# Class Curriculum

Topics of Each Lesson are Found Below

First Semester: Differentiation | Second Semester: Integration

Lessons are Subject to Change

Section | Topic |
---|---|

P |
Preparation for Calculus |

P.1 | Graphs and Models |

P.2 | Linear Models and Rates of Change |

P.3 | Functions and Their Graphs |

Chapter 1 |
Limits and Their Properties |

1.2 | Finding Limits Graphically and Numerically |

1.3 | Evaluating Limits Analytically |

1.4 | Continuity and One-Sided Limits |

1.5 | Infinite Limits |

3.5 | Limits at Infinity |

Chapter 2 |
Differentiation |

2.1 | The Derivative and the Tangent Line Problem |

2.2 | Basic Differentiation Riles and Rates of Change |

2.3 | Product and Quotient Rules and Higher-Order Derivatives |

2.4 | The Chain Rule |

2.5 | Implicit Differentiation |

2.6 | Related Rates |

Chapter 5 |
Logarithmic, Exponential, and Other Transcendental Functions |

5.1 | The Natural Logarithmic Function: Differentiation |

5.3 | Inverse Functions |

5.4 | Exponential Functions : Differentiation and Integration |

5.5 | Bases Other than e and Applications |

5.6 | Inverse Trigonometric Functions :Differentiation |

Chapter 3 |
Applications of Differentiation |

3.1 | Extrema on an Interval |

3.2 | Rolle's Theorem and the Mean Value Theorem |

3.3 | Increasing and Decreasing Functions and the First Derivative Test |

3.4 | Concavity and the Second Derivative Test |

3.5 | Limits at Infinity |

3.6 | A Summary of Curve Sketching |

3.7 | Optimization Problems |

3.9 | Differentials |

Chapter 4 |
Integration |

4.1 | Antiderivatives and Indefinite Integration |

4.2 | Area |

4.6 | Numerical Integration |

4.3 | Riemann Sums and Definite Integrals |

4.4 | The Fundamental Theorem of Calculus |

4.5 | Integration by Substitution |

Chapter 5 |
Logarithmic, Exponential, and Other Transcendental Functions |

5.2 | The Natural Logarithmic Function: Integration |

5.4 | Exponential Functions: Differentiation and Integration |

5.5 | Bases Other Than e and Applications |

5.7 | Inverse Trigonometric Functions: Integration |

Chapter 6 |
Differential Equations |

6.1 | Slope Fields and Euler's Method |

6.2 | Differential Equations: Growth and Decay |

6.3 | Separation of Variables and the Logistic Equation |

Chapter 7 |
Applications of Integration |

7.1 | Area of a Region Between Two Curves |

7.2 | Volume: The Disk Method |

Chapter 8 |
Integration Techniques, L'Hopital's Rule, and Improper Integrals |

8.1 | Basic Integration Rules |

8.7 | Indeterminate Forms and L'Hopital's Rule |