# Course Information

**Exam Information**

__Evening Exam Schedules__

__Evening Exam Schedules__

Final Exam Schedule SP 24

Alternative Exam Sign Up Due Dates SP 24

__Conflict and Make up Exam Information__

__Conflict and Make up Exam Information__

**Information about signing up for a Conflict/Make up/Extended Time Exam**

- After you sign up for the exam you will
__only__be contacted if we determine that there is an issue with your request. Otherwise, you will be added to the list for the exam. you will receive an email with room information. See link for deadline dates above.__After the deadline to sign up for a makeup/conflict exam passes,__- When you sign up for the exam check the box stating
**"send me an email receipt of my responses"**at the end of the form to confirm you completed the form correctly.

Alternative Exam Sign Up Due Dates SP 24

All conflict exams are scheduled the same day as the regular exam, but at an earlier time, 4:50pm - 6:05pm.

All make up exams are scheduled for the same time as the regular exam, 6:15pm-7:30pm but at a later date.

All extended time exams (for SDR students only) are scheduled for the same date and time as the regular exam, but account for 50% extended time and end at 8:10pm.

**Extended Time Exam Signup Link**

## Course Coordinators

Amine Benkiran (azb165@psu.edu) – MATH 21, 22, 26 and 41

James Hager (jah14@psu.edu) – MATH 33, 34, 35, 36, 38

David Little (dpl14@psu.edu) – MATH 110 and 111

Joseph Roberts (jpr223@psu.edu) and Lisa Melanson (lmm63@psu.edu) – MATH 140

Joseph Roberts (jpr223@psu.edu) and Isaac Sunseri (ixs5268@psu.edu) – MATH 141

Eric Simring (eis108@psu.edu) – MATH 140B and 141B

Kathryn Stewart (kls6625@psu.edu) – MATH 220

Matthew Willyard (mcw20@psu.edu) and Nicholas Stepanik (nxs371@psu.edu) – MATH 230, 231 and 232

Nestor Handzy (nzh100@psu.edu) – MATH 250, 251, and 252

## Course Information

The mathematics department offers courses that are designed for STEM and Non-STEM majors.

Courses designed for Non-STEM majors include MATH 33, 34, 35, 36, 37 and 38. Students may want to look at the sample problems for each of these courses when deciding on which course to choose. These sample problems are included below under each course.

When choosing a course from the following list (MATH 21, 22, 26, 41, 110, 140, 141, 220, 230, 231, 250 or 251) students should look at the course prerequisites as well as the sample problems for the course and sample problems for prerequisite courses. The prerequisites and sample problems are included below under each course.

#### Course Description

Algebraic expressions; linear, absolute value equations and inequalities; lines; systems of linear equations; integral exponents; polynomials; factoring. This course may not be used to satisfy the basic minimum requirements for graduation in any baccalaureate degree program.

#### Prerequisites

MATH 3 or satisfactory performance on the mathematics placement exam.

#### Syllabi

**Course Description**

MATH 21 serves as both a preparatory algebra course for some students and as a terminal course for others who only need this level of mathematics. MATH 21 bridges the gap between elementary algebra and courses in pre-calculus mathematics by developing student proficiency with the mechanics of basic algebra.

The course presents algebra concepts beginning with rational expressions, equations, and applications. Concepts of exponent and root are developed and merged, followed by the study of quadratic equations and inequalities. Coordinate geometry is introduced with linear equations, inequalities, systems, and their graphs, extending to an introduction of conic sections.

Students entering MATH 21 should be able to add, subtract, multiply, and divide whole numbers and fractions (rational numbers) and should have an understanding of basic algebra concepts like negative numbers, factoring quadratics, and solving linear equations.

This course may fulfill three credits of the quantification portion of the general education requirement for students in some majors. Students successfully completing MATH 21 may take MATH 22, MATH 26 or MATH 41.

