# Undergraduate Advising

## Course Transfer Information

To assist those who wish to transfer 1000- and 2000-level mathematics courses, we provide information about how each is taught by the Department of Mathematics at the University of South Florida.

### 1000-level

MAC 1105 — College Algebra

For the sake of transfer evaluation, the Department of Mathematics and Statistics at the University of South Florida provides the following historical information about this course.

- Course description (content and prerequisites)

### Course Format

The course follows the Math Emporium model: Students meet twice a week for 50-minute overview sessions and must spend 2 hours per week in the SMART Lab. Successful completion of the course merits 3 semester hours of credit and provides sufficient background for either Precalculus or non-trigonometric Calculus. There are four tests plus an optional final exam.

**Text:** *Precalculus: A Unit Circle Approach, *3rd Edition, by Ratti, McWaters, and Skrzypek

### COURSE CONTENT

**1. Graphs and Function**s (4 weeks)

1.1 Graphs of Equations

1.2 Lines

1.3 Functions

1.4 A Library of Functions

1.5 Transformations of Functions

1.6 Combining Functions; Composite Functions

1.7 Inverse Functions

**2. Polynomial and Rational Functions** (4 weeks)

2.1 Quadratic Functions

2.2 Polynomial Functions

2.3 Dividing Polynomials and the Rational Zeros Test

2.4 Rational Functions

2.5 Polynomial and Rational Inequalities

2.6 Zeros of a Polynomial Function (omit)

2.7 Variation

**3. Exponential and Logarithmic Functions** (4 weeks)

3.1 Exponential Functions

3.2 Logarithmic Functions

3.3 Rules of Logarithms

3.4 Exponential and Logarithmic Equations and Inequalities

3.5 Logarithmic Scales; Modeling (omit)

**7. Systems of Equations and Inequalities **(2 weeks)

7.1 Systems of Equations in Two Variables

7.2 Systems of Linear Equations in Three Variables (omit)

7.3 Systems of Inequalities

7.4 Matrices and Systems of Equations (omit)

7.5 Determinants and Cramer's Rule (omit)

7.6 Partial-Fraction Decomposition (omit)

7.7 Matrix Algebra (omit)

7.8 The Matrix Inverse (omit)

MAC 1147 — Precalculus Algebra and Trigonometry

For the sake of transfer evaluation, the Department of Mathematics and Statistics at the University of South Florida provides the following historical information about this course.

- Course description (content and prerequisites)

### Course Format

The course follows the Math Emporium model: Students meet twice a week for 75-minute lectures and must spend 2 hours per week in the SMART Lab. Successful completion of the course merits 4 semester hours of credit and provides sufficient background for the calculus sequences MAC 2281, 2282, 2283 and MAC 2311, 2312, 2313. There are four tests plus a final exam. The final exam is cumulative and all multiple choice.

