Math 2450 H01 Fall 2024 |
Professor: Eugenio Aulisa Phone: 806-834-6684 Meetings: MWF at 11:40-12:50 in MATH 012 Office Hours: MWF 1:00-2:00pm Math 226
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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, Sep 18 11:40am-12:50pm
MATH 012
worth 15% of the final grade
Exam #2: Wed, Oct 16 11:40am-12:50pm
MATH 012
worth 20% of the final grade
Exam #3: Wed, Nov 13 11:40am-12:50pm
MATH 012
worth 20% of the final grade
Final Exam: Thu, Dec 5, 1:30pm-4:00pm
MATH 012
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
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
Classes start and end always on time. Students are not allowed to leave the class before the end of the hour without authorization. During class time it is not allowed to text, chat or sleep. Please put in silent mode all your electronic devices.
9.1, Introduction to Vectors (2D)
9.2, The Equations of the Coordinate Planes
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, 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
9.5, 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, Introduction to Quadric Surfaces
9.7, Quadric Surface: The Ellipsoid
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
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
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
11.4, 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, 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)
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
12.1, Introduction to Double Integrals and Volume
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
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
12.5, 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
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 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
13.5, 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