**Prerequisites**

Math 4 or satisfactory performance on the mathematics placement examination

#### MATH 21 Syllabi

**Sample Problems**

**Sample Problem Answers**

#### Course Description

College Algebra II represents a significant opportunity for students to discover the beauty and practical power of mathematics. Concepts and skills are taught while at the same time a sense of algebra's utility in the real world is imparted. This course provides in-depth coverage of college algebra topics that students continuing in mathematics will require. This is the kind of mathematics that students will use the rest of their lives in many fields.

MATH 22 is a preparatory course intended to provide mathematical background in algebra with a function/graph emphasis required in calculus courses. Linear, polynomial, rational, exponential and logarithmic functions and their graphs provide necessary models for mathematical applications.

Students entering MATH 22 should be competent in operations (adding, subtracting, multiplying and dividing) with rational (fractional) expressions. Students should be able to solve linear and absolute value inequalities and be able to simplify rational expressions with exponents.

Students who understand the concepts of MATH 22 will have the basic algebra skills sufficient for taking Business Calculus, MATH 110. Students studying engineering or science may enroll in MATH 22 and MATH 26 concurrently as preparation for Calculus, MATH 140. Alternately, students may take MATH 41 which covers the content of both MATH 22 and MATH 26 in a single course.

MATH 22 Syllabi

#### Prerequisite

MATH 21 or satisfactory performance on the mathematics placement examination

#### Sample Problems

#### Sample Problem Answers

#### Course Description

Trigonometry is a field of mathematics in which the geometric properties of the angles and edges of triangles are used to measure lengths. Real-world problems involving trigonometry are common in engineering, physics, construction and design.

This course is well suited for students who need sufficient mastery of trigonometry for use in fieldwork as well as those continuing on to engineering, kinesiology, surveying and physical sciences. Intermediate algebra skills are assumed. MATH 26 provides the trigonometry skills and concepts essential to success in calculus courses. Topics include right-triangle relationships, unit circle, sine, cosine, and tangent functions and their applications, inverse trigonometric functions, identities, and trigonometric form of complex numbers.

Students who enroll in MATH 26 often enroll concurrently in MATH 22, College Algebra II. Students who understand the material in MATH 26 and MATH 22 are fully prepared for the trigonometry-based calculus course MATH 140. Alternately, students may take MATH 41 which covers the content of both MATH 22 and MATH 26 in a single course.

Class size, frequency of offering, and evaluation methods will vary by location and instructor. For these details check the specific course syllabus.

**Prerequisite**

MATH 21 or satisfactory performance on the mathematics placement examination

**MATH 26 Syllabi**

#### Sample Problems

#### Sample Problem Answers

#### Course Description

This course is intended to build the specific quantitative reasoning skills needed by workers in Allied Health Professions, such as nurses or therapists. Students will become fluent in proportional reasoning in a variety of contexts, including unit conversion, drug dosage calculations, probability, and logarithmic scales. Students gain the tools to communicate and reason about covariation in scenarios such as exponential growth and decay. Student will also apply tools of probability and descriptive statistics to gain literacy in risk and uncertainty in health settings, such as making sense of effect sizes in research literature.

