The Center of Academic Progress (CPU, Centro de Progreso Universitario) was established in 2002 as part of the activities related to the Title V project, which ended in 2006. After this time period, the Center became part of the institutional commitment to support students and was appointed to the Office of the Dean of Arts and Sciences. Thanks to this effort, the Center still continues to offer academic support services to our students during their first years of college (first 72 credits).

The Center of Academic Progress works in coordination with the academic departments and the Dean of Arts and Sciences, as well as with counselors and subject coordinators, who serve as links between tutors and professors. Students who attend regularly will be evaluated based on modern educational methods, and will also be granted honor points that will be added to their grade in the course, according to the standards of each teacher (see additional information).

The CPU uses different methods to provide tutoring. Students receive the service in small groups where, in addition to getting their questions answered, they learn to develop and strengthen their teamwork skills, among other benefits. Tutoring services are offered in the fields of Mathematics, Spanish, English, Physics, and some Engineering classes as such as Statics, Computers, etc. These services are provided pending the availability of tutors.

The page for the Center of Academic Progress (CPU) is designed for its use by PUPR students. You will be able to view modules on course topics that will help you as a refresher; plus there are reviews classified by subject and links to tutoring services by other institutions. You can visit our subject index and use the review modules, which are listed by subject and are also linked under the syllabus for the the selected course.

We are located on the 3rd floor of Building M, Polytechnic University of Puerto Rico, Hato Rey, PR. Our tutoring service hours are Monday through Thursday, from 7:00am to 8:30pm; and Friday, from 8:00am to 3:00pm. Our office hours are Monday through Thursday, from 8:00am to 5:00pm; and Friday, from 8:00am to 3:00pm. You may call us at (787) 622 -8000 ext. 274, 331, visit us in office M – 305, or e-mail us at milmartinez@pupr.edu.

Sincerely,

Dra. Milagros Martinez-Roche, Director

**Center of Academic Progress**

The CPU is a tutoring program geared towards a constant search for alternative instructional support to adequately meet the changing needs of the student population of the Polytechnic University of Puerto Rico.

To ensure that tutoring services include educational strategies that will contribute to:

- strengthening metacognitive skills
- developing student creativity
- promoting a sense of institutional belonging, and
- improving upon their teamwork skills.

To adhere to a philosophy of constant self-assessment for the following components:

- the CPU as a student services organization
- strategies for retention and promotion
- assessment of strategies or work plans
- evaluation of rates of effectiveness for tutors.

Maximize CPU staff performance through training programs (office staff, tutors and tutor students) that includes the following topics:

- teamwork
- student retention
- educational strategies in tutoring
- case management and procedures
- data entry to the computer system
- specific topics of specialized and technological content, mainly for tutors and tutor students, etc.

The CPU is committed to the comprehensive development of future professionals educated at the Polytechnic University of Puerto Rico.

** Dr. Milagros Martínez-Roche **

Director

** Miss. Ketsy Lugo **

Administrative Assistant

Mathematics

** Prof. Bienvenido Rafael Leo Ramírez **

Math Tutor

** Prof. Intriago Carolina Serrano **

Math Tutor

** Prof. Ismael De la Rosa Maldonado **

Math Tutor

** Erik Collazo Guerrero **

Math Tutor

** Julián Fletcher Ortiz **

Math Tutor

** Roberto Ruiz Domenech **

Math Tutor – Night Sessions

** Marcos Santana Francisco **

STEM Tutor

Spanish

** Elizabeth Urbina **

Spanish Tutor

** Joselyn Ramírez Maldonado **

Spanish Tutor

English

** María R. Iglesias Carrasquillo **

English Tutor

** Andrinés González Rivera **

English Tutor

** Oscaralexis Rodríguez Justiniano **

Language Lab Technician

Physics

** Rafael López González **

Physics Tutor

The CPU uses various methodologies to offer tutoring services to PUPR students. There are tutoring services on the subjects of Mathematics, Spanish, English, Physics, and some Engineering classes, such as Statics, Dynamics, and Computers, among others. These services are provided pending the availability of tutors.

These services are offered to students assembled in small groups where, in addition to having their questions answered, they learn to develop and strengthen their teamwork skills, among other benefits.