**Text:** *Precalculus: A Unit Circle Approach*, 3rd Edition, by Ratti, McWaters, and Skrzypek

### COURSE CONTENT

**4. Trigonometric Functions** (2.5 weeks)

4.1 Angles and Their Measure

4.2 The Unit Circle: Trigonometric Functions of Real Numbers

4.3 Trigonometric Functions of Angles

4.4 Graphs of the Sine and Cosine Functions

4.5 Graphs of the Other Trigonometric Functions

4.6 Inverse Trigonometric Functions

**5. Analytic Trigonometry** (2 weeks)

5.1 Trigonometric Identities

5.2 Sum and Difference Formulas

5.3 Double-Angle and Half-Angle Formulas

5.4 Product-to-Sum and Sum-to-Product Formulas (omit)

5.5 Trigonometric Equations

**6. Applications of Trigonometric Functions** (2 weeks)

6.1 Right-Triangle Trigonometry

6.2 The Law of Sines

6.3 The Law of Cosines

6.4 Vectors (omit)

6.5 The Dot Product (omit)

6.6 Polar Coordinates

6.7 Polar Form of Complex Numbers: DeMoivre's Theorem (omit)

**7. Systems of Equations and Inequalities** (1 week)

7.1 Systems of Equations in Two Variables

7.2 Systems of Linear Equations in Three Variables

7.3 Systems of Inequalities (omit)

7.4 Matrices and Systems of Equations (omit)

7.5 Determinants and Cramer's Rule (omit)

7.6 Partial-Fraction Decomposition

7.7 Matrix Algebra (omit)

7.8 The Matrix Inverse (omit)

**8. Analytic Geometry** (1.5 weeks)

8.1 Conic Sections: Overview

8.2 The Parabola

8.3 The Ellipse

8.4 The Hyperbola

8.5 Rotation of Axes (omit)

8.6 Polar Equations of Conics (omit)

8.7 Parametric Equations (omit)

**9. Further Topics in Algebra** (2 weeks)

9.1 Sequences and Series

9.2 Arithmetic Sequences: Partial Sums

9.3 Geometric Sequences and Series

9.4 Mathematical Induction (omit)

9.5 The Binomial Theorem

9.6 Counting Principles (omit)

9.7 Probability (omit)

MGF 1106 — Finite Mathematics

For the sake of transfer evaluation, the Department of Mathematics and Statistics at the University of South Florida provides the following historical information about this course.

- Course description (content and prerequisites)

### Course Format

The course follows the Math Emporium model: Students meet twice a week for 50-minute lectures and must spend 2 hours per week in the SMART Lab. The course is intended for students who do not need to take calculus as part of their major degree program. The course fulfills 3 semester hours of the Gordon Rule Computation requirement, provided a grade of C-minus or better is achieved. There are four tests plus a final exam. The final exam is cumulative and all multiple choice.

**Text:** *Thinking Mathematically*, 7th Edition, by Blitzer

### COURSE CONTENT

**2. Set Theory** (3 weeks)

2.1 Basic Set Concepts

2.2 Subsets

2.3 Venn Diagrams and Set Operations

2.4 Set Operations and Venn Diagrams with Three Sets

2.5 Survey Problems

**3. Logic** (3 weeks)

3.1 Statements, Negations, and Quantified Statements

3.2 Compound Statements and Connectives

3.3 Truth Tables for Negation, Conjunction, and Disjunction

3.4 Truth Tables for the Conditional and the Biconditional

3.5 Equivalent Statements and Variations of Conditional Statements

3.6 Negations of Conditional Statements and De Morgan’s Laws

3.7 Arguments and Truth Tables (omit)

3.8 Arguments and Euler Diagrams (omit)

**11. Counting Methods and Probability Theory** (4 weeks)

11.1 The Fundamental Counting Principle

11.2 Permutations

11.3 Combinations

11.4 Fundamentals of Probability

11.5 Probability with the Fundamental Counting Principle, Permutations, and Combinations

11.6 Events Involving Not and Or; Odds

11.7 Events Involving And; Conditional Probability

11.8 Expected Value (omit)

**12. Statistics **(3 weeks)

12.1 Sampling, Frequency Distributions, and Graphs

12.2 Measures of Central Tendency

12.3 Measures of Dispersion

12.4 The Normal Distribution

12.5 Problem Solving with the Normal Distribution (if time permits)

12.6 Scatter Plots, Correlation, and Regression Lines (omit)

MGF 1107 — Mathematics For Liberal Arts

- Course description (content and prerequisites)

### Course Format

This course meets twice a week for 75-minute lecture sessions. The course is intended for students who do not need to take calculus as part of their major degree program. The course fulfills 3 semester hours of the Gordon Rule Computation requirement and also 3 hours of the General Education Quantitative Methods requirement, provided a grade of C-minus or better is achieved. There are typically four midterm exams plus an optional cumulative final exam.

**Text:** *Excursions in Modern Mathematics*, 9th Edition, by Tannenbaum

### COURSE CONTENT

**1 The Mathematics of Elections** (2-3 weeks)

1.1 The Basic Elements of an Election

1.2 The Plurality Method

1.3 The Borda Count Method

1.4 The Plurality-with-Elimination Method (Instant Runoff Voting)

1.5 The Method of Pairwise Comparisons

1.6 Fairness Criteria and Arrow's Impossibility Theorem

**4 The Mathematics of Apportionment **(2-3 weeks)

4.1 Apportionment Problems and Apportionment Methods

4.2 Hamilton's Method

4.3 Jefferson's Method

4.4 Adams's and Webster's Methods

4.5 The Huntington-Hill Method

4.6 The Quota Rule and Apportionment Paradoxes

**10 Financial Mathematics **(2-3 weeks)

10.1 Percentages

10.2 Simple Interest

10.3 Compound Interest

10.4 Retirement Savings

10.5 Consumer Debt

**13 Fibonacci Numbers and the Golden Ratio** (If time allows.)

13.1 Fibonacci Numbers

13.2 The Golden Ratio

13.3 Gnomons

13.4 Spiral Growth in Nature

**14 Censuses, Surveys, Polls, and Studies** (2 weeks)

14.1 Enumeration

14.2 Measurement

14.3 Cause and Effect

**15 Graphs, Charts, and Numbers** (1-2 weeks)

15.1 Graphs and Charts

15.2 Means, Medians, and Percentiles

15.3 Ranges and Standard Deviations

### Calculus and Differential Equations

MAC 2233 — Business Calculus

- Course description (content and prerequisites)