#### Prerequisites

Math 4 or satisfactory performance on the mathematics placement examination

**MATH 32 Syllabi**

#### Course Description

Mathematical analysis of sustainability: measurement, flows, networks, rates of change, uncertainty and risk, applying analysis in decision making; using quantitative evidence to support arguments; examples. MATH 33 Mathematics for Sustainability (3) (GQ) This course is one of several offered by the mathematics department with the goal of helping students from non-technical majors partially satisfy their general education quantification requirement. It is designed to provide an introduction to various mathematical modeling techniques, with an emphasis on examples related to environmental and economic sustainability. The course may be used to fulfill three credits of the GQ requirement for some majors, but it does not serve as a prerequisite for any mathematics courses and should be treated as a terminal course. The course provides students with the mathematical background and quantitative reasoning skills necessary to engage as informed citizens in discussions of sustainability related to climate change, resources, pollution, recycling, economic change, and similar matters of public interest. Students apply these skills through writing projects that require quantitative evidence to support an argument. The mathematical content of the course spans six key areas: "measuring" (representing information by numbers, problems of measurement, units, estimation skills); "flowing" (building and analyzing stock-flow models, calculations using units of energy and power, dynamic equilibria in stock-flow systems, the energy balance of the earth-sun system and the greenhouse effect); "connecting" (networks, the bystander effect, feedbacks in stock-flow models); "changing" (out-of-equilibrium stock-flow systems, exponential models, stability of equilibria in stock-flow systems, sensitivity of equilibria to changes in a parameter, tipping points in stock-flow models); "risking" (probability, expectation, bayesian inference, risk vs uncertainty; "deciding" (discounting, uses and limitations of cost-benefit analysis, introduction to game theory and the tragedy of the commons, market-based mechanisms for pollution abatement, ethical considerations).

#### Course Description

The mathematics of money course allows students to learn mathematical techniques that aid in the understanding of life's financial decisions, such as those involving interest, annuities, investments, retirement plans, taxes, credit cards, and mortgages. The goal of this course is to help students develop the knowledge and skills needed to make sound financial decisions. The U.S. Department of Treasury has stated that "Today's complex financial-services market offers consumers a vast array of products and providers to meet their financial needs. This degree of choice requires that consumers be equipped with the knowledge and skills to evaluate the options and identify those that best suit their needs and circumstances." This course will help students obtain this knowledge and skills.

Some examples of the types of problems that students in this course learn to solve are:

- A person decides that the most they can afford to pay each month for a car loan is $375. If their credit union offers a five-year car loan at a 6 percent interest rate, what is the most they can afford to pay for a car?
- A person would like to have $1,000,000 in their 401(k) account in 30 years. How much money would they need to deposit into their account each month if they expect to earn 8 percent interest on their investments and anticipate an annual inflation rate of 3.5 percent?
- A credit card carries an interest rate of 18.5 percent. How much interest would a person owe for the billing month if their average daily balance was $745.09?

This course may be used to fulfill three credits of the quantification portion of the general education requirement for some majors, but does not serve as a prerequisite for any mathematics courses and should be treated as a terminal course.

Class size, frequency of offering and evaluation methods will vary by location and instructor. For these details check the specific course syllabus.

#### Prerequisite

MATH 4 or satisfactory performance on the mathematics placement exam

#### MATH 34 Syllabi

#### Sample Problems

#### Course Description

This course presents a general view of a number of mathematical topics to a non-technical audience, often relating the mathematical topics to a historical context, and providing students with an opportunity to engage with the mathematics at an introductory level. Although some variation in topics covered may take place among different instructors at different campuses, an example of such a course focuses on a number theory theme throughout the course, beginning with the Greeks' view of integers, the concept of divisors, the calculation of greatest common divisors (which originates with Euclid), the significance of the prime numbers, the infinitude of the set of prime numbers (also known to the ancient Greeks), work on perfect numbers (which continues to be a topic of research today), and the work of Pythagoras and his famous Theorem. The course then transitions to the work of European mathematicians such as Euler and Gauss, including work on sums of two squares (which generalizes the Pythagorean Theorem), and then considering Euler's phi function, congruences, and applications to cryptography.

#### Syllabi

#### Sample Problems

#### Course Description

This course will provide students the mathematical background and quantitative skills in various mathematical applications in such areas which are related to voting, fair divisions which includes apportionment methods, and the understanding and application of basic graph theory such as Euler and Hamilton circuits. This course may be used by students from non-technical majors to satisfy 3 credits of their General Education Quantification (GQ) requirement. This course does not serve as a prerequisite for any mathematics courses and should be treated as a terminal course.

