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