Math 2450 Honors 01 Spring 2023 Professor: Eugenio Aulisa Office: Math 226 email: eugenio.aulisa@ttu.edu Phone: 806-834-6684 Meetings: TR at 12:30-2:20 in MATH 115 Office Hours: TR 9:00-11:00 Math 226 or daily using the WebWork Email Tool

# Calculus III with applications

## Textbook

Calculus
K. Smith, M. Strauss and M. Toda, Kendall Hunt, 7th National Edition.

## Syllabus

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

The following link provides a tutorial on how to use WeBWork

Introduction to 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.

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: Thur, Feb 9 12:30-2:20pm MATH 115 worth 15% of the final grade Exam #2: Thur, Mar 9, 12:30-2:20pm MATH 115 worth 20% of the final grade Exam #3: Thur, Apr 13, 13:30-2:20pm MATH 115 worth 20% of the final grade Final Exam: Fri, May 5, 4:30-7:00pm MATH 115 worth 30% of the final grade

Overall grade: a perfect score in all tests and homeworks results in a overall grade of 105% .

Exam Policies

Students are expected to take the midterm exams and the final exam as scheduled. There are no make ups for the examinations, except for reasons of illness, stated in writing by a medical doctor, observance of a religious holiday, university justified field trips or work conflicts. Usually, no other reasons are accepted (events, plane tickets, weddings, ...).

Class Policies

If Texas Tech University campus operations are required to change because of health concerns related to the COVID-19 pandemic, it is possible that this course will move to a fully online delivery format. Should that be necessary, students will need to have access to a webcam and microphone for remote delivery of the class.

## Class Time Table With Short Videos by Topic

Review of Sections 9.1-9.4

9.1, Introduction to Vectors (2D)

9.1, Vector Operations (2D)

9.1, The Unit Vector (2D)

9.2, Plotting Points in 3D

9.2, The Equations of the Coordinate Planes

9.2, Cylindrical Surfaces

9.2, Vectors in Space

9.2, The Equation of the Sphere

9.3, Ex. Dot Product of Vectors - 3D

9.3, Ex: Find the Angle Between Two Vectors in Three Dimensions

9.3, Ex: Vector Projection in Three Dimensions

9.4, Vector Cross Product

9.4, Ex: Find the Cross Product of Two Vectors

9.4, Ex: Find Two Unit Vectors Orthogonal to Two Given Vectors

9.4, Ex: Properties of Cross Products - Cross Product of a Sum and Difference

9.4, Ex: Find the Area of a Triangle Using Vectors - 3D

Complete HW01 by Tue Jan 24

Sections 9.5-9.7

9.5, Introduction to Parametric Equations

9.5, Converting Parametric Equation to Rectangular Form

9.5, Parametric Equations of a Circle

9.5, Ex: Find Parametric Equations For Ellipse Using Sine And Cosine From a Graph

9.5, Parametric Equations of a Line in 3D

9.5, Vector Equation, Parametric Equations and Symmetric Equation Passing Through Two Points (3D)

9.6, Determining the Equation of a Plane Using a Normal Vector

9.6, Graphing a Plane Using Intercepts

9.6, Ex: Find an Equation of a Plane Containing a Given Point and the Intersection of Two Planes

9.6, Ex: Find the Parametric Equations of the Line of Intersection of Two Planes Using Vectors

9.6, Ex: Find the Equation of a Plane Given Three Points in the Plane Using Vectors

9.6, Find an Equation of a Plane Containing a Line and Orthogonal to a Given Plane

9.6, Determining the Distance Between a Plane and a Point

9.6, Determining the Distance Between a Line and a Point

9.7, The Equation of the Sphere

9.7, Quadric Surface: The Hyperboloid of Two Sheets

9.7, Quadric Surface: The Hyperboloid of One Sheets

9.7, Quadric Surface: The Elliptical Cone

9.7, Quadric Surface: The Elliptical Paraboloid

9.7, Quadric Surface: The Hyperbolic Paraboloid

Complete HW02 by Tue Jan 31

Sections 10.1-10.2, 10.4

10.1, Introduction to Vector Valued Functions

10.1, The Domain of a Vector Valued Function

10.1, Determine a Vector Valued Function from the Intersection of Two Surfaces

10.1, Limits of Vector Valued Functions

10.2, The Derivative of a Vector Valued Function

10.2, Properties of the Derivatives of Vector Valued Functions

10.2, The Derivative of the Cross Product of Two Vector Valued Functions

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

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

10.2, Indefinite Integration of Vector Valued Functions

10.2, Ex: Integrate a Vector Valued Function

10.2, Indefinite Integration of Vector Valued Functions with Initial Conditions

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

10.4, Determining the Unit Tangent Vector

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

10.4, Determining the Unit Normal Vector

10.4, Arc Length Using Parametric Equations

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

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

10.4, Determining Curvature of a Curve Defined by a Vector Valued Function

Complete HW03 by Tue Feb 7

### Exam 1 on Thur Feb 9

Sections 11.1-11.3

11.1, Introduction to Functions of Two Variables

11.1, Level Curves of Functions of Two Variables

11.2, Limits of Functions of Two Variables

11.3, First Order Partial Derivatives

11.3, Implicit Differentiation of Functions of One Variable Using Partial Derivatives

