Math 2450 Section Distance 01

Spring 2015

 

 

Dr. Eugenio Aulisa
Office: Math 222
Phone: 806-834-6684

email: eugenio.aulisa@ttu.edu

Office Hours: by appointment

 

Calculus III with applications


Textbook

Calculus
K. Smith, M. Strauss and M. Toda, Kendall Hunt, 6th National Edition.


Online Homework : Click here to Enter



The following link provides a tutorial on how to use WeBWork

Introduction to WeBWork.pdf


Students should also read the tutorial on entering answers in WeBWork

How to Enter Answers in WeBWork.pdf 


Course Description

This course covers Calculus of several variables. The concepts are extensions of the concepts from Calculus I. It is necessary to remind the students of those basic concepts, as the course progresses. Multivariable Calculus is an important tool in Science and Engineering. The instructor should emphasize the importance of all relevant concepts, including: curves and surfaces in Euclidean 3-space, length and curvature, area and volume; surfaces, partial derivatives, total differential, tangent planes to surfaces; gradient; vector-valued functions; path integral; Stokes' theorem, which should be stated, with an emphasis on its important particular cases, Green's Theorem and Divergence Theorem - followed by a few basic examples.


Grading Policy

Homework is worth 20% of the final grade.
However in order to pass the class your overall grade in the HW at the end of the semester should be at least 50%. This may appear radical, but besides the exams, the HW system is a major tool the instructor has to asses your class performances. The instructor will check regularly your HW score and let you know if you are not on track.

Examinations:
Exam #1: Wed, February 11, 5:30-6:30 room Math110 worth 15% of the final grade
Exam #2: Wed, March 11, 5:30-6:30 room Math110 worth 20% of the final grade
Exam #3: Wed, April 22, 5:30-6:30 room Math110 worth 20% of the final grade
Final Exam: Mon, May 11, 10:30-1:00 worth 30% of the final grade

Overall grade: a perfect score in all tests and homeworks results in a overall grade of 105% .
If your overall score is less than 60% you will receive an F grade, in between 60-69% you will receive a D grade, in between 70-79% you will receive a C grade, in between 80-89% you will receive a B grade, in between 90-99% you will receive an A grade, with 100% or more you will receive A+.




Exam Policy

Students are expected to take the midterm exams and the final exam as scheduled. Students who live close enough to Lubbock (75 miles around Lubbock) will have to take the midterm exams and final exam at Texas Tech University in Lubbock at the Mathematics and Statistics department. If students have a conflict in schedule or are far away from Lubbock, they need to provide necessary documentation, and arrange a different place and/or time for examination. In that cased, depending on their geographic location, each student should make arrangements with a certified testing service. In case no agreeable solution can be found, the Texas Tech University Testing Services in Lubbock will be designated to administer the examination. Testing centers (including the TTU Testing Center) charge a fee to administer the exam.

The following link can be used to obtain a copy of the proctor form in Adobe Acrobat(.pdf) format

Proctor form PDF File  


Syllabus

The following link can be used to obtain a copy of the sylabus in Adobe Acrobat(.pdf) format

Sylabus PDF File  


This is a distance class, all the students enrolled in this class should be highly responsible in managing their schedule. This course moves very fast. If you fall behind, even by one section, you may not be able to catch up, since each section generally depends very heavily on the ones before. A student enrolled in this class has to be capable to read and understand the textbook. If in the past you struggled in self-lecturing mathematics, then this is not the class for you and it is highly recommended you switch to a face-to-face class. The instructor expects for the student to read each section of the textbook, watch the videos and read the class-notes before attempting to solve the homework problems. When asking for help you need to show all your work, by typing it on the email (better) or by attaching a scanned copy of your work. When asking for help for a WebWork problem it is recommended you use the button email to the instructor at the bottom of the screen, otherwise you may not get any answer.


