Welcome to Collin College
Math 2415.WS1 Syllabus
Spring 2019 - CRN 21509
http://faculty.collin.edu/rkhoury

Course: Math 2415.WS1 (Calculus III)  Instructor: Dr. R. Khoury
Math Lab: D203  972-881-5921 - http://www.collin.edu/studentresources/tutoring/ Office: D226        Announcement: Canvas
Meeting Time: Online - Credit hours: 4  Lecture hrs: 3  Lab hrs: 3 Office hours: Online and by appointment
Chat Room: Online  Generic College Syllabus E-mail: rkhoury@collin.edu 
Final Exam: Online (See Calendar) http://www.collin.edu/academics/final_exam_schedule.html Phone: 972-881-5909
Last day to withdraw this class is March 22nd                Census Day: February 4th Required Graphing Calculators: Any calculator

Catalog Description: Advanced topics in calculus, including vectors and vector-valued functions, partial differentiation, Lagrange multipliers, multiple integrals, and Jacobians; application of line integral, including Green's Theorem, the Divergence Theorem, and Stokes' Theorem. Lab included.

Required Textbook and Supplements:

Multivariable Calcul…, 9781305266643 Textbook: Calculus, Early Transcendentals  - James Stewart - 8th edition - 2016 - Cengage Learning

Choice 1: Textbook plus WebAssign


Choice 2: E-Book plusWebAssign
(Preferred)

Instructional DVD Series are posted in Canvas. Student Solutions Manual is optional

https://www.cengage.com/c/calculus-early-transcendentals-8e-stewart

                                                                       

Course Description:  This course studies advanced topics in calculus, including vectors and vector-valued functions, partial differentiation, Lagrange Multipliers,
multiple integration and Jacobians; application of the line integral, including Green’s Theorem, the Divergence Theorem, and Stoke’s theorem. Lab included.
 
 

Course Credit Hours: 4             Lecture Hours: 3          Lab Hours: 3             Clinical/Recitation Hours: 0

 

Placement Assessment(s): Prior to enrolling in this course, the student must demonstrate eligibility to enroll in the following: MATH 2318, MATH 2320, or higher.

 

Prerequisite: MATH 2414 or equivalent                                     Concurrent Enrollment:   None                              Corequisite: None 

                                                                                       

Student Learning Outcomes: Upon successful completion of this course, students should be able to do the following:
 

1. Perform calculus operations on vector-valued functions, including derivatives, integrals, curvature, displacement, velocity, acceleration and torsion.
2. Perform calculus operations on functions of several variables, including partial derivatives, directional derivatives and multiple integrals.
3. Find extrema and tangent planes.
4. Solve problems using the Fundamental Theorem of Line Integrals, Green's Theorem, the Divergence Theorem, and Stokes' Theorem.
5. Apply the computational and conceptual principles of calculus to the solutions of real-world problems.
 

Withdrawal Policy: Under section 51.907 of the Texas Education Code, students may not withdraw from more than six

 courses including any course a transfer student has withdrawn from at another Texas institute of higher education. For

 exemptions, visit http://www.collin.edu/gettingstarted/register/withdrawal.html. Please see your instructor before you withdraw

and the current Collin Registration Guide for the last day to withdrawal.

 

Course Withdrawal: To drop this class, you need to do the following:

1. Attain a Drop/Add sheet from the registrar’s office;

2. Turn in the completed form to the office of Admission and Records 972-881-5710 on or prior to the drop deadline date.

3. All students will receive an F if they do not finish this class and do not withdraw on or prior to the drop deadline date.

4. Make sure your course withdrawal satisfies the college withdrawal policy.
 

Collin College Academic Policies:  “See the current Collin Student Handbook.”

 

Americans with Disabilities Act:

Collin College will adhere to all applicable federal, state and local laws, regulations and guidelines with respect to providing

reasonable accommodations as required to afford equal opportunity. It is the student’s responsibility to contact the ACCESS

office, SCC-G200 or 972.881.5898 (V/TTD: 972.881.5950) to arrange for appropriate accommodations. See the current Collin

Student Handbook for additional information.


