# Math 181/182 - Calculus and Mathematical Modeling for the Life Sciences I/II

## Course Coordinator

Miriam Castillo-Gil (miriamc@iastate.edu)

## Catalog Description

MATH 181. Calculus and Mathematical Modeling for the Life Sciences I.
(4-0) Cr. 4. F.S. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra, 1 year of high school geometry, 1 semester of trigonometry or enrollment in MATH 142
Exponential and logarithm functions, difference equations, derivatives, and applications of the derivative. Examples taken from biology. Only one of MATH 151, MATH 160, the sequence MATH 165- MATH 166, or the sequence MATH 181-MATH 182 may be counted towards graduation.

MATH 182. Calculus and Mathematical Modeling for the Life Sciences II.
(4-0) Cr. 4. S. Prereq: MATH 181
Integration, first and second order differential equations, applications of the definite integral, introduction to multivariable calculus. Examples taken from biology. Only one of MATH 151, MATH 160, the sequence MATH 165-MATH 166, or the sequence MATH 181-MATH 182 may be counted towards graduation.

## Textbook For both Math 181 and Math 182

Calculus for the Life Sciences: A Modeling Approach By James L. Cornette and Ralph A. Ackerman. Published and distributed by the Mathematical Association of America (e-book). http://www.maa.org/ebooks/CLS

## Syllabus

Times are suggested based on a 15-week semester of 59 class meetings, allowing 13 days for reviews, quizzes and exams.

Course Chapter & Sections Topics Time
Math 181 Ch 1 - Mathematical Models of Biological Processes 8 days
§§1.1-1.10
Chapter 2 - Functions as Descriptions of Biological Patterns 7 days
§§ 2.1-2.4,2.6-2.8
Chapter 3 - The Derivative 8 days
§§ 3.1-3.3 & 3.5-3.6
Chapter 4 - Continuity and the Power Chain Rule 5 days
§§ 4.1-4.6
Chapter 5 - Derivatives of Exponential and Logarithmic Functions 7 days
§§ 5.1-5.6
Chapter 6 & 7 - Derivatives of Products, Quotients and Composition of Functions
Trigonometric Functions
5 days
§§ 6.1 - 6.3, 7.1-7.2
Chapter 8 - Applications of Derivatives 4 days
§§ 8.1 - 8.2
Review for Final Exam 2 days

Math 182 Chapter 9 - The Integral 6 days
§§9.1, 9.2, 9.4, 9.5, 9.6
Chapter 10 - Fundamental Theorem of Calculus 7 days
§§ 10.1, 10.3, 10.4, 10.5
Chapter 11 - Applications of Fundamental Theorem of Calculus 7 days
§§ 11.1-11.4
Chapter 13 - Two Variable Calculus 11 days
§§ 13.1-13.3
Chapter 17 - Differential Equations 7 days
§§ 17.1, 17.2, 17.3, 17.8, 17.7
Chapter 18 - Second-order and Systems of Two First-order Differential Equations 6 days
§§ 18.1

Review for Final Exam 2 days

## Objectives For Math 181

The student who successfully completes this course should be able to do the following:

### Mathematical Models of Biological Processes

• Build a mathematical model from experimental data of bacterial growth
• Solve the difference equation P(t+1)-P(t)=rP(t)
• State the definitions of Doubling time and Half-life
• Solve the difference equation P(t+1)-P(t)=rP(t)+b

### The Derivative

• Compute limits of ratios of polynomials as the variable goes to a finite or infinite limit
• Compute simple derivatives from the definition
• Compute derivatives using quick rules

### Applications of Derivatives

• Find the equation of the tangent to a the graph of a function.
• Tell where functions are increasing and where they are decreasing
• Find the maxima and minima of functions
• Solve word problems to find maxima and minima
• Use the chain rule

### More Advanced Differentiation

• Solve equations involving exponential and logarithmic functions
• Differentiate exponential and logarithmic functions
• Differentiate sine and cosine functions
• Solve word problems involving exponential, logarithmic, and trigonometric functions
• Compute and use second derivatives

## Objectives For Math 182

The student who successfully completes this course should be able to do the following:

### Integration

• Find antiderivatives of simple functions, using polynomial, exponential, logarithm, sine, and cosine functions
• Use antiderivatives to solve word problems
• Perform integration using substitution
• Perform integration using parts

### Fundamental Theorem of Calculus

• Use the Fundamental Theorem of Calculus to compute definite integrals
• Find the area under a curve and above the x-axis in the plane
• Find the area between two curves in the plane
• Find volumes of three-dimensional shapes obtained by revolution of planar areas using washers, disks, and shells
• Find masses of three-dimensional shapes using densities
• Find arc length and surface area

### Multivariable Calculus

• Interpret functions of more than one variable
• Find partial derivatives
• Find the equations of tangent planes to the graphs of functions of two variables
• Locate and classify critical points of functions of two variables
• Maximize and minimize functions of two variables
• Compute double integrals over a rectangle

### First-order Differential Equations

• Find solutions to separable differential equations
• Find solutions to linear differential equations

### Second-order Differential Equations

• Find the general solutions of second-order homogeneous linear differential equations with constant coefficients
• Solve systems of two differential equations with initial conditions

None available.

## Official Math Department Policies

The Math Department Class Policies page describes the official policies that all instructors have to follow. It covers rules on make-up exams, cheating, student behavior, etc.

## Students With Disabilities

If you have a documented disability and require accommodations, you should obtain a Student Academic Accommodation Request (SAAR) from the Disability Resources office (Student Services Building, Room 1076, 294-6624 or TDD 294-6335, disabilityresources@iastate.edu or accommodations@iastate.edu). Please contact your instructor early in the semester so that your learning needs may be appropriately met.

More information about disability resources in the Mathematics Department can be found at http://www.math.iastate.edu/Undergrad/AccommodationPol.html.