#### Course Description

Finite math includes topics of mathematics which deal with finite sets. Sets and formal logic are modern concepts created by mathematicians in the mid 19th and early 20th centuries to provide a foundation for mathematical reasoning. Sets and formal logic have lead to profound mathematical discoveries and have helped to create the field of computer science in the 20th century. Today, sets and formal logic are taught as core concepts upon which all mathematics can be built.

In this course, students learn the elementary mathematics of logic and sets. Logic is the symbolic, algebraic way of representing and analyzing statements and sentences. While students will get just a brief introduction to logic, the mathematics used in logic are found at the heart of computer programming and in designing electrical circuits.

Problems of counting various kinds of sets lead to the study of combinatorics, the art of advanced counting. For example, if a room has twenty chairs and twelve people, in how many ways can these people occupy the chairs? And are you accounting for differences in who sits in particular chairs, or does it only matter whether a chair has a body in it? These kinds of counting problems are the basis for probability. In order to calculate the chance of a particular event occurring you must be able to count all the possible outcomes.

MATH 37 is intended for students seeking core knowledge in combinatorics, probability and mathematical logic but not requiring further course work in mathematics. Students entering the class will benefit from having some experience with basic algebra and solving word problems.

The course may be used to fulfill three credits of the quantification portion of the general education requirement for some majors, but does not serve as a prerequisite for any mathematics courses and should be treated as a terminal course.

Class size, frequency of offering, and evaluation methods will vary by location and instructor. For these details check the specific course syllabus.

#### Short Description

Matrices and vectors; transformations; systems of linear equations; convex sets and linear programming.

#### Long Description

Many problems we have to solve in day-to-day practice require the simultaneous determination of several different but interrelated unknowns. Although many problems of this form have been studied throughout the long history of mathematics, only in the early 20thcentury did the systematic approach we now refer to as linear algebra emerge. Matrices and linear algebra are now accepted as the single most essential tool need for the solution of these problems.

In addition, linear algebra provides students their first introduction to the concept of dimension in an abstract setting where things with 4,5, or even more dimensions are often encountered.

In the simplest situations, many of these problems can be represented as A x = b, where x is our vector of unknowns, A is a matrix, and b is a vector of constants.

Math 38 is intended for students requiring some understanding of the concepts of linear algebra for their major, but not requiring any calculus course work. Students who are also required to take calculus course work should instead take Math 220 after completion of an appropriate prerequisite.

#### Prerequisite

2 units of high school mathematics

#### Syllabi

#### Sample Problems

#### Course Description

MATH 41 is a one-semester pre-calculus course, which combines the material from MATH 22 and MATH 26. Please refer to MATH 22 and MATH 26 descriptions.

Students who understand the material in MATH 41 are fully prepared for the trigonometry-based calculus course MATH 140. MATH 41 is not needed for Business Calculus MATH 110 as MATH 41 includes trigonometry topics not necessary in that course.

Class size, frequency of offering, and evaluation methods will vary by location and instructor. For these details check the specific course syllabus

#### Prerequisite

Math 21 or satisfactory performance on the mathematics placement examination

#### Syllabus

#### Sample Problems

#### Sample Problem Answers

#### Course Description

TECHNIQUES OF CALCULUS I (4) Functions, graphs, derivatives, integrals, techniques of differentiation and integration, exponentials, improper integrals, applications. Students may take only one course for credit from MATH 110, 140, 140A, and 140B. Prerequisite: MATH 22 or satisfactory performance on the mathematics proficiency examination.