You need to have both the Class Key (your instructor will give you that) and the Access Code (buy from Collin's bookstore) to enroll in WebAssign.

 

Five steps to remember:
1. Go to www.webassign.net (WebAssign) through Canvas
2. Click on Have a Class Key link, fill in the class key in the pop-up window.
3. Create a user name and password for yourself and make sure you use your Cougar email as your official email address.
4. You log in using your user name and password.
5. Enter the Access Code. (If you don't have Access Code, you can buy it from the bookstore, directly from Cengage, or online through WebAssign)


Textbook:

 

Required Graphing Calculators and supplies: Any

Minimum Technology Requirement: http://www.collin.edu/academics/ecollin. 
 

Minimum Student Skills: e-Collin Student Qualifications

Find out if you are ready to take an online course by completing the e-learning readiness assessment SmarterMeasure http://www.collin.edu/academics/ecollin/ This is an important tool that helps determine your skills for taking an online course. From the Smarter Measure assessment, you will discover information about your:

  1. Reading Speed and Comprehension

  2. Technical Competency and Knowledge

  3. Typing Speed and Accuracy

  4. Personal Attributes that relate to distance learning success

Please visit the e-Collin support website (http://online.collin.edu) and select SmarterMeasure http://www.collin.edu/academics/ecollin/ to take this assessment.

 

Netiquette Expectations:  (Expectations for electronic discussions and mail communication)

1.  Standards of courtesy and respect must be maintained at all times in our online “classroom.” Join in to the discussion, but remember that this is still a “classroom” setting and that respect and 

     consideration are crucial for any intellectual discussions.
2.  Discussion areas are the place for intelligent and respectful airing of ideas. Name-calling and personal attacks are not permitted.
3.  Any violation of the standards of appropriate behavior online will be reported to the Dean of Students and appropriate disciplinary action will be taken by the college.


Academic Ethics: The college may initiate disciplinary proceedings against a student accused of scholastic dishonesty. Scholastic dishonesty includes, but is not limited to, statements, acts, or omissions related to applications for enrollment or the award of a degree, and/or the submission of material as one’s own work that is not one’s own. Scholastic dishonesty may involve one or more of the following acts: cheating, plagiarism, collusion, and/or falsifying academic records. Cheating is the willful giving or receiving of information in an unauthorized manner during an examination, illicitly obtaining examination questions in advance, using someone else’s work for assignments as if it were one’s own, copying computer disks or files, and any other dishonest means of attempting to fulfill the requirements of a course. Plagiarism is the use of an author’s words or ideas as if they were one’ s own without giving credit to the source, including, but not limited to, failure to acknowledge a direct quotation. Contact the Dean of Students at 972-881-5604 for the student disciplinary process and procedures or consult the Collin College Student Handbook.

Academic penalty for scholastic dishonesty: Students will receive a zero on those assignments where they were found guilty by the Dean of Students for scholastic dishonesty, i.e., cheating, collusion, etc. as stated above; also, for repeated occurrences of these incidences, students will receive a failing grade in this class section.

Course Resources:  None.

 

Course Requirements:

  1. Read assigned material in WebAssign as assigned in the course calendar.

  2. Watch all four DVD lectures in Canvas and in WebAssign.

  3. Work and submit all assigned Lab sections problems posted in WebAssign.

  4. Complete and submit on time the four Exams posted in Canvas in the testing center or through ProctorU.

  5. Complete and submit on time the Final exam posted in Canvas in the testing center or through ProctorU.

It is highly recommended to read each section before you watch instructional lectures and read the e-book in WebAssign. You are expected to copy lecture notes as you watch them and use your notes to study for each exam. Also, you are expected to work all Lab problems as assigned in WebAssign for each section; and most of all, it is highly recommended to work the Exam's review problems before taking each Exam as well as the Final. All Exams are similar to the Exam's review problems, lectures, and Labs. You are expected to use any of the Collin's Math Labs located while studying. Online Lab problems in WebAssign are graded.