11.3, Second Order Partial Derivatives

Complete HW04 by Tue Feb 21

Sections 11.4-11.6

11.4, Differentials of Functions of Two Variables

11.4, Applications of Differentials of Functions of Several Variables

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

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

11.5, Partial Implicit Differentiation

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

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

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

11.6, Directional Derivatives

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

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

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

11.6, Determining a Unit Normal Vector to a Surface

11.6, Verifying the Equation of a Tangent Plane to a Surface

11.6, Determining the Equation of a Tangent Plane

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

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

Complete HW05 by Tue Feb 28

Sections 11.7-11.8

11.7, Determining the Relative Extrema of a Function of Two Variables

11.7, Applications of Extrema of Functions of Two Variables I

11.7, Applications of Extrema of Functions of Two Variables II

11.7, Applications of Extrema of Functions of Two Variables III

11.7, Absolute Extrema of Functions of Two Variables

11.8, Lagrange Multipliers - Part 1

11.8, Lagrange Multipliers - Part 2

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

Complete HW06 by Tue Mar 7

### Exam 2 on Thur Mar 9

Sections 12.1-12.2

12.1, Introduction to Double Integrals and Volume

12.1, Fubini's Theorem

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

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

12.2, Double Integrals and Volume over a General Region - Part 1

12.2, Double Integrals and Volume over a General Region - Part 2

12.2, Evaluating Double Integrals

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

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

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

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

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

12.2, Setting up a Double Integral Using Both Orders of Integration

12.2, Double Integrals: Changing the Order of Integration - Example 1

12.2, Double Integrals: Changing the Order of Integration - Example 2

Complete HW07 by Tue Mar 28

Sections 12.3-12.4

12.3, Introduction to Double Integrals in Polar Coordinates

12.3, Double Integrals in Polar Coordinates - Example 1

12.3, Double Integrals in Polar Coordinates - Example 2

12.3, Area Using Double Integrals in Polar Coordinates - Example 1

12.3, Area Using Double Integrals in Polar Coordinates - Example 2

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

12.4, Surface Integrals with Explicit Surface Part 1

12.4, Surface Integrals with Explicit Surface Part 2

Complete HW08 by Tue Apr 4

Sections 12.5, 12.7-12.8

12.5, Triple Integrals and Volume - Part 1

12.5, Triple Integrals and Volume - Part 2

12.5, Triple Integrals and Volume - Part 3

12.5, Changing the Order of Triple Integrals

12.7, Introduction to Cylindrical Coordinates

12.7, Triple Integrals Using Cylindrical Coordinates

12.7, Triple Integral and Volume Using Cylindrical Coordinates

12.7, Rewrite Triple Integrals Using Cylindrical Coordinates

12.7, Introduction to Spherical Coordinates

12.7, Triple Integral and Volume Using Spherical Coordinates

12.8, Double Integral: Change of Variables Using the Jacobian

12.8, Triple Integral: Change of Variables Using the Jacobian

Complete HW09 by Tue Apr 11

### Exam 3 on Thur Apr 13

Sections 13.1-13.4

13.1, Introduction to Vector Fields

13.1, The Divergence of a Vector Field

13.1, The Curl of a Vector Field

13.2, Defining a Smooth Parameterization of a Path

13.2, Line Integrals in R^2

13.2, Line Integrals in R^3

13.2, Line Integral of Vector Fields

13.2, Line Integrals in Differential Form

13.3, Determining the Potential Function of a Conservative Vector Field

13.3, The Fundamental Theorem of Line Integrals - Part 1

13.3, The Fundamental Theorem of Line Integrals - Part 2

13.3, Fundamental Theorem of Line Integrals - Closed Path/Curve

13.4, Green's Theorem - Part 1

13.4, Green's Theorem - Part 2

13.4, Determining Area using Line Integrals

Complete HW10 by Tue Apr 25

Sections 13.5 - 13.7

13.5, Surface Integral with Explicit Surface Part 1

13.5, Surface Integral with Explicit Surface Part 2

13.5, Surface Integral of a Vector Field - Part 1

13.5, Surface Integral of a Vector Field - Part 2

13.6, Stoke's Theorem - Part 1

13.6, Stoke's Theorem - Part 2

13.7, The Divergence Theorem - Part 1

13.7, The Divergence Theorem - Part 2

Complete HW011 by Tue May 2