Math 11AB, *Calculus with Applications*, is the recommended calculus sequence for most students majoring in the biological sciences.

When selecting and enrolling in your course, you should consider prerequisites, your (prospective) major requirements, and scheduling. Verify the requirements for your (prospective) major in the General Catalog before enrolling in your course. Knowing which topics will be covered in your course can help you to prepare for success.

## Prerequisites

Before enrolling in Math 11A, you must satisfy one of the following prerequisites:

MP tier 300 or higher, *or*

AP Calculus (AB or BC) score of 3 or higher, *or*

completion of AMS 3 or Math 3 with a grade of C or better.

Before enrolling in Math 11B, you must satisfy one of the following prerequisites:

Completion of Math 11A with a grade of C or better, *or*

AP Calculus AB score of 4 or 5, *or*

AP Calculus BC score of 3 or higher.

## Who should take Math 11AB?

Students in the following majors must complete one of the following calculus sequences: Math 11AB 19AB.

Biochemistry & Molecular Biology*

Biology BS^{†}

Chemistry (BA or BS)^{‡}

Earth Sciences^{†}

Ecology & Evolutionary Biology*

Environmental Sciences^{‡}

Environmental Studies/Earth Sciences^{†}

Human Biology^{†}

Marine Biology*

Molecular, Cellular, & Developmental Biology^{†}

Neuroscience^{†}

Plant Sciences*

*The first quarter of calculus must be completed before declaring these majors. Both quarters of calculus must be completed prior to graduation.

^{†}Calculus not required to declare major, but must be completed prior to graduation.

^{‡}Both quarters of calculus must be completed before declaring these majors.

*Note:* The Biology BA doesn’t require calculus.

Chemistry 1A has a prerequisite of MP tier 300 or higher, or corequisite of Math 3.

## Topics and text

Usual text for **Math 11AB**, *Calculus with Applications*:

** BioCalculus: Calculus for Life Sciences** by James Stewart and Troy Day.

Math 11A covers Chapters 1–4; Math 11B covers Chapters 5–7.

Gray sections are skipped and chapters not covered aren't shown.

WARNING: The text may be changed at the instructor's discretion.

#### 1. Functions and Sequences

1.1 Four Ways to Represent a Function

1.2 A Catalog of Essential Functions

1.3 New Functions from Old Functions

1.4 Exponential Functions

1.5 Logarithms; Semi-log and Log-log Plots

1.6 Sequences and Difference Equations

#### 2. Limits

2.1 Limits of Sequences

2.2 Limits of Functions at Infinity

2.3 Limits of Functions at Finite Numbers

2.4 Limits: Algebraic Methods

2.5 Continuity

#### 3. Derivatives

3.1 Derivatives and Rates of Change

3.2 The Derivative as a Function

3.3 Basic Differentiation Formulas

3.4 The Product and Quotient Rules

3.5 The Chain Rule

3.6 Exponential Growth and Decay

3.7 Derivatives of the Logarithmic and Inverse Tangent Functions

3.8 Linear Approximations and Taylor Polynomials

#### 4. Applications of Derivatives

4.1 Maximum and Minimum Values

4.2 How Derivatives Affect the Shape of a Graph

4.3 L’Hospital’s Rule: Comparing Rates of Growth

4.4 Optimization

4.5 Recursions: Equilibria and Stability

4.6 Antiderivatives

#### 5. Integrals

5.1 Areas, Distances, and Pathogenesis

5.2 The Definite Integral

5.3 The Fundamental Theorem of Calculus

5.4 The Substitution Rule

5.5 Integration by Parts

5.6 Partial Fractions

5.7 Integration Using Tables and Computer Algebra Systems

5.8 Improper Integrals

#### 6. Applications of Integrals

6.1 Areas Between Curves

6.2 Average Values

6.3 Further Applications to Biology

6.4 Volumes

#### 7. Differential Equations

7.1 Modeling with Differential Equations

7.2 Phase Plots, Equilibria, and Stability

7.3 Direction Fields and Euler''s Method

7.4 Separable Equations

7.5 Systems of Differential Equations

7.6 Phase Plane Analysis