- Be a regular PUPR student
- Be registered in one or more of the courses for which we offer tutoring services.
- Get formally registered for tutoring services during the enrollment period. (Enrollment periods are announced at the beginning of each quarter.)

- Visit office M – 305 during the enrollment period, which is determined at the beginning of each quarter.
- Fill out an application for registration for each tutoring service you want to receive.
- You must fully complete your application.
- Bring your properly authorized official PUPR registration.
- Submit your completed application so we can register your enrollment in our database.
- Once you have formally registered, you may begin receiving our services.

Registration Form for Tutoring Services

Request Form for Tutoring Services

You may receive honor points for regularly attending your tutoring services, at the discretion of your course professor. These points may be added as a bonus to your class grade. Allocation of points may vary according to the subject and criteria established by the professor.

- Points are awarded by combining two criteria: attendance and academic achievement.
- You must be officially registered in the tutoring service.
- You must have attended your tutoring services more than six times.
- You must exhibit satisfactory performance in your tutoring sessions. (Demonstrate academic achievement.)
- The tutor will send a score report to your professor.
- The professor will determine how to allocate the points.

Registration Form for Tutoring Services

Request Form for Tutoring Services Registration Calendar WI-13

In this segment you will find information divided by subjects according to your course of interest. Select the course for which you want information.

MATH0102 Preparatory Math

Appendix – Strategies for Learning

Part I:

- Adding Integers
- Subtracting Integers
- Multiplying Integers
- Dividing Integers
- Laws of Exponents
- Order of Operations

Part II:

- Fractions
- Multiplying Fractions
- Dividing Fractions
- Adding and Subtracting Fractions
- Adding, Subtracting, Multiplying and Dividing Mixed Fractions

Part III:

- Geometry
- Decimals
- Adding and Subtracting Decimals
- Multiplying Decimals
- Dividing Decimals
- Square Roots
- Fractions, Decimals and Percentages
- Percentage Cases
- Percentage Exercises

Part IV:

- Plane Geometry Figures
- Right Triangle and Pythagorean Theorem
- Polygon Perimeter and Area
- Circles: Area and Circumference
- Surface Area and Volume
- Parallel Lines and Angles

New Topic: Scientific Notation

Study Guides assigned by Dr. Capella:

MATH0106 Basic Algebra

Part I:

- Translation of Algebra Expressions
- Simplification and Evaluation of Algebra Expressions
- Solving Equations
- Formulas
- Strategies to Solve Math Word Problems
- Solving Applied Math World Problems
- Natural Exponents
- Zero Exponents and Negative Integers
- Rational Exponents

Part II:

- Polynomials
- Adding and Subtracting Polynomials
- Multiplying Polynomials
- Dividing Polynomials by Monomials
- Dividing Polynomials by Polynomials
- Factoring by Common Factors and Grouping
- Factoring Trinomials (x2+bx+c)
- Factoring Trinomials (ax2+bx+c)

Part III:

- Special Factoring and Factoring Strategies
- Simplifying Rational Expressions
- Multiplying and Dividing Rational Expressions
- Adding and Subtracting Rational Expressions
- Complex Fractions
- Rational Equations (Problem Solutions)

Part IV:

- Other Radicals with Variables
- Simplfying Radical Expressions
- Adding and Subtracting Radical Expressions
- Multiplying and Dividing Radical Expressions
- Solving Radical Equations

New Topic:

MATH0110 Intermediate Algebra

Part I:

- Absolute Value Equations
- Quadratic Equations, Applications
- Linear Inequalities
- Absolute Value Inequalities
- Non-linear Inequalities

Part II:

- Rectangular Coordinates
- Distance and Midpoint
- Straight Lines: Inclination, Intersection, Equation, Parallel and Perpendicular Lines, Graphs
- Graphs for Linear, Quadratic, Absolute Value and Other Equations
- Circle

Part III:

Part IV:

- Function Properties: Increasing, Decreasing, Even and Odd, Positive, Negative
- Graph Transformations and Symmetry
- Inverse Functions
- Quadratic Functions f(x) = a(x-h)^2 + k
- Graphs and Transformations

MATH1330 Precalculus I

Part I:

- Review of previous knowledge
- Polynomial Functions
- Rational Functions
- Polynomial Division; Synthetic Division
- Real Zeros in a Polynomial Functions
- Complex Numbers; Quadratic Equations with Negative Discriminants
- Complex Zeros: Algebra Fundamental Theorem
- Practice for Part I