#### Prerequisite

MATH 22 or MATH 40 or MATH 41 or satisfactory performance on the mathematics placement examination

#### Math 110 Syllabi

#### Sample Problems

#### Sample Problem Answers

#### MATH 110 Learning Course Packets

- Precalculus Review
- Functions
- Limits & Continuity
- Derivatives
- Marginal Analysis & Elasticity
- Implicit Differentiation & Related Rates
- Curve Sketching
- Optimization
- Exponential & Logarithmic Functions
- Compound Interest
- Indefinite Integrals
- Definite Integrals
- Applications of Definite Integrals
- Integration by Parts & Improper Integrals

#### Course Description

Math 111 is the second course in a sequence of calculus content tailored primarily to first-year business students with an emphasis on economics, business, and social science application. Although it provides standalone instruction in the core elements of differential and integral calculus, applications are chosen to dovetail with typical models discussed in first-year finance, economics, and social science coursework.

Content discussed in Math 111 includes:

1.Functions of several variables and their real-world business applications

2.Partial derivatives, and their relevance to economics’ applications

3.Maxima and Minima of Functions of Several Variables

4.Methods of Least Squares

5.Constrained Maxima and Minima and Lagrange Multiplier Techniques

6.Total differentials to approximate change or error

7.Double integrals and their applications to business models

8.Differential Equations and their application to business models

9.Solutions to Differential Equations using separation of variable techniques

10. Use Euler's method to approximate solutions to Differential Equations

#### Course Description

MATH 140 is the first course in a two-or three-course calculus sequence for students in science, engineering and related fields. Students enrolling in MATH 140 should have demonstrated.

proficiency in pre-calculus mathematics, either by a satisfactory score on the ALEKS exam, or satisfactory completion of MATH 22 (College Algebra II) AND MATH 26 (Trigonometry) OR MATH 41 (College Algebra and Trigonometry).

Calculus is an important building block in the education of any professional who uses quantitative analysis. This course introduces and develops the mathematical skills required for analyzing change and creating mathematical models that replicate real-life phenomena. The goals of our calculus courses include to develop the students' knowledge of calculus techniques and to use the calculus environment to develop critical thinking and problem solving skills.

The concept of limit is central to calculus; MATH 140 begins with a study of this concept. Differential calculus topics include derivatives and their applications to rates of change, related rates, linearization, optimization, and graphing techniques. The Fundamental Theorem of Calculus, relating differential and integral calculus begins the study of Integral Calculus. Antidifferentiation and the technique of substitution is used in integration applications of finding areas of plane figures and volumes of solids of revolution. Trigonometric functions are included in every topic.

Class size, frequency of offering, and evaluation methods will vary by location and instructor. For these details check the specific course syllabus.

An honors version of this course is offered at least once per year.

#### Prerequisite

MATH 22 and MATH 26 or MATH 26 and satisfactory performance on the mathematics placement examination or MATH 40 or MATH 41 or satisfactory performance on the mathematics placement examination

#### MATH 140 Syllabi

#### Sample Problems

#### Sample Problem Answers

These are exams and solutions from the past 2 years. Warning: The schedule, content, and content focus for Fall 2023 do not necessarily match these, so you should not expect them to prepare you for any Fall 2023 exams. See your Canvas page for the Fall 2023 course materials.

#### Course Description

Calculus is an important building block in the education of any professional who uses quantitative analysis. This course introduces and develops the mathematical skills required for analyzing change and creating mathematical models that replicate real-life phenomena. The goals of our calculus courses include to develop the students' knowledge of calculus techniques and to use the calculus environment to develop critical thinking and problem solving skills. The concept of limit is central to calculus; this concept is studied early in the course. Differential calculus topics include derivatives and their applications to rates of change, related rates, linearization, optimization, and graphing techniques. The Fundamental Theorem of Calculus, relating differential and integral calculus begins the study of Integral Calculus. Antidifferentiation and the technique of substitution is used in integration applications of finding areas of plane figures and volumes of solids of revolution. Trigonometric functions are included in every topic. Students may only take one course for credit from MATH 110, 140, 140A, 140B, or 140H')

#### Prerequisite

MATH 22 and MATH 26 or MATH 26 and satisfactory performance on the mathematics placement examination or MATH 40 or MATH 41 or satisfactory performance on the mathematics placement examination

#### MATH 140B Syllabi

#### Sample Problems

#### Sample Problem Answers

#### Course Description

MATH 141 is the second course in a two-or three-course calculus sequence for students in science, engineering and related fields.

