Math 3A Course Topics

Calculus of a Single Variable, Early Transcendental Functions (2nd ed.)

by Larson, Hostetler & Edwards (D.C. Heath)

Categories: 1. Must be covered in detail.
2. Must be covered at least briefly.

3. Do not cover unless you have extra time after adequately doing 1 & 2.

Category Section Topic

1

A.1

Real Numbers and the Real Line

1

A.2

The Cartesian Plane

1

P.1

Graphs of Equations

1

P.2

Lines in the Plane

1

P.3

Functions

1

3

A.3

P.4

Review of Trigonometric Functions

Fitting Models to Data

1

P.5

Inverse Functions

1

P.6

Exponential and Logarithmic Functions

1

1.1

A Preview of Calculus

1

1.2

Finding Limits Graphically and Numerically

1

1.3

Evaluating Limits Analytically

1

1.4

Continuity and One-Sided Limits

1

1.5

Infinite Limits

1

2.1

The Derivative and the Tangent Line Problem

1

2.2

Basic Differentiation Rules and Rates of Change

1

2.3

The Product and Quotient Rules and Higher Order Derivatives

1

2.4

The Chain Rule

1

2.5

Implicit Differentiation

1

1

2

2.6

2.7

2.8

Derivatives of Inverse Functions

Related Rates

Newton's Method

1

3.1

Extrema on an Interval

1

3.2

Rolle's Theorem and the Mean Value Theorem

1

3.3

Increasing and Decreasing Functions and the First Derivative Test

1

3.4

Concavity and the Second Derivative Test

1

3.5

Limits at Infinity

1

3.6

A Summary of Curve Sketching

1

3.7

Optimization Problems

1

3.8

Differentials

3

3.9

Business and Economics Applications

1

4.1

Antiderivatives and the Indefinite Integral

1

4.2

Area

1

4.3

Riemann Sums and Definite Integrals

1

4.4

The Fundamental Theorem of Calculus

1

4.5

Integration by Substitution

2

4.6

Numerical Integration

1

4.7

The Natural Logarithmic Function and Integration