Part II:

- Angles and their Measurements
- Trigonometric Functions: Focus on the Unit Circle
- Properties of Trigonometric Functions
- Trigonometry of the Right Triangle
- Function Graphs: Sine and Cosine
- Function Graphs: Tangent, Cotangent, Cosecant and Secant
- Sinusoidal Graphs
- Practice for Part II

Part III:

- Trigonometric Identities
- Formula for Angle Sum and Differences
- Double-Angle and Half-Angle Formulas
- Inverse Trigonometric Formulas; Sine, Cosine and Tangent
- Trigonometric Equations
- Trigonometry of Right Angle
- Law of Sines
- Law of Cosines
- Practice for Part III
- Practice for Part I, II and III

MATH1340 Precalculus II

Part I:

- Introduction to the Course, Review
- Polar Coordinates
- Polar Equations and their Graphs
- Complex Numbers
- Vectors, Dot Product
- Practice for Part I

Part II:

- Exponential Functions
- Logarithmic Functions
- Logarithmic Properties
- Exponential and Logarithmic Equations
- Applications
- Practice for Part II

Part III:

- Conic Sections
- Parabola
- Ellipses
- Hyperbola
- Systems of Linear Equations
- Matrices
- Determinants
- Matrix Algebra
- Partial Factions
- Practice for Part III
- Practice for Part I, II and III

MATH2310 Calculus I

Part I:

- Introduction to the Course
- Find Numerical and Graph Limits
- Analytical Evaluation of Limits
- Continuity and Limits on One Side
- Infinte Limits
- Limits in the Infinite
- Derivatives and the Problem of Tangent Lines
- Basic Rules for Differentiation and Rates of Change
- Rules for Product and Quotient and Higher Order Derivatives
- Practice for Part I

Part II:

- Rules for Chains
- Implicit Differentiation
- Related Rates
- Extreme Values in an Interval
- Increasing and Decreasing Functions and First Derivative Test
- Concavity and Second Derivative Test
- Practice for Part II

Part III:

- Summary for Drawing Graphs
- Optimization Exercises
- Antiderivatives and Indefinite Integrals
- Properties of Definite Integrals
- Calculus Fundamental Theorem
- Integration by Substitution
- Natural Logarithm Function and Integration
- Exponential Functions: Differentiation and Integration
- Other Exponential Functions: Differentiation and Integration
- Practice for Part III
- Practice for Part I, II and III

MATH2320 Calculus II

Part I:

- Introduction to the Course
- Differentiation of Inverse Trigonometric Functions
- Inverse Trigonometric Functions: Integration
- Hyperbolic Functions
- Area Between Curves
- Volumes of Solids of Revolution: Discs and Rings
- Volumes of Solids of Revolution: Cylindrical Shells
- Practice for Part I

Part II:

- Surface Area and Arc Length of Solids of Revolution
- Moments and Center of Mass
- Integration by Parts
- Trigonometric Substitutions
- Partial Factions
- Indeterminate Forms and L’Hopital’s Rule
- Improper Integrals
- Practice for Part II

Part III:

- Plane Curves and Parametric Equations
- Calculus and Parametric Equations
- Coordinates and Polar Graphs
- Polar Equations for Conic Sections
- Integrals in Polar Coordinates: Area Between Curves, Arc Length and Surface Area
- Practice for Part III
- Practice for Part I, II and III

MATH2330 Calculus III

Part I:

- Successions
- Series and Convergence
- Integral Test and p-Series
- Series Comparison
- Series Alternantes, Absolute and Conditional Convergence
- Ratio and Root Test for Series of Nonnegative Terms
- Polynomials and Taylor Series Approximation
- Practice for Part I

Part II:

- Power Series
- Operations with Power Series
- Taylor and Maclaurin Series
- Vectors in the Plane
- Vectors in Space
- Dot Product of Two Vectors and its Applications
- Cross Product of Two Vectors in Space
- Lineas and Planes in Space
- Practice for Part II

Part III:

- Surfaces in Space
- Cylindrical and Spherical Coordinates
- Vector Functions Limits and Continuity
- Differentiation and Integration of Vector Functions
- Velocity and Accelerotion, Projectile Motion
- Tangent and Unit Normal Vectors
- Arc Length and Curvature
- Practice for Part I, II and III

MATH3310 Differential Equations

Part I:

- Definition & Terminology
- Initial – Value Problems
- Differential Equations of Order One
- Separable Equations
- Linear Equations
- Exact Differential Equations
- Solutions by Substitutions

- Modeling With First-Order Differential Models
- Differential Equations as Mathematical Models
- Linear Equation, Non Linear Equations

- Practice for Part I

Part II:

- Higher – Order Differential Equations
- Preliminary Theory: Linear Equations
- Reduction of Order
- Homogeneous Linear Equations With Constant Coefficients
- Undetermined Coefficients Superposition Approach
- Undetermined Coefficients Annihilator Approach
- Variation of Parameters
- Cauchy-Euler Equation

- Practice for Part II

Part III:

- Modeling With Higher-Order Differential Equations
- Linear Equations: Initial-Value Problems
- Linear Equations: Boundary-Value Problems

- Laplace Transform
- Definition
- Inverse Transforms & Derivatives Transforms
- Translation Theorems
- Additional Properties

- Practice for Part III
- Practice for Part I, II and III

MATH3320 Linear Algebra

Part I:

- Introduction to Systems Of Linear Equations
- Gaussian Elimination and Gauss-Jordan Eliminations
- Applications of Systems of Linear Equations
- Operations with Matrices
- Properties of Matrix Operations
- The Inverse of a Matrix
- Elementary Matrices
- The Determinant of a Matrix
- Evaluation of a Determinant Using Elementary Operations
- Properties of Determinants
- Application of Determinants
- Practice for Part I

Part II:

- Vectors in R n
- Vector Spaces
- Subspaces de Spaces Vectorials
- Spanning Sets and Linear Independence
- Basic And Dimension
- Bank of a Matrix and System of Linear Equations
- Coordinates and Change of Basic
- Length and Dot Product in Rn Orthonormal Base: Gram-Schmidt Process
- Practice for Part II

Part III:

- Introduction to Linear Transformation
- The Kernel and Range of a Linear Transformation
- Matrices for Linear Transformations
- Transition Matrices and Similarity
- Eigen Values and Eigen Vectors
- Practice for Part III

MATH1310 Math for Business Administration I

Part I:

- Introduction to the Course
- Functions, Linear Functions
- Function Graphs, Linear Equation Systems, Applications for Functions
- Quadratic Equations, Quadratic Functions, Applications for Quadratic Functions
- Special Functions
- Practice for Part I

Part II:

- Matrices, Multiplication of Matrices, Gauss-Jordan Method
- Matrix Inverse
- Linear Inequalities in a Variable
- Linear Inequalities in Two Variables
- Linear Programming, Graphical Method
- Simplex Method Maximizing
- Simplex Method Duality and Minimization
- Simplex Method with Mixed Constraints
- Practice for Part II

Part III:

- Exponential Function
- Logarithmic Function
- Exponential and Logarithmic Equations
- Simple Interest and Sequences
- Compound Interest, Geometric Sequences
- Future Value of an Annuity
- Present Value of an Annuity
- Amortization
- Practice for Part III
- Practice for Part I, II and III

MATH1310 Math for Business Administration II

Part I:

- Introduction to the Course
- Probability
- Union and Intersection of Events
- Conditional Probability
- Probability Trees and Bayes’ Formula
- Counting, Permutations and Combinations
- Permutations, Combinations and Probability
- Probability, and Binomial Experiments
- Discrete Probability Distribution
- Binomial Distribution
- Descriptive Statistics
- Normal Distribution
- Practice for Part I

Part II:

- Limits
- Continuous Functions
- Derivatives, Rate of Change and Tangent to a Curve
- Derivative Formula
- Product and Quotient Rule
- Chain and Power Rule
- Use of Derivative Formula
- Higher Order Derivative
- Applications in Management and Economy
- Practice for Part II

Part III:

- Relative Maxium and Minimum: Graphs of Concave Curves, Inflection Points
- Optimization in Management and Economy
- Derivatives of Logarithmic Functions
- Derivatives of Exponential Functions
- Indefinite Integral
- The Power Rule
- Integrals of Logarithmic and Exponential Functions
- Area Under a Curve
- Definite Integral; Algebra Fundamental Theorem
- Area Between Two Curves
- Practice for Part III
- Practice for Part I, II and III

