Math 2450 Honors 01

Spring 2020

 

 

Professor: Eugenio Aulisa
Office:Online

email: eugenio.aulisa@ttu.edu

Asynchronous method

Office hours: daily by email communication and
on TR 12:00-2:00pm on Teams for face-to-face video communication and chat

 


Because of the COVID-19 Texas Tech contingency plan, this is now a distance class

Please review the new class website and syllabus.

The old face to face class website and syllabus can be found at

face to face class old website


Calculus III with applications


Textbook

Calculus
K. Smith, M. Strauss and M. Toda, Kendall Hunt, 7th 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: Thu, Feb 13, 12:30-1:50 room MATH 115 worth 15% of the final grade
Exam #2: Thu, Mar 12, 12:30-1:50 room MATH 115 worth 20% of the final grade
Exam #3: Thu, Apr 16, 12:30-1:50 On Webwork worth 20% of the final grade
Final Exam: Tue, May 12, 10:30-1:00 On Webwork 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 Policies


See below some general exam information and rules:

1) Students are expected to take the third and final exam on Webwork as scheduled.
2) Exam 3 will cover chapter 12 (HW07-HW09), the Final Exam is comprehensive and it covers chapters 9 to 13 (HW01-HW11).
3) In each exam there will be several multiple choice questions.
4) The correct answer is ALWAYS among the 5 choices: I never use the "None of the above" choice.
5) You will have only ONE ATTEMPT to get it right.
6) To submit your work, you need to press the "Grade Test" button at the very bottom of the page . After you press it, you cannot change any of your answers. Be sure to complete all your work before pressing it.
7) The "Grade Test" button should be pressed before the due date otherwise a 0% score will be recorded.
8) The test score and solution keys will be available after 2-3 days
9) If you experience any technical problem during the exam, DO NOT WAIT, but immediately notify me during or after the test. When you notify me, be sure to explain carefully what happened, and be ready to take action. There is no much to do for me if you contact me (OR IF YOU TAKE ACTION) after days have passed.




Class Policies

Students with less/equal than 4 missed classes up to March 14th will receive 4% extra credit on the final grade. This is now a distance class, all the students enrolled 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. The instructor expects for the student to read each section of the textbook and watch the videos on the class website before attempting to solve the homework problems. A detailed timeline for the rest of the semester is given below.


Syllabus

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

Updated Syllabus for Online Class  


Class Material and Timeline



CHAPTER 12, MULTIPLE INTEGRATION



SECTIONS 12.1 and 12.2, HW07

12.1 DOUBLE INTEGRAL OVER RECTANGULAR REGIONS

Book
Definition of Double Integral, Properties of Double Integrals, Volume Interpretation (ex.1), Iterated Integration (ex.2, ex.4)

Videos

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  


12.2 DOUBLE INTEGRAL OVER NONRECTANGULAR REGIONS

Book
Double Integrals over Type I and II Regions (ex.2), More on Area and Volume (ex.3, ex.4),
Choosing the Order of Integration in a Double Integral (ex.5, ex.6)

Notes

Review of section 12.2  


Videos

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 03/31/2020 at 11:59pm CST



SECTIONS 12.3-12.5, HW08

12.3 DOUBLE INTEGRALS IN POLAR COORDINATES

Book
Change of Variables in Polar Form, Area and Volume in Polar Form (ex.1, ex.2, ex.3, ex.5)

Notes

Review of section 12.3  


Videos

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  


12.4 SURFACE AREA

Book
Definition of Surface Area (ex.1, ex.2), Surface Area Projections (ex.3)

Notes

Review of section 12.4  


Videos

Surface Integrals with Explicit Surface Part 1  

Surface Integrals with Explicit Surface Part 2  


12.5 TRIPLE INTEGRALS

Book
Definition of Triple Integrals, Iterated Integration (ex.1, ex.2), Volume by Triple Integration (ex.3, ex.4)

Notes

Review of section 12.5  


Videos

Triple Integrals and Volume - Part 1  

Triple Integrals and Volume - Part 2  

Triple Integrals and Volume - Part 3  

Changing the Order of Triple Integrals  




HW08 is due 04/07/2020 at 11:59pm CST



SECTIONS 12.7-12.8, HW09

12.7 CYLINDRICAL AND SPHERICAL COORDINATES

Book
Cylindrical Coordinates (ex.1), Integration in Cylindrical Coordinates (ex.2, ex.3)
Spherical Coordinates (ex.4), Integration in Spherical Coordinates (ex.5, ex.7)

Notes

Review of section 12.7  


Videos

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  



12.8 JACOBIAN: CHANGE OF VARIABLES

Book
Change of Variables in Double Integrals (ex1, ex.3, ex.4),Change of Variables in Triple Integrals (ex.6)