### Course Format

The course has two 75-minute auditorium lectures per week and a 50-minute peer-led guided-inquiry session on Friday. Successful completion of the course merits 3 semester hours of credit. The schedule outlined below allows time for four midterm exams plus a cumulative final exam, which are the norms for this course.

**Text: ***Calculus with Applications, Brief Version*, 11th Edition, by Lial, Greenwell & Ritchie

### COURSE CONTENT

Note: Review concepts will be covered throughout the course as needed.

**1. Linear Functions** (0.5 weeks)

1-1 Slopes and Equations of Lines

1-2 Linear Functions and Applications

1-3 The Least Squares Line (omit)

**2. Nonlinear Functions **(0.5 weeks)

2-1 Properties of Functions

2-2 Quadratic Functions: Translation and Reflection

2-3 Polynomial and Rational Functions

2-4 Exponential Functions

2-5 Logarithmic Functions

2-6 Applications: Growth and Decay; Mathematics of Finance

**3. The Derivative** (3 weeks)

3-1 Limits

3-2 Continuity

3-3 Rates of Change

3-4 Definition of the Derivative

3-5 Graphical Differentiation

**4. Calculating the Derivative **(3 weeks)

4-1 Techniques for Finding Derivatives

4-2 Derivatives of Products and Quotients

4-3 The Chain Rule

4-4 Derivatives of Exponential Functions

4-5 Derivatives of Logarithmic Functions

**5. Graphs and the Derivative** (2 weeks)

5-1 Increasing and Decreasing Functions

5-2 Relative Extrema

5-3 Higher Derivatives, Concavity, and the Second Derivative Test

5-4 Curve Sketching

**6. Applications of the Derivative** (3 weeks)

6-1 Absolute Extrema

6-2 Applications of Extrema

6-3 Further Business Applications: Economic Lot Size; Economic Order Quantity; Elasticity
of Demand

6-4 Implicit Differentiation

6-5 Related Rates

6-6 Differentials: Linear Approximation

**7. Integration** (2 weeks)

7-1 Antiderivatives

7-2 Substitution

7-3 Area and the Definite Integral

7-4 The Fundamental Theorem of Calculus

7-5 The Area Between Two Curves

7-6 Numerical Integration

**8. Further Techniques and Applications of Integration** (omit)

**9. Multivariable Calculus** (omit)

MAC 2241 — Life Sciences Calculus I

For the sake of course transfer evaluation, the Department of Mathematics and Statistics at the University of South Florida provides the following historical information about this course.

- Course description (content and prerequisites)

**Course Format**

The course has two different formats: daytime sections have two 75-minute auditorium lectures per week and one 50-minute help session; evening sections have two 75-minute lectures per week. Successful completion of the course merits 3 semester hours of credit. The schedule outlined below allows time for four midterm exams plus a cumulative final exam, which are the norms for this course.

**Text:** *Biocalculus: Calculus, Probability, and Statistics for the Life Sciences*, by Stewart and Day

### COURSE CONTENT

**Chapter 1. Functions and Sequences** (two weeks)

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

**Chapter 2. Limits** (two weeks)

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

**Chapter 3. Derivatives** (four weeks)

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

**Chapter 4. Applications of Derivatives** (three weeks)

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

**Chapter 5. Integrals** (two weeks)

5.1 Areas, Distances, and Pathogenesis

5.2 The Definite Integral

5.3 The Fundamental Theorem of Calculus

5.4 The Substitution Rule (if time permits)

5.5 Integration by Parts (if time permits)

5.6 Partial Fractions (omit)

5.7 Integration Using Tables and Computer Algebra Systems (omit)

5.8 Improper Integrals (omit)

MAC 2242 — Life Sciences Calculus II

For the sake of course transfer evaluation, the Department of Mathematics and Statistics at the University of South Florida provides the following historical information about this course.