ENGI2110 Statics

Part I:

- General Principles. Mechanics. Newton’s Three Laws of Motion. Newton’s Law of Gravity
- Force Vectors. Scalar and Vectors. Vector Operations. Vector Addition. Additions of a System of Coplanar Forces. Cartesian Vectors. Addition and Subtraction
- Position Vectors. Force Vector Directed Along a Line. Dot Product
- Equilibrium of a Particle. Free Body Diagram. Coplanar Force Systems.
- Force System Resultant. Moment of a Force. – Scalar Formulation. Cross Product. Moment of a Force – Vector Formulation.
- Moment of a Force About a Specified Axis. Couples
- Equivalent System. Reduction of a Force and Couple System Distributed Loading.
- Practice Part I

Part II:

- Equilibrium of a Rigid Body. Equilibrium in two Dimensions. Free Body Diagram. Equations of Equilibrium. Two and three-force members.
- Equilibrium in Three Dimensions. Freee Body Diagrams. Equations of Equilibrium
- Structural Analysis of Simple Trusses
- Method of Joints and Method of Sections
- Frames and Machines
- Practice Part II

Part III:

- Center of Gravity. Centroid and Center of Mass. Composite Bodies.
- Moments of Inertia. Parallel-Axis Theorem. Moment of Inertia for Composite Areas
- Internal Forces. Internal Forces Developed in Structural Members.
- Shear and Moment Equations And Diagrams
- Relations between Distributed Load, Shear and Moment
- Friction

In this section, you will find information by general topics on English. Click on the topic or the Word or Acrobat icons.

**Exponential and Logarithmic Functions**

You will learn to change exponential expressions into logarithmic expressions and viceversa, and to use logarithmic properties.

**Trigonometric Identities**

You will learn basic trigonometric identities and problems proposed for their development.

**Word Problems**

You will strengthen your skills to analyze, interpret and solve math word problems. It contains some suggested exercises.

**Limits, Graphic Focus**

Methodology to solve limit problems, contains examples and suggested exercises.

**Technological Tools**

The objective is to demonstrate, provide and explain the use of some of the available technological tools to be used in the creation of future workshops and/or learning modules.

**Solutions for Problems**

Solving word problems is one of the most commonplace difficulties for students in courses that include math and/or physics knowledge.

**Synthetic Division**

Solution of a Polynomial Division (long division and shortcut).

**Strategies to Solve Word Problems**

An explanation of the process to solve math problems.

**Elementary Theory of Groups**

Review on the concept of groups.

**Graph Interpretation**

Review on Graphs.

**Mean, Median and Mode **

Review on Statistics.

Khan Academy Paul’s Online Math Notes COW – Calculus on the Web

In this segment you will find information divided by subjects according to your course of interest. Select the course about which you want information.

SPAN 0100 Español Preparatorio

I. Palabras variables e invariables de la oración

II. División silábica y acentuación

- Reglas de la división silábica
- Hiato
- Diptongo
- Triptongo

- Acentuación

- Prosódica
- Ortográfica
- Diacrítica

III. Ortografía dudosa

- Uso de la
- B y V
- C, Z y S
- G y J
- H
- Y y Ll
- R y RR

- Homógrafos, homófonos y parónimos

IV. Ortografía y redacción

- Letras mayúsculas
- Signos de puntuación

SPAN 0110 Gramática

Parte I:

El Lenguaje como sistema

- Lectura y comprensión del texto literario
- Nociones generales de la Lingüistica
- definiciones
- lenguaje
- monema, semantema, lexema
- fonema
- fengua/idioma
- jerga
- coloquio
- dialecto
- creación de palabras
- derivación
- composición
- parasíntesis
- préstamo
- lenguaje como sistema
- estructuralismo
- significado/significante
- habla, lengua, norma

- Práctica de la parte I

Parte II:

La oración

- Lectura y comprensión del texto literario
- La oración
- Significado de la oración por la actitud del hablante
- Clases de oraciones
- simples
- compuesta