Attendance Policy: This is an online course with a Lab component in which students are required to complete Labs, Exams, and Final.

 

Aspects of the class: All Labs are in WebAssign, while Exams, and Final are online in Canvas. Once you submit your worked problems, both you and I can see your graded scores. Also, you should be able to see the Labs and Exams questions after you submit them in WebAssign and in Canvas.

Method of EvaluationStudents will receive a zero grade on every missed Exam and Lab. No makeup is allowed under any circumstances. Otherwise, grades will be assigned based on the average of the following tasks. Open and read instructions before taking your Exams and Labs.

20% Four Lab assignments (To be taken in WebAssign through Canvas)
60% Four Exams (
Drop one lowest exam grade) To be taken online in WebAssign through Canvas in the testing center or through ProctorU
20% Comprehensive Final Exam taken online in WebAssign through Canvas in the testing center or through ProctorU

Lab grades will be be automatically graded and posted in WebAssign, while Exams, and Final grades will be automatically graded and grades will be posted in Canvas. Discussions posted in the discussion board will not be graded. Your course letter grade will be assigned as follows:

90-100 = A              80-89 = B              70-79 = C             60-69 = D                 0-59 = F

Each Lab section consists of 25 questions. Labs are in WebAssign.

Exam questions are similar to the Lab and Exam review questions. Each Exam consists of 25 questions and each question is worth 4 points. Each exam must be taken in the testing center through Canvas or through ProctorU. You are only allowed any graphing calculator and one 4" by 6" index card. Nothing else. A testing center employee will offer you blank scratch papers to be turned in before you leave. Also, you should only login to Canvas and do not open any other tabs beside the assessment tab or any browsers or use any other devices or cell phones.

Final exam questions are similar to the Lab and and Exam questions. Final consists of 25 questions and each question is worth 4 points. Final exam must be taken in the testing center in WebAssign through Canvas or through ProctorU. You are allowed any graphing calculator on the Exam and one 4" by 6" index card. Nothing else. A testing center employee will offer you blank scratch papers to be turned in before you leave. Also, you should only login to Canvas and do not open any other tabs beside the assessment tab or any browsers or use any other devices or cell phones.

Makeup Policy: Every student is expected to take all assessments and submit them according to the course calendar. No makeup is allowed under any circumstances and beyond the assessments posted dates in the course calendar. A zero grade will be assigned to every missed assessment. Students
 
cannot take any assessment beyond the posted dates in Canvas. Your grade will be assigned based on the average of the above tasks.

Requirements for Participation in Online Discussion or Collaborative Activities: Students are required to participate in self introductions but discussions will not be graded.
 

Evaluation of Instructions: Collin College seeks to improve the learning experience of all students. To assist in evaluating courses, students will be requested to complete an evaluation of instruction form near the end of the semester through the Distance Learning Department.

Additional information:

Course Calendar
Math Lab Hours
On Line Tutoring: Through NetZero
 https://www.collin.edu/studentresources/tutoring/.        
Canvas Help line:
972-377-1777
WebAssign help: 800-354-9706


I reserve the right to change any term on this syllabus at any time during the semester.
 

Copyright © This site was last edited on Wednesday, January 16, 2019 - Dr. Raja Khoury - Collin College -  All Rights Reserved

__________________________________________________________________________________________________________________________________________________________________________


 

Welcome to Collin College
Math 2415 Calendar
Spring 2019
http://faculty.collin.edu/rkhoury

1. Read the e-book and work the assigned online Lab problems in WebAssign. Use the online step by step solution to selected Lab problems.

2. Work suggested textbook Exam review problems by using the optional student's solution manual for step by step solution to selected problems.

3. Take advantage of free onsite tutoring located at Collin's Math Labs or through NetTutor https://www.collin.edu/studentresources/tutoring/.