Videos

Review of Sections 9.1-9.4

Vector Basics  

Vector Component Form  

Scalar Multiplication  

Adding and Subtracting Vectors  

Vector Operations - Example 1  

Standard Unit Vectors  

Magnitude of a Vector  

Magnitude of a Vector - Example 1  

Unit Vector  

How to Normalize a Vector  

3D Vectors  

Vector Dot Product  

Dot Product - Example 1  

Using Dot Product to Find the Angle Between Two Vectors  

Finding Angles Using Dot Products - Example 1  

Vector Projections  

Vector Projections - Example 1  

Vector Cross Product  

Vector Cross Product - Example 1  

Vector Cross Product - Extra Theory  




HW01 is due 01/21/2015 at 11:59pm CST



Section 9.5

Parametric Equations  

Graphing Parametric Equations  

Eliminating the Parameter  

Eliminating the Parameter - Example 1  

Differences in the Parametrization  

How to Parametrize a Curve  

Parametrization - Example 1  

Lines in Space  

Lines in Space - Example 1  

Lines in Space - Example 2  

Lines in Space - Symmetric Equations  

Lines in Space - Parametric to Symmetric  

Lines in Space - Symmetric to Parametric  

Lines in Space - Are These Lines Parallel?  

Section 9.6

Equations of Planes in Space  

Plane in Space - Extra Theory  

Standard vs General Form of a Plane  

Normal Vector of a Plane  

Equation of a Plane - Example 1  

Equation of a Plane - Example 2  

Equation of a Plane - Example 3  

Distance Between a Point and a Plane  

Distance Between a Point and a Plane - Example 1  

Distance Between a Point and a Line  

Distance Between a Point and a Line - Example 1  

Angle Between Two Planes  

Angle Between Two Planes - Example 1  

Line of Intersection of Two Planes  

Section 9.7

The Equation of the Sphere  

Introduction to Quadric Surfaces  

Quadric Surface: The Ellipsoid  

Quadric Surface: The Hyperboloid of Two Sheets  

Quadric Surface: The Hyperboloid of One Sheets  

Quadric Surface: The Elliptical Cone  

Quadric Surface: The Elliptical Paraboloid  

Quadric Surface: The Hyperbolic Paraboloid  




HW02 is due 01/29/2015 at 11:59pm CST



Section 10.1

Introduction to Vector Valued Functions  

The Domain of a Vector Valued Function  

Determine a Vector Valued Function from the Intersection of Two Surfaces  

Limits of Vector Valued Functions  

Section 10.2

The Derivative of a Vector Valued Function  

Properties of the Derivatives of Vector Valued Functions  

The Derivative of the Cross Product of Two Vector Valued Functions  

Determining Where a Space Curve is Smooth from a Vector Valued Function  

Determining Velocity, Speed, and Acceleration Using a Vector Valued Function  

Indefinite Integration of Vector Valued Functions  

Ex: Integrate a Vector Valued Function  

Indefinite Integration of Vector Valued Functions with Initial Conditions  

Ex: Find the Velocity and Position Vector Functions Given the Acceleration Vector Function  

Section 10.4

Determining the Unit Tangent Vector  

Ex: Find a Unit Tangent Vector to a Space Curve Given by a Vector Valued Function  

Determining the Unit Normal Vector  

Arc Length Using Parametric Equations  

Determining Arc Length of a Curve Defined by a Vector Valued Function  

Ex: Determine Arc Length of a Helix Given by a Vector Valued Function  

Determining Curvature of a Curve Defined by a Vector Valued Function  




HW03 is due 02/08/2015 at 11:59pm CST


Lecture Notes from Spring 2014

Lecture Notes for sections 9.1-9.5  

Lecture Notes for section 9.6  

Lecture Notes for sections 9.7 and 10.1  

Lecture Notes for section 10.2  

Lecture Notes for section 10.4  



Exam 1 is scheduled in room Math110, Mathematics Building on Wednesday February 11 at 5:30 pm. Exam 1 is comprehensive of Sections 9.5-9.7, 10.1, 10.2, 10.4 (HW02 and HW03). However to be prepared for the exam all the material reviewed in sections 9.1-9.4 (HW01) is necessary. To prepare for the exam review all 40 problems in HW02 and HW03. You need to know how to solve each of them without the use of the book, formula sheets and/or calculator. The exams consists of 6 questions and should be completed in 50 mins. A sample of how the exam is structured is given below. You need to bring with you a pencil, an eraser and student ID. A blank page at the end of the test is provided for scratch work, and other will be available if needed.

