Welcome to Collin College
Math 2415.S02 Syllabus
Spring 2019 - CRN 22016
http://faculty.collin.edu/rkhoury

Course: Math 2415.S02 (Calculus III)  Instructor: Dr. R. Khoury
Math Lab: D203  972-881-5921 and online tutoring:  http://www.collin.edu/studentresources/tutoring/ Office: D226
Class Time: 1:00 PM - 3:45 PM, TR - Credit hours: 4  Lecture hrs: 3  Lab hrs: 3 Office hours: 12:00 - 1:00 PM TR
Classroom: BB218  Generic College Syllabus E-mail: rkhoury@collin.edu 
Final Exam: Tuesday, May 14, 1:00 - 3:00 PM  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 plus WebAssign


Instructional DVD Series are posted at http://faculty.collin.edu/rkhoury/Math_2415/Math_2415_Calendar_Spring_Semester.htm. Student's Solution manual is optional.

Course Measurable Learning Outcomes: Upon completion of this course the student should be able to:

  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, and directional derivatives, and multiple integrals.

  3. Find extrema and tangent planes to surfaces. (Critical Thinking)

  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. (Communication Skills

Course Requirements: It is highly recommended to read each section before I cover it in class. You are expected to copy lecture notes and use them to study for each exam. Also, you are expected to work all Lab problems as assigned in the WebAssign for each Lab; and most of all, it is highly recommended to completely finish all lab problems before taking each exam,  All exams are similar to the Lab problems and lectures. You are expected to use the Math Lab located in D203 while working your Lab problems. Homework problems are optional and are not graded.

Grading Policy: Students will receive a zero grade on every missed exam. Otherwise, grades will be assigned based on the average of the following tasks.

25% Four WebAssign Lab assignments

55% Four in class Exams
20% Comprehensive in class Final Exam

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

You are only allowed TI graphing calculators on the exam. I will offer you blank scratch papers to be turned in before you leave.

Makeup Policy: Every student is expected to take all exams and submit all labs according to the course calendar. No makeup is allowed without proper written documentation
prior to the exam date and a zero grade will be assigned to every missed exam or lab. Students cannot retake any of the exams or the final. Your grade will be assigned based on the average of the above tasks.
Every student is responsible for any assignment given during his/her absence.

Student Technical Support is provided 24/7 for students at (972) 377-1777 or at sts@collin.edu.

College Repeat Policy: See the “Repeating Courses” section of the Registration Guide for more information.


Late Assignment Policy: Students who do not turn in their Labs on time will suffer a 25% daily deduction on their Lab grades.

Withdrawal Regulation: Students who enroll as an entering freshman or a first-time college student in undergraduate courses at any Texas public community college, technical institute, health sciences institution, or any public university offering undergraduate courses must comply with the legislation of TEC51.907. Visit the Collin webpage: http://www.collin.edu/gettingstarted/register/withdrawal.html.  Please consult your instructor before you withdraw and check the current Collin Registration Guide for the last official day to withdraw.

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 withdraw from this class, you need to do the following:
1. Attain a Drop/Add form from the office of Admission and Records, 972-881-5710,
2. Turn in the completed Drop/Add form to the office of Admission and Records on or prior the withdrawal deadline,
3. Make sure your course withdrawal satisfies the college withdrawal policy;
4. Alternatively, log in to CougarWeb and follow the detailed instructions to online withdraw from this particular section.
5. You may receive an F if you do not finish this class and do not withdraw on or prior to the withdrawal deadline.

Religious Holy Days: In accordance with section 51.911 of the Texas Education Code, the college will allow a student who is absent from class for the observance of a religious holy day to take an examination or complete an assignment scheduled for that day within a reasonable time. Please refer to the current Collin Student Handbook.

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 each fall and spring semester.

ADA Statement: It is the policy of Collin County Community College to provide reasonable accommodations for qualified individuals who are students with disabilities. This 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 educational opportunity. It is the student’s responsibility to contact the ACCESS office, or call 972.881.5898 (V/TTD: 972.881.5950) in a timely manner to arrange for appropriate accommodations.