Read instructions before taking your Exams and Labs
Math 2415 Online - Spring 2019
Assignment Lab availability in WebAssign Exam availability in Canvas Sections covered
Exam 1 and Lab 1 Lab 1 is available on
Jan 22 - Feb 17
Exam 1 is available on Feb 11 - 17 12.1- 12.6, 13.1 - 13.4
Exam 2 and Lab 2
Lab 2 is available on
Feb 18 - Mar 24
Exam 2 is available on Mar 18- 24
Mar 22 is last day to withdraw
14.1 - 14.8
Exam 3 and Lab 3 Lab 3 is available on
Mar 25 - Apr 21
Exam 3 is available on April 15 - 21 15.1 - 15.9
Exam 4 and Lab 4 Lab 4 is available on
Apr 22 - May 12
Exam 4 is available on May 6 - 12 16.1 - 16.9
Comprehensive Final Exam is available in Canvas on May 13 - 18 in the testing center or online through ProctorU.
Sections covered 12.1- 12.6, 13.1 - 13.4, 14.1 - 14.8, 15.1 - 15.9, 16.1 - 16.9
 

Suggested Weekly schedule

Date Section #

Section Title (Students' Learning Objectives)

Jan 22-27 Introductions
12.1
12.2

12.3
12.4
Introductions
Three-Dimensional Coordinate Systems
Vectors

The Dot Product
The Cross Product
Jan 28-Feb 3 12.5
12.6
13.1
Equations of Lines and Planes
Cylinders and Quadric Surfaces
Vector Functions and Space Curves
Feb 4-10 13.2
13.3
13.4
Derivatives and Integrals of Vector Functions
Arc Length and Curvature
Motion in Space: Velocity and Acceleration
Feb 11-17 Lab 1 is Due
Exam 1
Take Exam 1 in WebAssign through Canvas in the testing center or through ProctorU
Feb 18-24 14.1
14.2

14.3
Functions of Several Variables
Limits and Continuity
Partial Derivatives
Feb 25-Mar 3 14.4
14.5
14.6
Tangent Planes and Linear Approximations
The Chain Rule
Directional Derivatives and the Gradient Vector
Mar 4-10 14.7
14.8
Maximum and Minimum Values
Lagrange Multipliers
Mar 11-17 Spring Break Spring Break
Mar 18-24 Lab 2 is Due
Exam 2
Take Exam 2  in WebAssign through Canvas in the testing center or through ProctorU
Last day to withdraw this class is March 22
Mar 25-31 15.1
15.2
15.3
Double Integrals over Rectangles
Double Integrals over General Regions
Double Integrals in Polar Coordinates
Apr 1-7 15.4
15.5
15.6
Applications of Double Integrals
Surface Area
Triple Integrals
Apr 8-14 15.7
15.8
15.9
Triple Integrals in Cylindrical Coordinates
Triple Integrals in Spherical Coordinates
Change of Variables in Multiple Integrals
Apr 15-21 Lab 3 is Due
Exam 3
Take Exam 3 in WebAssign through Canvas in the testing center or through ProctorU
Apr 22-28 16.1
16.2
16.3
16.4
16.5
Vector Fields
Line Integrals
The Fundamental Theorem for Line Integrals
Green’s Theorem
Curl and Divergence
Apr 29-May 5 16.6
16.7
16.8
16.9
Parametric Surfaces and Their Areas
Surface Integral
Stokes’ Theorem
The Divergence Theorem
May 6-12 Lab 4 is Due
Exam 4
Submit Lab 4 in WebAssign
Take Exam 4 WebAssign through Canvas in the testing center or through ProctorU
May 13-18 Comprehensive
Final
Take Final Exam in WebAssign through Canvas in the testing center or through ProctorU

·  Calculus I and II videos are listed below

Calculus III - Videos 

Find distances between points in space and find midpoints of line segments in space

Write the standard forms of the equations of spheres and find the centers and radii of spheres