Calculus is an important building block in the education of any professional who uses quantitative analysis. This course further introduces and develops the mathematical skills required for analyzing growth and change and creating mathematical models that replicate real-life phenomena. The goals of our calculus courses include to develop the students' knowledge of calculus techniques and to use the calculus environment to develop critical thinking and problem solving skills.

This course covers the following topics: logarithms, exponentials, and inverse trigonometric functions; applications of the definite integral and techniques of integration; sequences and series; power series and Taylor polynomials; parametric equations and polar functions.

An honors version of this course is offered at least once per year.

#### Prerequisite

MATH 140 or MATH 140A or MATH 140B or MATH 140E or MATH 140G or MATH 140H

#### MATH 141 Syllabi

#### Sample Problems

#### Sample Problem Answers

These are exams and solutions from the past 2 years. Warning: The schedule, content, and content focus for Fall 2023 do not necessarily match these, so you should not expect them to prepare you for any Fall 2023 exams. See your Canvas page for the Fall 2023 course materials.

#### Course Description

MATH 141B: Calculus and Biology II - 4 Credits. Techniques of integration and applications to biology; elementary matrix theory, limits of matrices, Markov chains, applications to biology and the natural sciences; elementary and separable differential equatios, linear rst-order differential equations, linear systems of differential equations, the Lotka-Volterra equations. Students may take only one course for credit from MATH 141, 141B, and 141H.

#### Prerequisite

MATH 140 or MATH 140A or MATH 140B or MATH 140E or MATH 140G or MATH 140H

#### Syllabus

#### Sample Problems

#### Sample Problem Answers

#### Course Description

Many problems we have to solve in day-to-day business, engineering, and science practice require the simultaneous study of several different but interrelated factors. Although problems of this form have been studied throughout the long history of mathematics, only in the early 20th century did the systematic approach we now refer to as linear algebra based on matrices emerge. Matrices and linear algebra are now recognized as the fundamental tool for foundational methods in statistics, optimization, quantum mechanics, and many other fields, and are an essential component of most subfields of mathematics. Linear algebra provides students their first introduction to the concept of dimension in an abstract setting where things with 4, 5, or even more dimensions are often encountered.

MATH 220 is a 2 credit course that teaches the core concepts of matrix arithmetic and linear algebra. It is a required course for many students majoring in engineering, science, or secondary education. In past coursework, students should have gained practice solving pairs of equations like 3 x + 4 y = 10, x - y = 1. This is a system of two linear equations with two unknowns and as a unique solution students can find by isolating and substituting. In linear algebra, this system is represented as A x = b, where x is a vector of unknowns, A is a matrix, and b is a vector of constants. Linear algebra is the field of mathematics that grew out of a need to solve systems like these and related problems with many unknown variables.

Topics covered in MATH 220 include matrix algebra, vectors, linear transformations, solution to systems of linear equations, determinants, matrix inverses, concepts of rank and dimension, eigenvalues, eigenvectors, and others as time permits. Course prerequisites can be filled by one semester of calculus. Students may take MATH 220 concurrently with MATH 141, MATH 230, or MATH 250. Students seeking a linear algebra course without a calculus prerequisite may consider MATH 38 as an alternative. After completing MATH 220, students can enroll in MATH 441 or MATH 484. MATH 441 provides more in-depth perspective on linear algebra. MATH 484 studies widely used applications of linear algebra to optimization problems.

An honors version of this course is offered at least once per year.

