# Calculus 1

### Course Info

Chapter P – PREPARATION FOR CALCULUS

• P.1  Graphs and Models
• P.2  Linear Models and Rates of Change
• P.3  Functions and Their Graphs
• P.4  Fitting Models to Data

Chapter 1 – LIMITS AND THEIR PROPERTIES

• 1.1  A Preview of Calculus
• 1.2  Finding Limits Graphically and Numerically
• 1.3  Evaluating Limits Analytically
• 1.4  Continuity and One-Sided Limits
• 1.5  Infinite Limits

Chapter 2 – DIFFERENTIATION

• 2.1  The Derivative and the Tangent Line Problem
• 2.2  Basic Differentiation Rules and Rates of Change
• 2.3  The Product and Quotient Rules and Higher-Order Derivatives
• 2.4  The Chain Rule
• 2.5  Implicit Differentiation
• 2.6  Related Rates

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
• 3.8  Newton’s Method
• 3.9  Differentials

Chapter 4 – INTEGRATION

• 4.1  Antiderivatives and Indefinite Integration
• 4.2  Area
• 4.3  Riemann Sums and Definite Integrals
• 4.4  The Fundamental Theorem of Calculus
• 4.5  Integration by Substitution
• 4.6  Numerical Integration

Chapter 5 – LOGARITHMIC, EXPONENTIAL, AND OTHER TRANSCENDENTAL FUNCTIONS

• 5.1  The Natural Logarithmic Function: Differentiation
• 5.2  The Natural Logarithmic Function: Integration
• 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
• 5.7  Inverse Trigonometric Functions: Integration
• 5.8  Hyperbolic Functions

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
• 6.4  First-Order Linear Differential Equations

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