Student Code of Conduct: It is a violation of the Student Code of Conduct (Section 7-2.4, Other Offenses, item S) to engage in the use of telecommunication or media devices during any class, Collin College lab or other learning environment; here, this includes social networking activities such as texting, talking on the phone, web-browsing from laptops or smart phones, or utilizing any other related electronic devices.

Academic Ethics: Every member of the Collin College community is expected to maintain the highest standards of academic integrity. Collin 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 one’s own work material that is not one’s own. Scholastic dishonesty may involve, but is not limited to, one or more of the following acts: cheating, plagiarism, collusion, use of annotated texts or teacher’s editions, use of information about exams posted on the Internet or electronic medium, and/or falsifying academic records. While specific examples are listed below, this is not an exhaustive list and scholastic dishonesty may encompass other conduct, including any conduct through electronic or computerized means.

Plagiarism is the use of an author’s words or ideas as if they were his or her own without giving credit to the source, including, but not limited to, failure to acknowledge a direct quotation.

Cheating is the willful giving or receiving of information in an unauthorized manner during an examination; collaborating with another student during an examination without authority; using, buying, selling, soliciting, stealing, or otherwise obtaining course assignments and/or examination questions in advance, copying computer or Internet files, using someone else’s work for assignments as if it were one’s own; or any other dishonest means of attempting to fulfill the requirements of a course.

Collusion is intentionally or unintentionally aiding or attempting to aid another in an act of scholastic dishonesty, including but not limited to, failing to secure academic work; providing a paper or project to another student; providing an inappropriate level of assistance; communicating answers to a classmate about an examination or any other course assignment; removing tests or answer sheets from a test site, and allowing a classmate to copy answers. See the Collin Student Handbook for additional information.

Academic Penalty for Scholastic Dishonesty: Students will receive a zero on every assignment 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.

Cell Phones and browsers: Cell phones and all other means of social media and browsers are not allowed to be used in the classrooms without formal permission of the instructor. Any violations will be reported to the Dean of students.

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

Disclaimer: 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

____________________________________________________________________________________________________________________________________________________________________________________________________________________________

 

Collin College
http://faculty.collin.edu/rkhoury
Math 2415.S02 - CRN 22016
Spring 201
9

Math 2415 Suggested Daily Assignments (Not graded)

 Instructor: Dr. Khoury

Class 
Day
Material Covered

Suggested Textbook Homework (Not graded)