- Course description (content and prerequisites)

**Course Format**

The course has two 75-minute auditorium lectures per week and a 50-minute peer-led guided-inquiry session on Friday. Successful completion of the course merits 3 semester hours of credit. The schedule outlined below allows time for four midterm exams plus a cumulative final exam, which are the norms for this course.

**Text: ***Biocalculus: Calculus, Probability, and Statistics for the Life Sciences*, by Stewart and Day

### COURSE CONTENT

**Chapter 3. Derivatives** (0.5 week)

3.8 Linear Approximations and Taylor Polynomials

**Chapter 5. Integrals** (2 weeks)

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

**Chapter 6. Applications of Integrals** (2 weeks)

6.1 Areas Between Curves

6.2 Average Values

6.3 Further Applications to Biology

6.4 Volumes

**Chapter 7. Differential Equations** (2 weeks)

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

**Chapter 8. Vectors and Matrix Models** (2.5 weeks)

8.1 Coordinate Systems

8.2 Vectors

8.3 The Dot Product

8.4 Matrix Algebra

8.5 Matrices and the Dynamics of Vectors

8.6 The Inverse and Determinant of a Matrix

8.7 Eigenvalues and Eigenvectors

8.8 Iterated Matrix Models

**Chapter 9. Multivariable Calculus** (2 weeks)

9.1 Functions of Several Variables

9.2 Partial Derivatives

9.3 Tangent Planes and Linear Approximations

9.4 The Chain Rule

9.5 Directional Derivatives and the Gradient Vector

9.6 Maximum and Minimum Values

**Chapter 10. Systems of Linear Differential Equations** (omit)

**Chapter 11. Descriptive Statistics** (omit)

**Chapter 12. Probability** (2 weeks)

12.1 Principles of Counting

12.2 What is Probability?

12.3 Conditional Probability

12.4 Discrete Random Variables

12.5 Continuous Random Variables

**Chapter 13. Inferential Statistics** (omit)

MAC 2281 — Engineering Calculus I

For the sake of course transfer evaluation, the Department of Mathematics and Statistics at the University of South Florida provides the following historical information about this course.

- Course description (content and prerequisites)

### Course Format

The course meets for approximately 55 hours during a 15-week semester. Successful completion of the course merits 4 semester hours of credit and provides sufficient background for either MAC 2282 (Engineering Calculus II) or MAC 2312 (Calculus II). The schedule outlined below allows time for four midterm exams plus a cumulative final exam, which are the norms for this course. (Note: A “lecture” is defined as a 50-minute time period.)

**Text:** *Essential Calculus: Early Transcendentals*, USF Custom Edition, by Stewart

**Alternate Text:** *Essential Calculus: Early Transcendentals,* 2nd Edition, by Stewart

### COURSE CONTENT

**1. Functions and Limits** (1 week)

1.1 Functions and Their Representations (review)

1.2 A Catalog of Essential Functions (review)

1.3 The Limit of a Function

1.4 Calculating Limits

1.5 Continuity

1.6 Limits Involving Infinity

Review

**2. Derivatives** (4 weeks)

2.1 Derivatives and Rates of Change

2.2 The Derivative as a Function

2.3 Basic Differentiation Formulas

2.4 The Product and Quotient Rules

2.5 The Chain Rule

2.6 Implicit Differentiation

2.7 Related Rates

2.8 Linear Approximations and Differentials

Review

**3. Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions** (1 week)

3.1 Exponential Functions (review)

3.2 Inverse Functions and Logarithms (review)

3.3 Derivatives of Logarithmic and Exponential Functions

3.4 Exponential Growth and Decay (omit)

3.5 Inverse Trigonometric Functions

3.6 Hyperbolic Functions

3.7 Indeterminate Forms and L'Hôpital's Rule

Review

**4. Applications of Differentiation** (3 weeks)

4.1 Maximum and Minimum Values

4.2 The Mean Value Theorem

4.3 Derivatives and the Shapes of Graphs

4.4 Curve Sketching (omit)

4.5 Optimization Problems

4.6 Newton's Method (omit)

4.7 Antiderivatives

Review

**5. Integrals** (2-3 weeks)

5.1 Areas and Distances

5.2 The Definite Integral

5.3 Evaluating Definite Integrals

5.4 The Fundamental Theorem of Calculus

Review

MAC 2282 — Engineering Calculus II

- Course description (content and prerequisites)

### Course Format

The course meets for approximately 55 hours during a 15-week semester. Successful completion of the course merits 4 semester hours of credit and provides sufficient background for either MAC 2283 (Engineering Calculus III) or MAC 2313 (Calculus III). The schedule outlined below allows time for four midterm exams plus a cumulative final exam, which are the norms for this course. (Note: A “lecture” is defined as a 50-minute time period.)

