Course Timeline for College Calculus
Chapter P: Preparation for Calculus
P-1 Graphs and Models

Viewing and interpreting graphs

Points of intersection

Symmetry
P-3 Functions and Their Graphs

Functions

Piece-wise functions

Even and odd functions

Composition of functions
P-4 Fitting Models to Data

Linear model with real-life data

Quadratic model with real-life data

Trigonometric model with real-life data
Chapter 1: Limits and Their Properties
1.1 A Preview of Calculus
1.2 Finding Limits Graphically and Numerically

Definition

Properties
1.3 Evaluating Limits Analytically

Trig Limits

Limits with radicals

Limits of composition functions

Limits of functions that agree at all but one point
1.4 Continuity and One-Sided Limits

One and two sided limits

Removable discontinuity

Nonremovable discontinuity – Jump, asymptote, or oscillating

Intermediate Value Theorem for continuous functions
1.5 Infinite Limits

Asymptotic behavior

End behavior

Visualizing limits
Chapter 2: Differentiation
2.1 The Derivative and the Tangent Line Problem

Tangent to a curve

Slope of a curve

Normal to a curve

Definition
2.2 Basic Differentiation Rules and Rates of Change

Constant, Power, Sum and Difference, and Constant Multiple Rules

Sine and Cosine

Rates of Change
2.3 Product and Quotient Rules and Higher-Order Derivatives

Product and Quotient Rules

Trigonometric functions

Second and higher order derivatives

Acceleration due to gravity
2.4 The Chain Rule

Composition of a function

Power Rule

Trig functions with the Chain Rule
2.5 Implicit Differentiation

Implicit and Explicit functions

Differential method

Second derivative implicitly

Slope, tangent, and normal
2.6 Related Rates

Applications to derivatives

Guidelines for related rate problems
Chapter 3: Applications of Differentiation
3.1 Extrema on an Interval

Relative extrema

Critical numbers

Finding extrema on a closed interval

Absolute extrema
3.2 Rolle’s Theorem and the Mean Value Theorem

Illustrating Rolle’s Theorem

Tangent line problems and instantaneous rate of change problems with the
Mean Value Theorem
3.3 Increasing and Decreasing Functions and the First Derivative Test

Testing for increasing and decreasing

First Derivative Test for extrema

Applications
3.4 Concavity and the Second Derivative Test

Testing for concavity

Points of inflection

Second Derivative Test for extrema
3.5 Limits at Infinity

Horizontal Asymptotes

Limits at infinity

Trig functions

Infinite limits at infinity
3.6 A summary of Curve Sketching

Rational functions

Radical functions

Polynomial function

Trig function
3.8 Newton’s Method

Approximate zeros
3.9 Differentials

Tangent line approximation

Error propagation
Chapter 4: Integration
4.1 Antiderivatives and Indefinite Integration

Definition

Integration Rules

Vertical Motion

Sigma notation

Upper and lower sums
4.2 Area
4.3 Riemann Sums and Definite Integrals

Subintervals with equal and unequal widths

Definition

Continuity

Area of a region

Properties of definite integrals
4.4 The Fundamental Theorem of Calculus

Guidelines for using FTC

Mean Value Theorem for integrals

Average Value of a function

Second fundamental theorem
4.5 Integration by Substitution

Composition function

Change of variables

Power rule for integration
4.6 Numerical Integration

Trapezoidal Rule

Simpson’s Rule
Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions, Chapter 6:
Differential Equations
5.1 The Natural Logarithmic Function: Differentiation

Definition

Properties of the Natural Logarithmic Function

Definition of e

Derivative of ln
5.2 The Natural Logarithmic Function: Integration

Log rule for integration

Trig functions
5.3 Inverse Function
5.4 Exponential Functions: Differentiation and Integration

Definition of

Operations and properties with exponential functions
6.1 Slope Fields and Euler’s Method

General and particular solutions

Slope fields – Visualizing and sketching

Approximating solutions with Euler’s method
6.2 Differential Equations: Growth and Decay

Growth and decay model
Chapter 7: Applications of Integration
7.1 Area of a Region Between Two Curves

Area between two curves

Intersecting curves
7.2 Volume: The Disk Method

Disk and washer method
7.3 Volume: The Shell Method