Exam 1 Solution Key  





MID TERM EXAM #1 ON FEBRUARY 11 at 5:30pm CST, ROOM MATH 110




Videos

Sections 11.1-11.3

Introduction to Functions of Two Variables  

Level Curves of Functions of Two Variables  

Limits of Functions of Two Variables  

First Order Partial Derivatives  

Implicit Differentiation of Functions of One Variable Using Partial Derivatives  

Second Order Partial Derivatives  




HW04 is due 02/22/2015 at 11:59pm CST



Sections 11.4-11.6

Differentials of Functions of Two Variables  

Applications of Differentials of Functions of Several Variables  

The Chain Rule for Functions of Two Variable with One Independent Variable  

Ex: Chain Rule - Function of Two Variables with One Independent Variable  

Partial Implicit Differentiation  

The Chain Rule for Functions of Two Variable with Two Independent Variables  

Ex: Chain Rule - Function of Two Variables with Two Independent Variable  

Ex: Chain Rule - Function of Two Variables with Three Independent Variable  

Directional Derivatives  

Ex: Find a Value of a Directional Derivative - f(x,y)=ln(x^2+y^2)  

The Gradient  

Ex: Find the Gradient of the Function f(x,y)=xy  

Ex: Use the Gradient to Find the Maximum Rate of Increase of f(x,y)=(4y^5)/x from a Point  

Determining a Unit Normal Vector to a Surface  

Verifying the Equation of a Tangent Plane to a Surface  

Determining the Equation of a Tangent Plane  

Ex 1: Find the Equation of a Tangent Plane to a Surface  

Ex 2: Find the Equation of a Tangent Plane to a Surface (Exponential)  




HW05 is due 03/01/2015 at 11:59pm CST



Sections 11.7 and 11.8

Determining the Relative Extrema of a Function of Two Variables  

Applications of Extrema of Functions of Two Variables I  

Applications of Extrema of Functions of Two Variables II  

Applications of Extrema of Functions of Two Variables III  

Absolute Extrema of Functions of Two Variables  

Lagrange Multipliers - Part 1  

Lagrange Multipliers - Part 2  

Maximize a Function of Two Variable Under a Constraint Using Lagrange Multipliers  




HW06 is due 03/08/2015 at 11:59pm CST






Lecture Notes from Spring 2014

Lecture Notes for sections 11.1  

Lecture Notes for section 11.2-11.3  

Lecture Notes for sections 11.4  

Lecture Notes for section 11.5 and 11.6  

Lecture Notes for section 11.6 and 11.7  

Lecture Notes for section 11.7  

Lecture Notes for section 11.8  



Exam 2 is scheduled in room Math110, Mathematics Building on Wednesday March 11 at 5:30 pm. Exam 2 is comprehensive of Sections 11.2-11.8 (HW04, HW05 and HW06). To prepare for the exam review all 50 problems in the homeworks. You need to know how to solve each of them without the use of the book, formula sheets and/or calculator. The exams consists of 6 questions and should be completed in 50 mins. A sample of how the exam is structured is given below. You need to bring with you a pencil, an eraser and student ID. A blank page at the end of the test is provided for scratch work, and other will be available if needed.

Exam 2 Solution Key  





MID TERM EXAM #2 ON MARCH 11 at 5:30pm CST, ROOM MATH 110




Videos

Sections 12.1-12.2

Introduction to Double Integrals and Volume  

Fubini's Theorem  

Ex: Evaluate a Double Integral to Determine Volume (Basic)  

Use a Double Integral to Find the Volume Under a Paraboloid Over a Rectangular Region  

Double Integrals and Volume over a General Region - Part 1  

Double Integrals and Volume over a General Region - Part 2  

Evaluating Double Integrals  

Ex: Double Integrals - Describe a Region of Integration (Triangle)  

Ex: Double Integrals - Describe a Region of Integration (Quadric)  

Ex: Double Integrals - Describe a Region of Integration (Advanced)  

Evaluate a Double Integral Over a General Region - f(x,y)=xy^2  

Evaluate a Double Integral Over a General Region with Substitution - f(x,y)=e^(x/y)  