Scalar Multiplication

Work- vectors

Find the dot product of two vectors and use the Properties of the Dot Product

Scalar projection of a vector

The cross product

Distance between a point and a plane

Sketch the quadric surface

Quadratic surfaces

Space curves and vector-valued functions

Space curves - A

Arc length parameter

Curvature

Formula for curvature

Calculus III - Videos

Find the first partial derivatives of functions of two variables

Multivariable functions: use a Cobb-Douglas production model

Read contour maps and sketch level curves of functions of two variables

Find the domains and ranges of functions of several variables

Limit of a function of two variables

Testing for continuity

Find the first partial derivatives of functions of two variables

Find the partial derivatives of functions of several variables

Second-Order Partial Derivatives

Linear Approximation and Differentials

Implicit differentiation

Find a directional derivative

Introduction to gradients

Understand the relative extrema of functions of two variables

Use the Second-Partials Test to find the relative extrema of functions of two variables

Find the maximum values of function using Lagrange Multipliers - A

Find the maximum values of function using Lagrange Multipliers - B

Use Lagrange multipliers with two constraints to find extrema of functions of several variables

Calculus III - Videos

Properties of Double Integrals

Iterated Integral in Two Variables

Calculate double integrals- Fubini's Theorem

Using Fubini's Theorem and Double Integrals to find Volume - A

Using Fubini's Theorem and Double Integrals to find Volume - B

Riemann sum

Double Integrals over a Rectangular Region

Use double integrals to find the volumes of solids - A

Use double integrals to find the volumes of solids - B

Evaluate double integrals

Iterated Integral in Two Variables

Properties of Double Integrals

Use Properties to Evaluate a Double Integral

Evaluate double integral using polar coordinate - A

Evaluate double integral using polar coordinate - B

Change to polar coordinates in a double integral

Moments and center of mass of a variable density planer lamina

Finding the center of mass

Finding the center of mass of a solid region - A

Finding the center of mass of a solid region - B

Use continuous probability density functions to answer questions about real-life situations