#### Prerequisite

MATH 110 or MATH 140 or MATH 140B or MATH 140E or MATH 140G or or MATH 140H

#### MATH 220 Syllabi

#### Sample Problems

#### Sample Problem Answers

#### Course Description

MATH 230 is the third and final course in the sequence of calculus courses. In the first year of their calculus studies, students learn concepts of differentiation and integration for functions with a single independent variable. MATH 230 is a course covering calculus computations involving 2 or more variables at the same time, a topic commonly called multivariable calculus. An intuitive and manipulative working knowledge of multivariable calculus is indispensable for electrostatics, fluid dynamics, solid mechanics, and many other fields of science and engineering that involve both space and time.

The differential calculus portion of the course includes the concepts of partial derivatives, gradients, divergence, and curl, multi-variable chain rule, coordinate system transformations, and differential equations, with applications to geometry and optimization. The integral calculus portion includes multiple integrals, line integrals and surface integrals, and generalizations of the fundamental theorem of calculus including Green's theorem, Stokes's theorem, and the divergence theorem.

This course is usually completed by students with majors in engineering programs, mathematics, sciences, and secondary education. MATH 230 is also offered as two 2-credit courses (MATH 231 and 232). Some students in certain science and engineering majors may be able to fulfill their major requirements with MATH 231 alone. On completing MATH 230, students may enroll in MATH 401, 405, 411, 412, and 421.

An honors version of this course is offered at least once per year.

#### Prerequisite

MATH 141 or MATH 141B or MATH 141E or MATH 141G or MATH 141H

#### MATH 230 Syllabi

#### Sample Problems

#### Sample Problem Answers

#### Course Description

MATH 231 covers only the differential calculus portion of MATH 230. Topics include partial derivatives, gradients, divergence, and curl, multi-variable chain rule, coordinate system transformations, and differential equations, with applications to geometry and optimization.

This course is completed by students in several programs in engineering, mathematics and the sciences and secondary education. For some programs, the integral portion of vector calculus is not required. For students in these programs, MATH 231 may be a more efficient alternative to MATH 230. Completion of MATH 231 and MATH 232 is equivalent to completion of MATH 230. On completing MATH 231, students may enroll in MATH 232, 401, 405, 411, 412.

An honors version of this course is offered at least once per year.

#### Prerequisite

MATH 141 or MATH 141B or MATH 141E or MATH 141G or MATH 141H

#### MATH 231 Syllabi

Sample Problems

#### Sample Problem Answers

#### Course Description

Multidimensional analytic geometry, double and triple integrals; potential fields; flux; Green's, divergence and Stokes' theorems. Students who have passed MATH 230 may not schedule this course for credit.

Enforced Prerequisite at Enrollment: MATH 231 or MATH 231H

#### Course Description

In calculus courses like MATH 140 and 141, students learn to calculate the derivative of a function and to use derivatives in simple applications. In MATH 250, students will learn how derivatives commonly appear in equations used to describe the world. Equations involving derivatives are called differential equations. Differential equations play an important role in modeling the real world. Newton's laws, Maxwell's laws of electromagnetism, Einstein's equations of general relativity, Euler and Bernoulli's beam equation, the Black-Scholes equation from finance, Perelson's viral-dynamics equations in biology, and the million-dollar Navier-Stokes equations are all differential equations used daily in their respective disciplines. Today, differential equations are one of the fundamental mathematical tools for the study of systems that change over time, and are used in most areas of science, engineering, and mathematics.

MATH 250 is an introductory course on ordinary differential equations. Ordinary differential equations are equations that involve derivative of a function with respect to only one variable. The goal of this course is to teach the students some of the elementary techniques in dealing with several fundamental types of equations. Some topics include linear equations involving only first and second derivatives, Laplace transforms, systems of linear equations involving only first derivatives, and phase-plane analysis.

This course is completed by many students with engineering, mathematics, sciences, and secondary education majors. Students needing a more complete introduction to differential equations should consider MATH 251, which is a 4-credit course covering all the material of MATH 250 plus an introduction to partial differential equations. Students who have passed MATH 251 may not schedule this course for credit. On completing MATH 250, students may enroll in MATH 405, 411, 412, 417, and 419.

