Calculus from the Ground Up

Title Pages
Table of Contents
Chapter 1: Introduction
Part I: Preliminaries
Chapter 2: A General Method for Solving Mathematics Problems
Chapter 3: Basic Tools: Lines
Chapter 4: Basic Tools: Variables and Functions
Chapter 5: Basic Tools: Graphs
Chapter 6: Calculus: The Big Picture
Part II: The Derivative
Chapter 7: The Derivative
Chapter 8: Basic Derivative Rules for Polynomials
Chapter 9: Basic Uses of the Derivative
Chapter 10: The Differential
Chapter 11: Differentials of Composite Functions
Chapter 12: Additional Differential Rules
Chapter 13: Multivariable Differentials
Chapter 14: Relating Rates Using Differentials
Chapter 15: Working with Problems Involving Differentials
Part III: The Integral
Chapter 16: The Integral as an Antidifferential
Chapter 17: The Integral as an Infinite Sum
Chapter 18: Using the Integral to Find the Area Under the Curve
Chapter 19: Integration and u-Substitution
Chapter 20: Other Geometric Uses of the Integral
Chapter 21: Transforming Equations for Integration
Chapter 22: Integration by Parts
Chapter 23: Problem-Solving Using the Integral
Chapter 24: Numeric Integration Techniques
Part IV: Manipulating Infinity
Chapter 25: Modeling Functions with Polynomial Series
Chapter 26: Advanced Topics in Polynomial Series
Chapter 27: Thinking About Infinity
Chapter 28: Limits: Finding Impossible and Non-Existent Values of Functions
Chapter 29: Limits: Finding Results Near Infinity
Chapter 30: Limits: Difficult Limits with L\'Hospital
Chapter 31: Conclusion
Part V: Appendices
Appendix A: Guide for Instructors
Appendix B: Liebniz Notation of Higher Order Differentials
Appendix C: Well-Known Calculus Theorems
Appendix D: Additional Uses of the Derivative
Appendix E: Additional Uses of the Integral
Appendix F: Proofs and Derivations
Appendix G: Additional Things to Know for Standardized Tests
Appendix H: Mathematical Formulas, Relationships, and Tables