- El sujeto y predicado
- función
- clases
- modificadores

- Lectura y comprensión del texto literario
- Errores frecuentes en la construcción de oraciones
- anfibología
- redundancia
- cacofonía
- equívoco
- pregunta múltiple

- El párrafo y sus características
- Lectura
- Características de un buen párrafo
- Tipos de párrafos
- narrativo
- descriptivo
- expositivo
- argumentativo

- La oración tesis
- La expresión escrita
- Conceptos preliminares de redacción
- Concordancia
- Concisión
- Tono
- Corrección

- Organización del Material
- Selección del tema
- la Biblioteca como recurso de la investigación

- Organización de ideas
- Resumen
- Bosquejo
- Redacción del texto
- Introducción del texto
- Cuerpo
- Conclusión
- Formato

- Conceptos preliminares de redacción
- Práctica de la parte II

Parte III:

- Evolución de la lengua española

- El español de Hispanoamérica
- El español de Puerto Rico: rasgos y particularidades

SPAN 1010 Géneros Literarios

Parte I:

- Study of a Topic in Prose and Poetry
- Difference Between Prose and Poetry
- Relationship Between Structure and Ideological Content
- Language: Characteristics and Functions and its relation with the Topic
- Comparison Between External and Internal Structure
- Stylistically Character of the Selected Work

SPAN 2010 Literatura Hispánica

Parte I:

- Literary Concept and its Aesthetic Manifestation
- Drama Concept
- Drama Elements
- Drama Structure
- Reading and Analysis of a Drama
- Critical Writing Workshop
- Critical Glossary for Drama as a Theater Work
- Stylistically Character of the Selected Work

- The Novel
- Its Origins and Concept
- its Characteristics
- Possible Analysis of a Selected Novel
- Workshop: Writing a Novel

In this section, you will find information by general topics on English.

Click on the topic or the Word or Acrobat icons.

Repaso general de ortografía

Repaso general de verbos

In this segment you will find information divided by subjects according to your course of interest. Select the course for which you want information.

ENGL 0100 Preparatory English

I.- Verb Be

- Be + subject Pronouns
- Affirmative and Negative Sentences
- Interrogative Sentences

II.- Pronouns

- Personal Pronouns
- Subjective Case
- Objective Case
- Possessive Case

- Reflexive Pronouns

III.- Nouns

- Plural Forms of Regular and Irregular Nouns
- Use of the Articles A/an
- Count and Non-Count Nouns 1
- Count and Non-Count Nouns 2
- Count and Non-Count Nouns 3
- Possessive Nouns

IV.- Verbs

- Simple Tenses
- Regular and Irregular Verbs
- Affirmative and Negative Sentences
- Interrogative Sentences
- Time Expression
- Pronunciation of the -ed ending
- Subject – Verb agreement

- Present Progressive Tense
- Spelling Rules
- Affirmative and Negative Sentences
- Yes/No Questions

V.- Adjectives and Adverbs

VI.- Prepositions

- Location
- Direction

ENGL 0110 English Grammar

- Review of Parts of Speech
- Topic Sentence
- Paragraph Development
- Main Idea
- Supporting
- Additional details

- Outlining
- Formal and Informal Outlines
- Developing and Subject
- Attitudes Toward Writing
- Writing Essays
- Thesis Statement
- Body (Transitional words)
- Conclusion

- Types Of Essay Development
- Description
- Narration
- Examples
- Process
- Argumentation
- Comparison – Contrast

- Reacting to Reading Selection

ENGL 1010 Essay

- Review of the Essay Structure
- Review of the Types of Essay Development
- Analyzing essays
- Reacting Critically to a Reading Selection
- What is Cooperative Learning
- Preparing Oral Presentation
- Suggested Reading from the Textbook
- What True Education Should do
- Become Educated
- Overcoming an Invisible Handicap
- Overcoming An Invisible Handicap
- How to Mark A Book
- Culture
- Values
- Who Needs Love! In Japan, Many Married Couples Survive Without It
- The Last Day Of Eden
- Language
- Euphemisms
- Learning to Write
- Why Spanish Translation
- Culture Diversity
- Critical Thinking
- A New Genetic Test Can Foretell Agonizing Death: Would you Take It?
- One Nation, One Language
- A Crime Of Compassion

ENGL 2010 Word Literature

Elements of Literature

- Short Story
- Plot and Structure
- Characterization
- Setting
- Theme
- Point Of View
- Diction
- Narrative Techniques

- Poetry
- Theme
- Form
- Imagery
- Figurative Language
- Denotation And Connotation
- Symbolism

- Drama
- Plot
- Character
- Theme
- Symbolism

In this section, you will find information by general topics on English. Click on your topic of interest.