#### Prerequisite

MATH 141 or MATH 141B or MATH 141E or MATH 141G or MATH 141H

#### MATH 250 Syllabi

#### Sample Problems

#### Sample Problem Answers

#### Course Description

In calculus courses like MATH 140 and 141, students learn to calculate the derivative of a function and to use derivatives in simple applications. In MATH 251, students will learn how derivatives commonly appear in equations used to describe the world. Equations involving derivatives are called differential equations. Differential equations play an important role in modeling the real world. Newton's laws, Maxwell's laws of electromagnetism, Einstein's equations of general relativity, Euler and Bernoulli's beam equation, the Black-Scholes equation from finance, Perelson's viral-dynamics equations in biology, and the million-dollar Navier-Stokes equations are all differential equations used daily in their respective disciplines. Today, differential equations are one of the fundamental mathematical tools for the study of systems that change over time, and are used in most areas of science, engineering, and mathematics.

MATH 251 is an introductory course on ordinary differential equations and partial differential equations. It is a 1-credit extension of MATH 250; this extra credit is used to allow the coverage of partial differential equations (which are not covered in MATH 250 because of time limitations). Partial differential equations are differential equations that involve derivatives with respect to more than one independent variable. Such equations are needed to understand phenomena like the vibration of a guitar string, the failure of an I-beam, and the diffusion of particles in fluid. The goal of this course is to teach the students some elementary techniques of ordinary and partial differential equations. Some of the topics covered in this course include first order ordinary differential equations, second order ordinary differential equations with constant coefficients, 2 × 2 linear systems with constant coefficients, stability of equilibrium solutions, Laplace transforms, Fourier series, partial differential equations which include the heat equation, wave equation and the Laplace equation.

MATH 251 fulfills all the differential equations training requirements fulfilled by MATH 250 and some majors require 251 in place of 250. On completing MATH 251, students may enroll in MATH 405, 411, 412, 417, and 419.

An honors version of this course is offered at least once per year.

#### Prerequisite

MATH 141 or MATH 141B or MATH 141E or MATH 141G or MATH 141H

#### MATH 251 Syllabi

#### Sample Problems

#### Sample Problem Answers

#### Course Descriptions

In MATH 252, students will learn how derivatives commonly appear in equations used to de-scribe the world. Equations involving derivatives are called differential equations and they play an important role in modeling the physical universe. Newton’s laws of motion, Maxwell’s laws of electromagnetism, Einstein’s equations of general relativity are all differential equations describing the rate that quantities change. Today, differential equations are one of the fundamental mathematical tools for the description of systems that change over time and are used in many areas of science, engineering, and mathematics.

MATH 252 is an introductory course on partial differential equations (abbreviated PDE’s)which involve derivatives with respect to more than one independent variable. Whereas ordinary differential equations use a single variable such as time, a PDE would include perhaps a time variable as well as a spatial variable. Such equations are needed to understand phenomena like the vibration of a guitar string in which different positions of the string move differently and therefore require multiple variables to describe the motion. The goal of this course is to teach students some elementary techniques for solving PDE’s, including such topics as the method of separation of variables, eigenvalue/eigenfunction computation, boundary value and initial value types, and decomposition of periodic functions into Fourier series. PDE’s studied include the wave equation, the heat equation, and Laplace’s equation. This course will also highlight the physical interpretation of the PDE and properties of solutions, which are meant to represent physical quantities.

Completing MATH 250 (a 3 credit class) and MATH 252 (a 1 credit class) is equivalent to completing MATH 251 (a 4 credit class), and after successful completion, students may enroll inMATH 405, 411, 412, 417, and 419. Class size, frequency of offering, and evaluation methods will vary by location and instructor. For these details check the specific course syllabus.