**Text:** *Essential Calculus: Early Transcendentals*, USF Custom Edition, by Stewart

**Alternate Text:** *Essential Calculus: Early Transcendentals*, 2nd Edition, by Stewart

### COURSE CONTENT

**5. Integrals** (1 week)

5.1 Areas and Distances (omit)

5.2 The Definite Integral (omit)

5.3 Evaluating Definite Integrals (omit)

5.4 The Fundamental Theorem of Calculus (review)

5.5 The Substitution Rule

Review

**6. Techniques of Integration** (3-4 weeks)

6.1 Integration by Parts

6.2 Trigonometric Integrals and Substitutions

6.3 Partial Fractions

6.4 Integration with Tables and Computer Algebra Systems

6.5 Approximate Integration

6.6 Improper Integrals

Review

7. Applications of Integration (3-4 weeks)

7.1 Areas between Curves

7.2 Volumes

7.3 Volumes by Cylindrical Shells

7.4 Arc Length

7.5 Area of a Surface of Revolution

7.6 Applications to Physics and Engineering (optional)

7.7 Differential Equations (omit)

Review

**8. Series** (6-7 weeks)

8.1 Sequences

8.2 Series

8.3 The Integral and Comparison Tests

8.4 Other Convergence Tests

8.5 Power Series

8.6 Representing Functions as Power Series

8.7 Taylor and Maclaurin Series

8.8 Applications of Taylor Polynomials

Review

MAC 2283 — Engineering Calculus III

- Course description (content and prerequisites)

### Course Format

The course meets for approximately 55 hours during a 15-week semester. Successful completion of the course merits 4 semester hours of credit. The schedule outlined below allows time for four midterm exams plus a cumulative final exam, which are the norms for this course. (Note: A “lecture” is defined as a 50-minute time period.)

**Text:** *Essential Calculus: Early Transcendentals*, USF Custom Edition, by Stewart

**Alternate Text:** *Essential Calculus: Early Transcendentals*, 2nd Edition, by Stewart

### COURSE CONTENT

**9. Parametric Equations and Polar Coordinates** (2 weeks)

9.1 Parametric Curves

9.2 Calculus with Parametric Curves

9.3 Polar Coordinates

9.4 Areas and Lengths in Polar Coordinates

9.5 Conic Sections in Polar Coordinates (omit)

Review

**10. Vectors and the Geometry of Space** (3-4 weeks)

10.1 Three-Dimensional Coordinate Systems

10.2 Vectors

10.3 The Dot Product

10.4 The Cross Product

10.5 Equations of Lines and Planes

10.6 Cylinders and Quadric Surfaces

10.7 Vector Functions and Space Curves

10.8 Arc Length and Curvature

10.9 Motion in Space: Velocity and Acceleration (optional)

Review

**11. Partial Derivatives** (3-4 weeks)

11.1 Functions of Several Variables

11.2 Limits and Continuity

11.3 Partial Derivatives

11.4 Tangent Planes and Linear Approximations

11.5 The Chain Rule

11.6 Directional Derivatives and the Gradient Vector

11.7 Maximum and Minimum Values

11.8 Lagrange Multipliers

Review

**12. Multiple Integrals** (3-4 weeks)

12.1 Double Integrals over Rectangles

12.2 Double Integrals over General Regions

12.3 Double Integrals in Polar Coordinates

12.4 Applications of Double Integrals

12.5 Triple Integrals

12.6 Triple Integrals in Cylindrical Coordinates (optional)

12.7 Triple Integrals in Spherical Coordinates (optional)

12.8 Change of Variables in Multiple Integrals (optional)

Review

**13. Vector Calculus** (2-3 weeks)

13.1 Vector Fields

13.2 Line Integrals

13.3 The Fundamental Theorem for Line Integrals

13.4 Green's Theorem (optional)

13.5 Curl and Divergence (optional)

13.6 Parametric Surfaces and Their Areas (optional)

13.7 Surface Integrals (optional)

13.8 Stokes' Theorem (optional)

13.9 The Divergence Theorem (optional)

Review

MAC 2311 — Calculus I

- Course description (content and prerequisites)

### Course Format

The course meets for approximately 55 hours during a 15-week semester. Successful completion of the course merits 4 semester hours of credit and provides sufficient background for either MAC 2312 (Calculus II) or MAC 2282 (Engineering Calculus II). The schedule outlined below allows time for four midterm exams plus a cumulative final exam, which are the norms for this course. (Note: A “lecture” is defined as a 50-minute time period.)

