Math 2450 Sec. 105 Spring 2017 |
Professor: Eugenio Aulisa email: eugenio.aulisa@ttu.edu Meetings: WF at 1:00pm-2:50pm in room MCOM 75 Office Hours: WF 9:00am-11:00am or by appointment in room 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: Fri, Feb 17, 2:00-2:50
room MCOM 75
worth 10% of the final grade
Exam #2: Wed, Mar 8, 2:00-2:50
room MCOM 75
worth 15% of the final grade
Exam #3: Wed, Apr 12, 2:00-2:50
room MCOM 75
worth 15% of the final grade
Exam #4: Wed, May 3, 2:00-2:50
room MCOM 75
worth 15% of the final grade
Final Exam: Mon, May 15, 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
Use of calculators and formula sheets in all the exams is not permitted. Electronic devices which can store formulas, including cell phones, should be turned off and stored during the exams.
Attendance and Class Policies
Attendance is mandatory! Students with less/equal than 4 missed classes for the entire semester will receive a bonus of 4% on the final grade. Students with more than 4 and less/equal than 8 missed classes for the entire semester will receive a bonus of 2% on the final grade. Students with more than 8 and less/equal than 12 missed classes will receive no bonus. Students with more than 12 missed classes will receive a penalty of 2% on the final grade. 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. I expect that students will read each section of the textbook in advance of the lecture. You must also attend every class. If you miss a class, it is your responsibility to find out what you missed (announcements, assignments, notes,...).
Adding and Subtracting Vectors
Magnitude of a Vector - Example 1
Using Dot Product to Find the Angle Between Two Vectors
Finding Angles Using Dot Products - Example 1
Vector Projections - Example 1
Vector Cross Product - Example 1
Vector Cross Product - Extra Theory
Eliminating the Parameter - Example 1
Differences in the Parametrization
Lines in Space - Symmetric Equations
Lines in Space - Parametric to Symmetric
Lines in Space - Symmetric to Parametric
Lines in Space - Are These Lines Parallel?
Standard vs General Form 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 - Example 1
Line of Intersection of Two Planes
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
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
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
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
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
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
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)
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
Maximize a Function of Two Variable Under a Constraint Using Lagrange Multipliers
Introduction to Double Integrals and Volume
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
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
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
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
The Divergence of a Vector Field
Defining a Smooth Parameterization of a Path
Line Integral of Vector Fields
Line Integrals in Differential Form
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
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
The Divergence Theorem - Part 1
The Divergence Theorem - Part 2
Lecture Notes for sections 9.1-9.5
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
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 12.4
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