Comparative Forms of Adjectives: Using- er

Direct Object and Indirect Object

Dictionary Language Tutorials Conversational English Online Writing Lab Writing Reference www.citationmachine.net

In this segment you will find information divided by subjects according to your course of interest. Select the course for which you want information.

Numerical Analysis / Calculus MATH 2310

Part I:

- Introduction to the Course
- Find Numerical and Graph Limits
- Analytical Evaluation of Limits
- Continuity and Limits on One Side
- Infinte Limits
- Limits in the Infinite
- Derivatives and the Problem of Tangent Lines
- Basic Rules for Differentiation and Rates of Change
- Rules for Product and Quotient and Higher Order Derivatives
- Practice for Part I

Part II:

- Rules for Chains
- Implicit Differentiation
- Related Rates
- Extreme Values in an Interval
- Increasing and Decreasing Functions and First Derivative Test
- Concavity and Second Derivative Test
- Practice for Part II

Part III:

- Summary for Drawing Graphs
- Optimization Problems
- Antiderivatives and Indefinite Integrals
- Properties of Definite Integrals
- Calculus Fundamental Theorem
- Integration by Substitution
- Natural Logarithm Function and Integration
- Exponential Functions: Differentiation and Integration
- Other Exponential Functions: Differentiation and Integration
- Practice for Part III
- Practice for Part I, II and III

ENGI 2110 Statics

Part I:

- General Principles. Mechanics. Newton’s Three Laws of Motion. Newton’s Law of Gravity
- Force Vectors. Scalar and Vectors. Vector Operations. Vector Addition. Additions of a System of Coplanar Forces. Cartesian Vectors. Addition and Subtraction
- Position Vectors. Force Vector Directed Along a Line. Dot Product
- Equilibrium of a Particle. Free Body Diagram. Coplanar Force Systems.
- Force System Resultant. Moment of a Force. – Scalar Formulation. Cross Product. Moment of a Force – Vector Formulation.
- Moment of a Force About a Specified Axis. Couples
- Equivalent System. Reduction of a Force and Couple System Distributed Loading.
- Practice Part I

Part II:

- Equilibrium of a Rigid Body. Equilibrium in two Dimensions. Free Body Diagram. Equations of Equilibrium. Two and three-force members.
- Equilibrium in Three Dimensions. Freee Body Diagrams. Equations of Equilibrium
- Structural Analysis of Simple Trusses
- Method of Joints and Method of Sections
- Frames and Machines
- Practice Part II

Part III:

- Center of gravity. Centroid and Center of Mass. Composite Bodies.
- Moments of Inertia. Parallel-Axis Theorem. Moment of Inertia for Composite Areas
- Internal Forces. Internal Forces Developed in Structural Members.
- Shear and Moment Equations And Diagrams
- Relations between Distributed Load, Shear and Moment
- Friction

ENGI3000 Circuit Analysis

In this tutorial I intend to make easy for you to understand your worst nightmare…

**ELECTRONICS CIRCUITS**

You may select here the topic you want to study.

- Voltage and Current.
- Power and Energy.
- Voltage and Current Sources.
- Resistance and Ohm’s law.
- Kirchhoff’s Law.
- Series and Parallel Resistors.
- Analysis of Circuits Containing Dependent Sources.
- Voltage and Current Divider Circuit.
- Measuring Voltage and Current.
- The Wheatstone Bridge
- Delta-to-Wye Equivalent Circuit.
- Node-Voltage Method for Circuit Analysis.
- Mesh-Current Method for Circuit Analysis.
- Source Transformation.
- Thevenin and Norton Equivalents.
- Maximum Power Transfer.
- Superposition.
- Inductors and Capacitors.
- Series-Parallel Combination of Inductors and Capacitors.
- The Natural and Step Response of an RL Circuit or an RC Circuit.
- The Phasor Concept.
- Passive Circuit Elements in the Frequency Domain.