**Text:** * Essential Calculus: Early Transcendentals*, USF Custom Edition, by Stewart

**Alternate Text:** *Essential Calculus: Early Transcendentals*, 2nd Edition, by Stewart

COURSE CONTENT

**1. Functions and Limits** (1 week)

1.1 Functions and Their Representations (review)

1.2 A Catalog of Essential Functions (review)

1.3 The Limit of a Function

1.4 Calculating Limits

1.5 Continuity

1.6 Limits Involving Infinity

Review

**2. Derivatives** (4 weeks)

2.1 Derivatives and Rates of Change

2.2 The Derivative as a Function

2.3 Basic Differentiation Formulas

2.4 The Product and Quotient Rules

2.5 The Chain Rule

2.6 Implicit Differentiation

2.7 Related Rates

2.8 Linear Approximations and Differentials

Review

**3. Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions** (1 week)

3.1 Exponential Functions (review)

3.2 Inverse Functions and Logarithms (review)

3.3 Derivatives of Logarithmic and Exponential Functions

3.4 Exponential Growth and Decay (omit)

3.5 Inverse Trigonometric Functions

3.6 Hyperbolic Functions

3.7 Indeterminate Forms and L'Hôpital's Rule

Review

**4. Applications of Differentiation** (3 weeks)

4.1 Maximum and Minimum Values

4.2 The Mean Value Theorem

4.3 Derivatives and the Shapes of Graphs

4.4 Curve Sketching (omit)

4.5 Optimization Problems

4.6 Newton's Method (omit)

4.7 Antiderivatives

Review

**5. Integrals** (2-3 weeks)

5.1 Areas and Distances

5.2 The Definite Integral

5.3 Evaluating Definite Integrals

5.4 The Fundamental Theorem of Calculus

Review

MAC 2312 — Calculus II

- Course description (content and prerequisites)

### Course Format

The course meets for approximately 55 hours during a 15-week semester. Successful completion of the course merits 4 semester hours of credit and provides sufficient background for either MAC 2313 (Calculus III) or MAC 2283 (Engineering Calculus III). The schedule outlined below allows time for four midterm exams plus a cumulative final exam, which are the norms for this course. (Note: A “lecture” is defined as a 50-minute time period.)

** Text:** *Essential Calculus: Early Transcendentals*, USF Custom Edition, by Stewart

**Alternate Text:** *Essential Calculus: Early Transcendentals*, 2nd Edition, by Stewart

COURSE CONTENT

**5. Integrals** (1 week)

5.1 Areas and Distances (omit)

5.2 The Definite Integral (omit)

5.3 Evaluating Definite Integrals (omit)

5.4 The Fundamental Theorem of Calculus (review)

5.5 The Substitution Rule

Review

**6. Techniques of Integration** (3-4 weeks)

6.1 Integration by Parts

6.2 Trigonometric Integrals and Substitutions

6.3 Partial Fractions

6.4 Integration with Tables and Computer Algebra Systems

6.5 Approximate Integration

6.6 Improper Integrals

Review

**7. Applications of Integration** (3-4 weeks)

7.1 Areas between Curves

7.2 Volumes

7.3 Volumes by Cylindrical Shells

7.4 Arc Length

7.5 Area of a Surface of Revolution

7.6 Applications to Physics and Engineering (optional)

7.7 Differential Equations (omit)

Review

**8. Series** (6-7 weeks)

8.1 Sequences

8.2 Series

8.3 The Integral and Comparison Tests

8.4 Other Convergence Tests

8.5 Power Series

8.6 Representing Functions as Power Series

8.7 Taylor and Maclaurin Series

8.8 Applications of Taylor Polynomials

Review

MAC 2313 — Calculus III

- Course description (content and prerequisites)

### Course Format

The course meets for approximately 55 hours during a 15-week semester. Successful completion of the course merits 4 semester hours of credit. The schedule outlined below allows time for four midterm exams plus a cumulative final exam, which are the norms for this course. (Note: A “lecture” is defined as a 50-minute time period.)