Find the expected values or means of continuous probability density functions

Definition of surface area

Surface area of a plane region

Find the surface area of the paraboloid

Triple integrals

Triple integrals: find the volume - A

Triple integrals: find the volume - B

Triple integrals in cylindrical coordinates- an overview

Triple integrals in spherical coordinates- an overview

Triple integrals in spherical coordinates

Change of Variables for Definite Integrals

Understand the concept of a Jacobian

Calculus III - Videos

Vector Fields - A

Vector Fields - B

Problem on Vector Field - A

Problem on Vector Field - B

Fundamental theorem for line integrals

Independence of path

Compute the Potential Function of a Conservative Vector Field

Curl

Divergence

Parametric surfaces

Problem on parametric surfaces

Surface area - B

Find the surface area of the paraboloid

Surface integrals

Problem on surface integrals - A

Problem on surface integrals - B

Divergence Theorem

Problem on Divergence Theorem - A

Problem on Divergence Theorem - B

Divergence Theorem

Fundamental theorem for line integrals

Second-order linear differential equation - A

Second-order linear differential equation - B 

Introduction to second-order nonhomogeneous linear equations - A

Introduction to second-order nonhomogeneous linear equations - B

Method of undetermined coefficients - A

Method of undetermined coefficients - B

Calculus I Review Videos

The Domain and Range of a Function - A

Apply the Vertical Line Test

Even and Odd Symmetry of Functions

Increasing and decreasing functions on an interval

Cubic, square root, and reciprocal functions

Find the domain of a rational function

Graphs of Logarithmic Functions

Transformations of functions

Operations with Functions

Find the composition of two functions

Graph the function using graphing calculators

Properties of Exponents

Evaluate and graph natural exponential functions

Evaluate and graph natural exponential functions

Find the inverse of a function

Find the inverse of a function

Evaluate natural logarithms and graph natural logarithm functions Part I

Evaluate natural logarithms and graph logarithm functions Part II

Evaluate the other inverse trigonometric functions

Find the equation of the tangent line

Find average velocity - A

Average and Instantaneous Velocity

An introduction to limits

Find limits of functions graphically and numerically

Different limits from the Right and Left

Investigating infinite limits

Use the properties of limits to evaluate limits of functions

Evaluate a limit of a polynomial function

Limits of Polynomial and Rational Functions

Evaluate one-sided limits

Limits of radical functions

The Squeeze Theorem

Formal Definition of Limit - A

Formal Definition of Limit - B

A Formal Definition of an Infinite Limit

Determine the continuity of functions

Continuous and Discontinuous Functions

Properties of Continuity

The Intermediate Value Theorem

Use the Intermediate Value Theorem to help locate zeros of polynomial functions

Limits at Infinity

Find the horizontal asymptotes of functions and find limits at infinity

Evaluation of limits at infinity for a rational function

Properties of limits at infinity

Find the horizontal asymptotes of functions and find limits at infinity

Definition of limits at infinity

Slope of tangent lines to a point on a curve

Find the equation of the tangent line

Tangent line with slope m- Part I

Find average velocity - A

Find the instantaneous rates of change of functions at points

Find the average rates of change of functions over intervals - A

Find the average rates of change of functions over intervals - B

Use the limit definition to find the derivatives of functions

Find the Derivative of a Function using the definition

Notations for the Derivative Function

Nondifferentiable Functions

Find higher-order derivatives

Find derivatives using the General Power Rule

The Constant Multiple Rule

The Sum Rule and the Difference Rule

Find the derivatives of natural exponential functions

The product rule

Find the derivatives of functions using the Quotient Rule

Derivatives of trigonometric functions

Find derivatives using the Chain Rule

The Chain Rule

Implicit differentiation

Derivatives of Inverse trigonometric functions- an overview

Derivatives of logarithmic functions with bases other than e

Logarithmic Differentiation - A

Logarithmic Differentiation - B

Find average rate of change

Average Rate of Change

Radioactive Decay and Law of Cooling

Related rates- ripples in a pond

Linear Approximation and Differentials

Hyperbolic functions

Hyperbolic Functions and Their Derivatives

Extrema of a function and the Extreme Value Theorem

Relative Extrema and the graph of a function - A

Find absolute extrema of continuous functions on a closed interval

Rolle's Theorem

The Mean Value Theorem- an overview

The Mean Value Theorem

Increasing and decreasing functions on an interval

Use the First-Derivative Test to find the relative extrema of functions

Determine the intervals on which the graphs of functions are concave upward or concave downward

Concavity and inflection points

Apply the Second Derivative Test - A

Apply the Second Derivative Test - B

Approximate limits that produce indeterminate forms

Review of Indeterminate Forms

L'Hôpital's Rule- Part I

L'Hôpital's Rule- Part I

Use L'Hopital's Rule to evaluate limits

Use L'Hospital's Rule to evaluate limits

Curve sketching- finding intercepts, critical points, test values

Curve sketching- testing f, f' and f'' over intervals

Curve Sketching: A Summary

Curve sketching- conclusions of interval tests

Curve sketching with intercepts and interval tests

Curve Sketching with an Asymptote

Graph the function using graphing calculators

Use a graphing utility to evaluate functions, to find intercepts, and to find zeros of a function

Optimization- finding maximum volume- set up

Optimization- finding maximum volume- solution

Solve business and economics optimization problems

Solve business and economics optimization problems

Find Marginal cost, revenue, and profit, given linear total cost, total revenue, and profit functions

