Multiple Variable Calculus | Summer Semester 2019

Course Description

Description: This course is the third part in the sequence the calculus courses offered at IUT. The course covers infinite series, vectors and multiple variable functions. Multivariable Calculus is the extension of Calculus to more than one variable. That is, in single variable calculus we study functions of a single independent variable, and in multivariable calculus we study functions of two or more independent variables. These functions are interesting in their own right, but they at the same time they have a lot fo applications in the real world problems.

Course structure: The content of the course is organized into 5 (five) major units. The Midterm Exam covers the topics of the first two units. The Final Exam is intended to check the knowledge and ability of students on the last three units:

  1. Infinite Sequences & Series. Taylor Series.
  2. Vectors and Vector Calculus. Analytical Geometry.
  3. Partial Derivatives
  4. Double Integrals and Line Integrals in the Plane
  5. Triple Integrals and Surface Integrals in 3-Space

Prerequisite(s): Single Variable Calculus (1) (Mandatory)


Course Format

Course Schedule: this is a 4-week intensive course. The schedule of the lectures

    • Monday & Tuesday: 2 lectures per day
    • Wednesday: practical session
    • Thursday & Friday: 2 lectures per day
    • Saturday: practical session

Attendance: It is mandatory to attend at least 20 (out of 28) lectures. The attendance lists are updated manually every day.

Homework and Quiz: there are 5 short quizzes and 7 homework assignments will be taken. The schedule of assignments

    • Monday & Thursday: homework assignments should be submitted;
    • Tuesday & Friday: homework exercises are assigned;
    • Tuesday & Friday: short quizzes are assigned during the lectures;

2 (two) worst quiz and homework results will be dropped to allow students to be absent.

Learning Materials

Tentative Course Outline

Lecture 3 | Convergence Test of Infinite Series

  • 3.1 | Alternating Series. Absolute convergence
  • 3.2 | Comparison & Limit Comparison Tests
  • 3.3 | Ratio Test of Convergence
  • 3.4 | Root Test of Convergence
Lec 3.1
Lec 3.2
Lec 3.3
Lec 3.4

Lecture 4 | Power Series

  • 4.1 | Power Series: Interval & Radius of Convergence
  • 4.2 | Taylor Series. Maclaurin Series
  • 4.3 | Applications of Taylor Series
Lec 4.1
Lec 4.2
Lec 4.3

Lecture 5 | Intro to Vectors in Higher Dimensions

  • 5.1 | Points in 3D
  • 5.2 | Add & subtract vectors geometrically
  • 5.3 | Create Position Vectors
  • 5.4 | 4 Operations with Vectors
  • 5.5 | Make Unit Vectors. Standard Unit Vectors.
Lec 5.1
Lec 5.2
Lec 5.3
Lec 5.4
Lec 5.5

Lecture 6 | Operations with Vectors

  • 6.1 | Dot product
  • 6.2 | Angles between two vectors
  • 6.3 | Projection vectors
  • 6.4 | Cross product. Its geometric meaning.
  • 6.5 | Equations on lines
Lec 6.1
Lec 6.2
Lec 6.3
Lec 6.4
Lec 6.5

Lecture 7 | Analytic Geometry

  • 7.1 | Dot product vs. Cross product
  • 7.2 | Vector equation of Planes
  • 7.3 | Scalar vs. Vector equation of planes
  • 7.4 | Planes through 3 points
  • 7.5 | Distance between a point and a plane
Lec 7.1
Lec 7.2
Lec 7.3
Lec 7.4
Lec 7.5

Lecture 7.1 | Intro to Vector Functions

  • 7.6 | Intro to Vector Functions
  • 7.7 | Derivatives of Vector Functions
  • 7.8 | Tangent Vector and Tangent Line
Lec 7.6
Lec 7.7
Lec 7.8

Exam Day

mid-term exam

review.Part 1 | Infinite Series

review.Part 2 | Vectors. Analytic Geometry

review.part 1
review.part 2

Lecture 8 | Arc Length & Curvature

    • 8.1 | Arc Length of a Vector Function
    • 8.2 | Tangent, Normal & Binormal Vectors
    • 8.3 | Curvature
    • 8.4 | Calculating the Curvature
Lec 8.1
Lec 8.2
Lec 8.3
Lec 8.4

Lecture 9 | Partial Derivatives

    • 9.1 | Intro to Partial Derivatives
    • 9.2 | Tangent Planes
    • 9.3 | Multivariable Chain Rule
    • 9.4 | Directional Derivatives
Lec 9.1
Lec 9.2
Lec 9.3
Lec 9.4

Lecture 10 | Gradient Vector

    • 10.1| Gradient Vector shows the Steepest Descent
    • 10.2| Max/Min values. Find the Saddle points.
Lec 10.1
Lec 10.2

Lecture 11 | Multiple Integration

    • 11.1 | Double Integral over Rectangular Areas
    • 11.2 | Double integral over general areas
    • 11.3 | Double integrals in polar coordinates
Lec 11.1
Lec 11.2
Lec 11.3

Lecture 12 | Multiple Integration (continued)

    • 12.1 | Surface Area using Double Integrals
    • 12.2 | Jacobian 2D: change of variables
    • 12.3 | Triple integration
    • 12.4 | Jacobian 3D: change of variables
Lec 12.1
Lec 12.2
Lec 12.3
Lec 12.4

Lecture 13 | Line Integrals

    • 13.1 | Line Integrals of Scalar Functions
    • 13.2 | intro to Vector Fields
    • 13.3 | Line Integrals in Vector Fields
    • 13.4 | Conservative Vector Fields
Lec 13.1
Lec 13.2
Lec 13.3

Lecture 14 | Final Review

Exam Day

final exam