**Text:** *Essential Calculus: Early Transcendentals*, USF Custom Edition, by Stewart

**Alternate Text:** *Essential Calculus: Early Transcendentals*, 2nd Edition, by Stewart

### COURSE CONTENT

**9. Parametric Equations and Polar Coordinates** (2 weeks)

9.1 Parametric Curves

9.2 Calculus with Parametric Curves

9.3 Polar Coordinates

9.4 Areas and Lengths in Polar Coordinates

9.5 Conic Sections in Polar Coordinates (omit)

Review

**10. Vectors and the Geometry of Space** (3-4 weeks)

10.1 Three-Dimensional Coordinate Systems

10.2 Vectors

10.3 The Dot Product

10.4 The Cross Product

10.5 Equations of Lines and Planes

10.6 Cylinders and Quadric Surfaces

10.7 Vector Functions and Space Curves

10.8 Arc Length and Curvature

10.9 Motion in Space: Velocity and Acceleration (optional)

Review

**11. Partial Derivatives** (3-4 weeks)

11.1 Functions of Several Variables

11.2 Limits and Continuity

11.3 Partial Derivatives

11.4 Tangent Planes and Linear Approximations

11.5 The Chain Rule

11.6 Directional Derivatives and the Gradient Vector

11.7 Maximum and Minimum Values

11.8 Lagrange Multipliers

Review

**12. Multiple Integrals** (3-4 weeks)

12.1 Double Integrals over Rectangles

12.2 Double Integrals over General Regions

12.3 Double Integrals in Polar Coordinates

12.4 Applications of Double Integrals

12.5 Triple Integrals

12.6 Triple Integrals in Cylindrical Coordinates (optional)

12.7 Triple Integrals in Spherical Coordinates (optional)

12.8 Change of Variables in Multiple Integrals (optional)

Review

**13. Vector Calculus** (2-3 weeks)

13.1 Vector Fields

13.2 Line Integrals

13.3 The Fundamental Theorem for Line Integrals

13.4 Green's Theorem (optional)

13.5 Curl and Divergence (optional)

13.6 Parametric Surfaces and Their Areas (optional)

13.7 Surface Integrals (optional)

13.8 Stokes' Theorem (optional)

13.9 The Divergence Theorem (optional)

Review

MAP 2302 — Differential Equations

- Course description (content and prerequisites)

### Course Format

The course meets for approximately 45 hours during a 15-week semester. Successful completion of the course merits 3 semester hours of credit. The schedule outlined below allows time for three midterm exams plus a cumulative final exam, which are the norms for this course.