Situations in which Newton's Method Fails

Newton's Method

Related rates- ripples in a pond, an overview

Newton's Method of approximating zeros - an overview

Newton's method of approximating zeros

Antiderivatives

Understand the definition of antiderivative

Use antiderivatives to solve real-life problems

The Area Problem

Approximation of the area under a curve using rectangles

Area of a region in the plane

Application - Uniform Motion Problem

Area from Riemann Sums - A

Riemann sum

Area from Riemann Sums - B

Evaluation of a definite integral as a limit- Part I

Evaluation of a definite integral as a limit- Part II

Use the Midpoint Rule to approximate definite integrals

Properties of the Definite Integral-Part A

Properties of the Definite Integral-Part B

Evaluate definite integrals using the Fundamental Theorem of Calculus

Use basic integration rules to find antiderivatives

Indefinite integrals - overview

Rules for Integration

Evaluation of indefinite integrals

Use definite integrals to solve marginal analysis problems

A Simple Integral by Substitution

Use substitution to evaluate definite integrals Part I

Use substitution to evaluate definite integrals Part II

Substitution in an Indefinite Integral

Use properties of even and odd functions to help evaluate definite integrals

Find the areas of regions bounded by two graphs

Calculus II Review Videos

Area Bounded by Two Curves

Calculate the area between two curves - B

Volume of Geometric Solids

The Disk Method

Apply the formula for the volume of a sphere: V = (4/3)Pi r³

Use the Washer Method to find volumes of solids of revolution with holes

Use vectors to find the work done by a force

Application: work done by a variable force - compressing a spring - A

Application: work done by a variable force - compressing a spring - B

Average value of a function

Mean Value Theorem for Integrals

Integration by parts- an overview

Integration by parts Part I

Integration by parts Part II

Use reduction formulas to find indefinite integrals

Integration by parts- integrand with a single term

Integrals of Trigonometric Functions

Integrals of other trig functions

Trigonometric substitution

Trigonometric substitution- an overview

Trigonometric substitution- rational powers

Integrals of Logarithmic Functions

Partial fractions decomposition- distinct linear and quadratic factors

Partial fractions decomposition- distinct linear factors

Partial fractions decomposition

Integrals of other trig functions

Integrate: using the table of integrals

Using tables to Evaluate Integrals

Use the Midpoint Rule to approximate definite integrals Part I

Use the Midpoint Rule to approximate definite integrals Part II

Use the Midpoint Rule to approximate definite integrals Part III

Using the Trapezoidal Rule to Approximate an Integral

The Trapezoidal Rule

Errors in the Trapezoidal Rule and Simpson's Rule

Simpson's Rule

Using Simpson's Rule to Approximate an Integral

Evaluate improper integrals with infinite limits of integration

Recognize improper integrals

Improper integrals

Improper integrals- an overview

Improper Integral with Infinite Interval

Evaluate improper integrals with infinite integrands

Improper Integral with Unbounded Discontinuity

Evaluate improper integrals with infinite integrands

Arc length parameter

Problem on hydrostatic force and pressure - A

Problem on hydrostatic force and pressure - B

Moments and center of mass of a variable density planer lamina

Finding the center of mass

Using Integrals to Find Consumer Surplus

Find the expected values or means of continuous probability density functions

Calculating Probability with Normal Distribution

The Concept of Differential Equations

Direction Fields

Separable Equations

Orthogonal trajectories

Logistic Growth

Exponential Growth and Decay

First-order linear differential equations

Applications of Differential Equations

Predator-prey differential equations

Analyzing predator-prey equations

Sketch the curve that is represented by a set of parametric equations

Arc length parameter

Surface area of a plane region

Plot points on the polar coordinate system

Graph polar equations by point plotting

Graph polar equations by point plotting

Graphing Polar equations with a calculator

Write equations of parabolas

Graph an ellipse with center at the origin

Write an equation of a hyperbola

Use Vertical and Horizontal Shifts to Sketch Functions

Polar equations of conics

Write the polar equation of a conic (ellipse, parabola, hyperbola) using eccentricity and the distance from the focus to the directrix

Write the terms of a sequence

Find the nth term of a sequence

Determine the convergence or divergence of sequences and find the limits of convergent sequences

Partial Sums

Sum Formula for Infinite Geometric Series

Use the nth-Term Test of Divergence to show that series diverge

Determine the convergence or divergence of p-series

Direct comparison test

Problem on direct comparison test

Alternating series

Problem on alternating series

Use the Ratio Test to determine the convergence or divergence of series - A

Use the Ratio Test to determine the convergence or divergence of series - B

Introduction to Power Series

Calculate Radius of Convergence for Power Series

Introduction to Taylor Series

A Taylor Series Example

Introduction to Taylor Polynomials

An Example with Taylor Polynomials - Part A

An Example with Taylor Polynomials - Part B

Use Taylor polynomials to determine the maximum errors of approximations - A

Use Taylor polynomials to determine the maximum errors of approximations - B