The Hong Kong University of Science and Technology

Vector Calculus for Engineers

This course is part of Mathematics for Engineers Specialization

Taught in English

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Jeffrey R. Chasnov

Instructor: Jeffrey R. Chasnov

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Course

Gain insight into a topic and learn the fundamentals

4.8

(1,319 reviews)

|

97%

Beginner level

Recommended experience

30 hours (approximately)
Flexible schedule
Learn at your own pace

What you'll learn

  • Vectors, the dot product and cross product

  • The gradient, divergence, curl, and Laplacian

  • Multivariable integration, polar, cylindrical and spherical coordinates

  • Line integrals, surface integrals, the gradient theorem, the divergence theorem and Stokes' theorem

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Assessments

25 quizzes

Course

Gain insight into a topic and learn the fundamentals

4.8

(1,319 reviews)

|

97%

Beginner level

Recommended experience

30 hours (approximately)
Flexible schedule
Learn at your own pace

See how employees at top companies are mastering in-demand skills

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This course is part of the Mathematics for Engineers Specialization
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There are 5 modules in this course

Vectors are mathematical constructs that have both length and direction. We define vectors and show how to add and subtract them, and how to multiply them using the dot and cross products. We apply vectors to study the analytical geometry of lines and planes, and define the Kronecker delta and the Levi-Civita symbol to prove vector identities. Finally, we define the important concepts of scalar and vector fields.

What's included

15 videos28 readings6 quizzes2 plugins

Scalar and vector fields can be differentiated. We define the partial derivative and derive the method of least squares as a minimization problem. We learn how to use the chain rule for a function of several variables, and derive the triple product rule used in chemical engineering. We define the gradient, divergence, curl, and Laplacian. We learn some useful vector calculus identities and derive them using the Kronecker delta and Levi-Civita symbol. We use vector identities to derive the electromagnetic wave equation from Maxwell's equation in free space. Electromagnetic waves form the basis of all modern communication technologies.

What's included

13 videos15 readings5 quizzes

Integration can be extended to functions of several variables. We learn how to perform double and triple integrals. We define curvilinear coordinates, namely polar coordinates in two dimensions, and cylindrical and spherical coordinates in three dimensions, and use them to simplify problems with circular, cylindrical or spherical symmetry. We learn how to write differential operators in curvilinear coordinates and how to change variables in multidimensional integrals using the Jacobian of the transformation.

What's included

12 videos24 readings5 quizzes

Scalar or vector fields can be integrated over curves or surfaces. We learn how to take the line integral of a scalar field and use the line integral to compute arc lengths. We then learn how to take line integrals of vector fields by taking the dot product of the vector field with tangent unit vectors to the curve. Consideration of the line integral of a force field results in the work-energy theorem. Next, we learn how to take the surface integral of a scalar field and use the surface integral to compute surface areas. We then learn how to take the surface integral of a vector field by taking the dot product of the vector field with the normal unit vector to the surface. The surface integral of a velocity field is used to define the mass flux of a fluid through a surface.

What's included

9 videos11 readings4 quizzes

The fundamental theorem of calculus links integration with differentiation. Here, we learn the related fundamental theorems of vector calculus. These include the gradient theorem, the divergence theorem, and Stokes' theorem. We show how these theorems are used to derive continuity equations and the law of conservation of energy. We show how to define the divergence and curl in coordinate-free form, and convert the integral version of Maxwell's equations into differential form.

What's included

13 videos21 readings5 quizzes

Instructor

Instructor ratings
4.8 (414 ratings)
Jeffrey R. Chasnov

Top Instructor

The Hong Kong University of Science and Technology
16 Courses204,041 learners

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