**Text: *** Fundamentals of Differential Equations*, 9th Edition, by Nagle, Saff, and Snider

COURSE CONTENT

**1. Introduction** (1 week)

1.1 Background

1.2 Solutions and Initial Value Problems

1.3 Direction Fields (optional)

1.4 The Approximation Method of Euler (omit)

**2. First Order Differential Equations** (2-3 weeks)

2.1 Introduction: Motion of a Falling Body

2.2 Separable Equations

2.3 Linear Equations

2.4 Exact Equations

2.5 Special Integrating Factors

2.6 Substitutions and Transformations

**3. Mathematical Models and Numerical Methods Involving First Order Equations** (1 week)

3.1 Mathematical Modeling

3.2 Compartmental Analysis

3.3 Heating and Cooling of Buildings

3.4 Newtonian Mechanics

3.5 Electrical Circuits (omit)

3.6 Numerical Methods: A Closer Look At Euler's Algorithm (omit)

3.7 Higher-Order Numerical Methods: Taylor and Runge-Kutta (omit)

**4. Linear Second Order Equations** (3-4 weeks)

4.1 Introduction: The Mass-Spring Oscillator

4.2 Homogeneous Linear Equations: The General Solution

4.3 Auxiliary Equations with Complex Roots

4.4 Nonhomogeneous Equations: The Method of Undetermined Coefficients

4.5 The Superposition Principle and Undetermined Coefficients Revisited

4.6 Variation of Parameters

4.7 Variable-Coefficient Equations (omit)

4.8 Qualitative Considerations for Variable-Coefficient and Nonlinear Equations

4.9 A Closer Look at Free Mechanical Vibrations

4.10 A Closer Look at Forced Mechanical Vibrations

**5. Introduction to Systems and Phase Plane Analysis** (omit)

5.1 Interconnected Fluid Tanks

5.2 Differential Operators and the Elimination Method for Systems

5.3 Solving Systems and Higher-Order Equations Numerically

5.4 Introduction to the Phase Plane

5.5 Applications to Biomathematics: Epidemic and Tumor Growth Models

5.6 Coupled Mass-Spring Systems

5.7 Electrical Systems

5.8 Dynamical Systems, Poincaré Maps, and Chaos

**6. Theory of Higher-Order Linear Differential Equations** (1-2 weeks)

6.1 Basic Theory of Linear Differential Equations

6.2 Homogeneous Linear Equations with Constant Coefficients

6.3 Undetermined Coefficients and the Annihilator Method

6.4 Method of Variation of Parameters

**7. Laplace Transforms** (2-3 weeks)

7.1 Introduction: A Mixing Problem

7.2 Definition of the Laplace Transform

7.3 Properties of the Laplace Transform

7.4 Inverse Laplace Transform

7.5 Solving Initial Value Problems

7.6 Transforms of Discontinuous Functions

7.7 Transforms of Periodic and Power Functions

7.8 Convolution

7.9 Impulses and the Dirac Delta Function (omit)

7.10 Solving Linear Systems with Laplace Transforms (omit)

**8. Series Solutions of Differential Equations** (1-2 weeks)

8.1 Introduction: The Taylor Polynomial Approximation

8.2 Power Series and Analytic Functions

8.3 Power Series Solutions to Linear Differential Equations

8.4 Equations with Analytic Coefficients

8.5 Cauchy-Euler (Equidimensional) Equations

8.6 Method of Frobenius

8.7 Finding a Second Linearly Independent Solution (omit)

8.8 Special Functions (omit)

**9. Matrix Methods for Linear Systems** (1-2 weeks)

9.1 Introduction

9.2 Review 1: Linear Algebraic Equations

9.3 Review 2: Matrices and Vectors

9.4 Linear Systems in Normal Form

9.5 Homogeneous Linear Systems with Constant Coefficients

9.6 Complex Eigenvalues (omit)

9.7 Nonhomogeneous Linear Systems (omit)

9.8 The Matrix Exponential Function (omit)

**10. Partial Differential Equations** (omit)

### Statistics

STA 2023 — Introductory Statistics I

- Course description (content and prerequisites)

### Course Format

This course meets twice a week for 75-minute lecture sessions and once a week for a 50-minute help session. The schedule outlined below allows time for three midterm exams and a cumulative final exam, which are the norms for this course.

**Text:** *Elementary Statistics: Picturing the World*, 6th Edition, by Larson and Farber

### COURSE CONTENT

#### PART ONE. DESCRIPTIVE STATISTICS

**1. Introduction to Statistics** (1 week)

1.1. An Overview of Statistics

1.2. Data Classification

1.3. Data Collection and Experimental Design

**2. Descriptive Statistics** (2 weeks)

2.1. Frequency Distributions and Their Graphs

2.2. More Graphs and Displays

2.3. Measures of Central Tendency

2.4. Measures of Variation

2.5. Measures of Position

#### PART TWO. PROBABILITY & PROBABILITY DISTRIBUTIONS

**3. Probability** (2 weeks)

3.1. Basic Concepts of Probability and Counting

3.2. Conditional Probability and the Multiplication Rule

3.3. The Addition Rule

3.4. Additional Topics in Probability and Counting (optional)

**4. Discrete Probability Distributions** (2 weeks)

4.1. Probability Distributions

4.2. Binomial Distributions

4.3. More Discrete Probability Distributions

**5. Normal Probability Distributions** (2 weeks)

5.1. Introduction to Normal Distributions and the Standard Normal Distribution

5.2. Normal Distributions: Finding Probabilities

5.3. Normal Distributions: Finding Values

5.4. Sampling Distributions and the Central Limit Theorem

5.5. Normal Approximations to Binomial Distributions

#### PART THREE. STATISTICAL INFERENCE

**6. Confidence Intervals** (2 weeks)

6.1. Confidence Intervals for the Mean (σ Known)

6.2. Confidence Intervals for the Mean (σ Unknown)

6.3. Confidence Intervals for Population Proportions

6.4. Confidence Intervals for Variance and Standard Deviation (omit)

**7. Hypothesis Testing with One Sample** (2 weeks)

7.1. Introduction to Hypothesis Testing

7.2. Hypothesis Testing for the Mean (σ Known)

7.3. Hypothesis Testing for the Mean (σ Unknown)

7.4. Hypothesis Testing for Proportions

7.5. Hypothesis Testing for Variance and Standard Deviation (omit)