Notes

Review of section 12.8  


Videos

Double Integral: Change of Variables Using the Jacobian  

Triple Integral: Change of Variables Using the Jacobian  




HW09 is due 04/14/2020 at 11:59pm CST






Take Exam 3 on Thu 04/16/2020 at 12:30pm CST



CHAPTER 13, VECTOR ANALYSIS


SECTIONS 13.1-13.4, HW10

13.1 VECTOR FIELDS, DIVERGENCE AND CURL

Book
Definition of Vector Field (ex.1), Divergence (ex.2) Curl(ex.3, ex.4)

Notes

Review of section 13.1  


Videos

Introduction to Vector Fields  

The Divergence of a Vector Field  

The Curl of a Vector Field  


13.2 LINE INTEGRALS

Book
Definition of Line Integral (ex.1, ex.2), Line Integral of Vector Fields (ex.4, ex.5, ex.6)

Notes

Review of section 13.2  


Videos

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  


13.3 THE FUNDAMENTAL THEOREM AND PATH INDEPENDENCE

Book
Fundamental Theorem of Line Integrals (ex.1), Conservative Vector Fields (ex.2, ex.3, ex.4, ex.5, ex.6)

Notes

Review of section 13.3  


Videos

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  


13.4 GREEN'S THEOREM

Book
Green's Theorem (ex.1, ex.2), Area as a Line Integral (ex.3)

Notes

Review of section 13.4  


Videos

Green's Theorem - Part 1  

Green's Theorem - Part 2  

Determining Area using Line Integrals  




HW10 is due 04/28/2020 at 11:59pm CST



SECTIONS 13.5-13.7, HW11

13.5 SURFACE INTEGRALS

Book
Surface Integrals (ex.1, ex.2), Flux Integrals (ex.3, ex.4)

Notes

Review of section 13.5  


Videos

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  


13.6 STOKES' THEOREM

Book
Stokes' Theorem (ex.1, ex.2, ex.3)

Notes

Review of section 13.6  


Videos

Stoke's Theorem - Part 1  

Stoke's Theorem - Part 2  


13.7 DIVERGENCE' THEOREM

Book
The Divergence Theorem (ex.1, ex.2, ex.3)

Notes

Review of section 13.7  


Videos

The Divergence Theorem - Part 1  

The Divergence Theorem - Part 2  




HW11 is due 05/05/2020 at 11:59pm CST






TAKE The Final Exam on Tue 05/12/2020 at 10:30am CST













Supplemental Videos and Class Material



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  

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  







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  







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  

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)  

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  







Class Lecture Notes

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 sections 10.1 and 10.2  

Lecture Notes for section 10.2  

Lecture Notes for section 10.4  

Lecture Notes for section 11.1  

Lecture Notes for sections 11.2 and 11.3  

Lecture Notes for section 11.4  

Lecture Notes for sections 11.5 and 11.6  

Lecture Notes for sections 11.6 and 11.7  

Lecture Notes for section 11.7  

Lecture Notes for section 11.8  

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  

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  








Class lecture videos, Spring 2015

from Magdalena Toda

TTU Math2450 Calculus3 Sec 9.5-9 6  

TTU Math2450 Calculus3 Sec 9.7  

TTU Math2450 Calculus3 Sec 10.1  

TTU Math2450 Calculus3 Sec 10.2 and 10.4 part 1  

TTU Math2450 Calculus3 Sec 10.2 and 10.4 part 2  

TTU Math2450 Calculus3 Sec 10.2 and 10.4 part 3  

TTU Math2450 Calculus3 Sec 11.1 and 11.2  

TTU Math2450 Calculus3 Sec 11.2 and 11.3  

TTU Math2450 Calculus3 Sec 11.4 part 1  

TTU Math2450 Calculus3 Sec 11.4 and 11.5  

TTU Math2450 Calculus3 Sec 11.5 and 11.6  

TTU Math2450 Calculus3 Sec 11.6 and 11.7  

TTU Math2450 Calculus3 Sec 11.7 and 11.8  

TTU Math2450 Calculus3 Sec 12.1 and 12.2  

TTU Math2450 Calculus3 Sec 12.3 (large board)  

TTU Math2450 Calculus3 Sec 12.3 (Substitute)  

TTU Math2450 Calculus3 Sec 12.4  

TTU Math2450 Calculus3 Sec 12.5  

TTU Math2450 Calculus3 Sec 12.6 - 12.7  

TTU Math2450 Calculus3 Sec 12.7 - 12.8  

TTU Math2450 Calculus3 chap. 10-11-12 review  

TTU Math2450 Calculus3 Sec 13.1 - 13.2  

TTU Math2450 Calculus3 Sec 13.2 - 13.3  

TTU Math2450 Calculus3 Secs 13.3  

TTU Math2450 Calculus3 Secs 13.4 -13.5  

TTU Math2450 Calculus3 Secs 13.6 - 13.7