Setting up a Double Integral Using Both Orders of Integration  

Double Integrals: Changing the Order of Integration - Example 1  

Double Integrals: Changing the Order of Integration - Example 2  




HW07 is due 03/29/2015 at 11:59pm CST



Sections 12.3-12.4

Introduction to Double Integrals in Polar Coordinates  

Double Integrals in Polar Coordinates - Example 1  

Double Integrals in Polar Coordinates - Example 2  

Area Using Double Integrals in Polar Coordinates - Example 1  

Area Using Double Integrals in Polar Coordinates - Example 2  

Double Integrals in Polar Form - Volume of a Half Sphere Over a Circle  

Surface Integrals with Explicit Surface Part 1  

Surface Integrals with Explicit Surface Part 2  




HW08 is due 04/05/2015 at 11:59pm CST



Sections 12.5 and 12.8

Triple Integrals and Volume - Part 1  

Triple Integrals and Volume - Part 2  

Triple Integrals and Volume - Part 3  

Changing the Order of Triple Integrals  

Introduction to Cylindrical Coordinates  

Triple Integrals Using Cylindrical Coordinates  

Triple Integral and Volume Using Cylindrical Coordinates  

Rewrite Triple Integrals Using Cylindrical Coordinates  

Introduction to Spherical Coordinates  

Triple Integral and Volume Using Spherical Coordinates  

Double Integral: Change of Variables Using the Jacobian  

Triple Integral: Change of Variables Using the Jacobian  




HW09 is due 04/12/2015 at 11:59pm CST



Sections 13.1 and 13.2

Introduction to Vector Fields  

The Divergence of a Vector Field  

The Curl of a Vector Field  

Defining a Smooth Parameterization of a Path  

Line Integrals in R^2  

Line Integrals in R^3  

Line Integral of Vector Fields  

Line Integrals in Differential Form  




HW10 is due 04/19/2015 at 11:59pm CST






Lecture Notes from Spring 2014

Lecture Notes for section 12.1  

Lecture Notes for sections 12.2 and 12.3  

Lecture Notes for sections 12.3 and 12.4  

Lecture Notes for sections 12.3-12.4 (review), 12.6-12.8 and 13.1  

Lecture Notes for sections 13.2 and 13.3  



Exam 3 is scheduled in room Math110, Mathematics Building on Wednesday April 22 at 5:30 pm. Exam 3 is comprehensive of Sections 12.1-12.5 12.7 13.1-13.2 (HW07, HW08, HW09 and HW10). To prepare for the exam review all problems in the homeworks. You need to know how to solve each of them without the use of the book, formula sheets and/or calculator. The exams consists of 8 questions and should be completed in 120 mins. A sample of how the exam is structured is given below. You need to bring with you a pencil, an eraser and student ID. A blank page at the end of the test is provided for scratch work, and other will be available if needed.

Exam 3 Solution Key  





MID TERM EXAM #3 ON APRIL 22 at 5:30pm CST, ROOM MATH 110




Videos

Sections 13.3-13.7

Determining the Potential Function of a Conservative Vector Field  

The Fundamental Theorem of Line Integrals - Part 1  

The Fundamental Theorem of Line Integrals - Part 2  

Fundamental Theorem of Line Integrals - Closed Path/Curve  

Green's Theorem - Part 1  

Green's Theorem - Part 2  

Determining Area using Line Integrals  

Surface Integral with Explicit Surface Part 1  

Surface Integral with Explicit Surface Part 2  

Surface Integral of a Vector Field - Part 1  

Surface Integral of a Vector Field - Part 2  

Stoke's Theorem - Part 1  

Stoke's Theorem - Part 2  

The Divergence Theorem - Part 1  

The Divergence Theorem - Part 2  




HW11 is due 05/05/2015 at 11:59pm CST






Lecture Notes from Spring 2014

Lecture Notes for sections 13.3 and 13.4  

Lecture Notes for sections 13.5-13.7  

Lecture Notes for sections 13.5-13.7 (review)  

Lecture Notes for Final Exam Review 1  

Lecture Notes for Final Exam Review 2  



The Final Exam is scheduled in room Math109, Mathematics Building, on Monday May 11 at 10:30 am. The Final Exam is comprehensive of Chapter 9-10-11-12-13. The exams consists of 12 multiple choice questions and 4 essay questions, and it should be completed in 2 hours and 30 mins. You need to bring with you a pencil, an eraser, your student ID, a blue book and an orange scantron. Samples for practicing for the finals can be find at the following link

Final Exam Practice Samples  

Also, in the last week of class SIAM and MAA student associations will sell the last two finals solution keys on the first floor of the Mathematics and Statistics building. These will help for extra practice, but they are neither required, nor provide additional material that has not been covered during the semester.





FINAL EXAM ON MAY 11 at 10:30am CST, ROOM MATH 109