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

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.

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% .

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

Syllabus

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

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.

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 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

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)

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

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

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

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