordinates
7.5 Conic Sections
Key Terms
Key Equations
Key Concepts
Chapter Review Exercises

A | Table of Integrals
B | Table of Derivatives
C | Review of Pre-Calculus

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