AMS/Econ 11AB, *Mathematical Methods for Economists*, is a single and multi variable calculus sequence focusing on applications to business and economics.

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

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.

*Note:* The Economics Department recommends Math 3, not AMS 3, for Economics students needing preparatory coursework.

## Who should take AMS/Econ 11AB?

AMS/Econ 11AB is the recommended calculus sequence for students in the following majors:

Business Management Economics

Economics

Environmental Studies/Economics

Global Economics.

The first quarter of calculus must be completed before declaring an Economics major. Both quarters must be completed prior to graduation.

The Math 11AB, 19AB, and 20AB calculus sequences are accepted for these majors, but Economics students who take a Math calculus sequence, rather than AMS/Econ 11AB, must also take Math 22 or 23A.

Students in the Economics/Mathematics combined major must take the Math 19AB calculus sequence. Students intending to pursue graduate studies in Economics are encouraged to take Math 19AB and Math 22 or 23A, rather than AMS/Econ 11AB.

## Topics and text

Commonly used text for **AMS/Econ 11AB**, *Math Methods for Economics:*

* Introductory Mathematical Analysis for Business, Economics, and the Life and Social Sciences*, 13th edition by Ernest Haeussler, Richard Paul, and Richard Wood.

WARNING: The text is subject to change at the instructor's discretion.

AMS/Econ 11A typically covers Chapters 3–4 and10-13; AMS/Econ 11B typically covers 14–15 and 17.

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

#### Part I. ALGEBRA

0. Review of Algebra

1. Applications and More Algebra

2. Functions and Graphs

#### 3. Lines, Parabolas, and Systems

3.1 Lines

3.2 Applications and Linear Functions

3.3 Quadratic Functions

3.4 Systems of Linear Equations

3.5 Nonlinear Systems

3.6 Applications of Systems of Equations

#### 4. Exponential and Logarithmic Functions

4.1 Exponential Functions

4.2 Logarithmic Functions

4.3 Properties of Logarithms

4.4 Logarithmic and Exponential Equations

#### Part III. CALCULUS

#### 10. Limits and Continuity

10.1 Limits

10.2 Limits (Continued)

10.3 Continuity

10.4 Continuity Applied to Inequalities

#### 11. Differentiation

11.1 The Derivative

11.2 Rules for Differentiation

11.3 The Derivative as a Rate of Change

11.4 The Product Rule and the Quotient Rule

11.5 The Chain Rule

#### 12. Additional Differentiation Topics

12.1 Derivatives of Logarithmic Functions

12.2 Derivatives of Exponential Functions

12.3 Elasticity of Demand

12.4 Implicit Differentiation

12.5 Logarithmic Differentiation

12.6 Newton's Method

12.7 Higher-Order Derivatives

#### 13. Curve Sketching

13.1 Relative Extrema

13.2 Absolute Extrema on a Closed Interval

13.3 Concavity

13.4 The Second-Derivative Test

13.5 Asymptotes

13.6 Applied Maxima and Minima

#### 14. Integration

14.1 Differentials

14.2 The Indefinite Integral

14.3 Integration with Initial Conditions

14.4 More Integration Formulas

14.5 Techniques of Integration

14.6 The Definite Integral

14.7 The Fundamental Theorem of Integral Calculus

14.8 Approximate Integration

14.9 Area between Curves

14.10 Consumers' and Producers' Surplus

#### 15. Methods and Applications of Integration

15.1 Integration by Parts

15.2 Integration by Partial Fractions

15.3 Integration by Tables

15.4 Average Value of a Function

15.5 Differential Equations

15.6 More Applications of Differential Equations

15.7 Improper Integrals

#### 17. Multivariable Calculus

17.1 Partial Derivatives

17.2 Applications of Partial Derivatives

17.3 Implicit Partial Differentiation

17.4 Higher-Order Partial Derivatives

17.5 Chain Rule

17.6 Maxima and Minima for Functions of Two Variables

17.7 Lagrange Multipliers

17.8 Lines of Regression

17.9 Multiple Integrals