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Course Info

  • APPLIED MATHEMATICS

APPLIED MATHEMATICS

About this Course

The content and material in this Massive Open Online Course "MAT538: Applied Mathematics" is designed to provide mathematical methods and solution techniques in the most apparent way for applications in science disciplines, geared towards beginning and advanced undergraduate students in applied sciences. The topics to be covered in this course include matrices and system of linear equations, vectors, partial differentiation, double integral and its applications, numerical methods, and Fourier series. The teaching task is formulated according to the syllabus and course learning outcomes, which include solving related mathematical problems using algebraic operations on matrices and vectors, partial derivative, and double integral. The students should be able to apply appropriate numerical methods in approximating integral and solution of initial value problems. To this end, students should start by making sure their ability to perform algebraic operations on matrices and vectors, as well as progress in identify numerical methods and the calculus of multivariate functions. To attract the interest of the student and facilitate reference to them, this course provides sufficient interesting activities and interactive quiz. Numerous current content such notes, videos, images, and examples are also provided to fulfil the students' needs. Throughout this course, students may ask any question in comment platform and the instructors will address the questions directly.

Course Syllabus

Syllabus Info
Matrices and System of Linear Equations
Basic concepts of matrices
Operations on matrices
Inverse of a matrix
Solution of system of linear equations

Vectors
Coordinate systems in two and three-dimensional space
Basic algebraic operations on vectors
Dot product of two vectors
Cross product of two vectors
Scalar triple product
Applications of vectors products

Partial Derivatives
Partial differentiation
The chain rule
Implicit differentiation
Relative maxima and minima of functions of two variables

Double Integrals
Double integrals over rectangular regions
Double integrals over nonrectangular regions
Double integrals in polar coordinates

Applications of Double Integrals
Area of the plane region
Volume of the solid bounded above by the surface and below by the region of integration
Center of mass of a lamina
Surface area

Numerical Methods
Trapezoidal rule and Simpson’s rule
Numerical solution of initial-value problems using Runge-Kutta method

Fourier Series
Odd and even functions
Periodic functions
Fourier series of periodic functions

Frequently Asked Questions

Course FAQ
Q1 : Why should I study Applied Mathematics?
A1 : In studying Applied Mathematics you will learn how to use a variety of mathematical and computational tools to solve problems in diverse fields, ranging from physics and engineering, to biology and medicine. You will develop the intellectual discipline and reasoning abilities needed to think through complex problems and develop sound practical solutions. A person with an education in Applied Mathematics is thus versatile and effective in meeting challenges in the workplace or industry.