Tuesday
Jan 22
Introductions
12.1
Introductions
12.1: 2, 3, 5, 7, 9, 11, 12, 13, 15, 19, 22, 23, 31, 33, 35, 39, 43, 44, 45, 47.
Thursday
Jan 24
12.2
12.3
12.2: 2, 3, 5, 7, 8, 13, 17, 21, 25, 26, 27, 29, 35, 37, 39, 41.
12.3: 1, 3, 5, 7, 9, 11, 13, 15, 19, 22, 23, 25, 27, 29, 35, 41, 43, 47, 49, 51, 53.
Tuesday
Jan 29
12.4
12.5
12.4: 3, 5, 7, 8, 11, 13, 15, 16, 19, 27, 31, 33, 35, 37, 38, 41, 45.
12.5: 1, 3, 5, 7, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 35, 37, 39, 41, 45, 47, 49, 51, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 76, 77, 78, 79.
Thursday
Jan 31
12.6
13.1
12.6: 3, 5, 7, 9, 11, 13, 17, 19, 21, 23, 25, 27, 29, 33, 37, 39, 41, 45, 47.
13.1: 1, 3, 5, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 41, 43, 45, 50.
Tuesday
Feb 5
13.2
13.3
Census Day: February 4
13.2: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 34, 35, 37, 39, 41, 47, 49, 51, 53, 55.
13.3: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 31, 33, 37, 43, 45, 47, 49, 53, 55, 57, 65.
Thursday
Feb 7
13.4 13.4: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 31, 37, 39, 41, 43, 45.
Tuesday
Feb 12
Review Review for Exam 1
Thursday
Feb 14
Exam 1 Take Exam 1 at 1:00 PM
Tuesday
Feb 19
Lab 1 is Due
14.1
Go over Exam 1
14.1: 3, 7, 9, 11, 13, 15, 19, 21, 23, 25, 29, 31, 32, 37, 41, 45, 49, 53, 55, 59, 61, 63, 65, 67, 69, 71.
Thursday
Feb 21
14.2
14.3
14.2: 3, 5, 7, 9, 11, 13, 25, 17, 21, 23, 25, 29, 31, 33, 35, 37, 39, 41.
14.3: 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 29, 31, 33, 39, 43, 45, 47, 49, 51, 52, 53, 55, 57, 59, 61, 63, 65, 67, 73, 77, 83, 97, 99.
Tuesday
Feb 26
14.4
14.5
14.4: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 31, 33, 35, 43, 45.
14.5: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 45.
Thursday
Feb 28
14.6
14.7
14.6: 4, 5, 7, 9, 11, 13, 15, 17, 18, 19, 20, 21, 23, 25, 27, 28, 29, 33, 39, 41, 43, 45, 49, 55, 57, 59, 61, 63.
14.7: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 31, 33, 35, 37, 41, 43, 45, 47, 49, 51, 53, 55.
Tuesday
Mar 5
14.8 14.8:  3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 39, 41, 43, 45.  
Thursday
Mar 7
Review Review for Exam 2
Tuesday
Mar 12
Spring Break Spring Break
Thursday
Mar 14
Spring Break Spring Break
Tuesday
Mar 19
Exam 2 Take Exam 2 at 1:00 PM
Thursday
Mar 21
Lab 2 is Due
15.1
Go over Exam 2
15.1: 1, 3, 5, 7, 9, 11, 12, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 47, 49.
Last day to withdraw this class is March 22
Tuesday
Mar 26
15.2
15.3
15.2: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 35, 37, 39, 45, 47, 49, 51, 53, 55, 57, 59, 61, 65, 67.
15.3: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41.
Thursday
Mar 28
15.4
15.5
15.4: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27.
15.5: 1, 3, 5, 7, 9, 11, 12, 13, 15, 21, 23.
Tuesday
Apr 2
15.6
15.7
15.6: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 47, 53, 55.
15.7: 1, 3, 5, 7, 9, 11, 12, 13, 15, 17, 19, 21, 23, 25, 27, 29.
Thursday
Apr 4
15.8 15.8: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 30, 31, 33, 35, 37, 41, 43, 48.
Tuesday
Apr 9
Review Review for Exam 3
Thursday
Apr 11
Exam 3 Take Exam 3 at 1:00 PM
Tuesday
Apr 16
Lab 3 is Due
16.1
Go over Exam 3
16.1 :
16.1: 1, 3, 5, 7, 9, 11, 12, 13, 14, 15, 16, 17, 18, 21, 23, 25, 29, 30, 31, 32, 33, 35.
Thursday
Apr 18
16.2
16.3
16.2: 1, 3, 5, 7, 9, 11, 12, 13, 15, 17, 19, 21, 23, 24, 25, 33, 39, 41, 45.
16.3: 1, 3, 5, 7, 9, 11, 13, 15, 17, 21, 23, 25, 26, 28, 29, 30, 31, 33, 35.
Tuesday
Apr 23
16.4
16.5
16.4: 1, 3, 5, 7, 9, 11, 13, 17, 19, 21, 25, 27, 29.
16.5: 1, 3, 5, 7, 9, 10, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31.
Thursday
Apr 25
16.6
16.7
16.6: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 26, 33, 35, 39, 41, 43, 47, 49, 51, 61, 63.
16.7: 1, 3, 4, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 39, 45, 47.
Tuesday
Apr 30
16.8
16.9
16.8: 1, 3, 5, 7, 9, 13, 15, 17, 19.
16.9: 1, 3, 5, 7, 9, 11, 13, 17, 19, 20, 24
Thursday
May 2
Review Review for Exam 4
Tuesday
May 7
Exam 4 Take Exam 4 at 1:00 PM
Thursday
May 9
Lab 4 is Due
Review
Go over Exam 4
Final Exam Review
Tuesday
May 14
Final Comprehensive Final Exam in class

·  Calculus I and II videos are listed below

Calculus III - Module I - 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 - Module II - 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 - Module 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 - Module IV - 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