Section
General
- Welcome to the Course
Welcome to MC Engineering Mathematics 1, a foundational course designed to strengthen your mathematical understanding and analytical skills for solving real-world engineering problems. This course introduces the fundamental principles and concepts in algebra and calculus, which are essential tools in engineering.
This micro-credential offers three modules. Module 1 introduces the fundamental principles and concepts in algebra that cover complex numbers, matrices, and vectors. In Module 2, you’ll explore Calculus that involves differentiation and integration techniques for single-variable functions. The final module 3 covers partial derivatives, helping you analyze engineering problems involving multivariable functions.
You will learn through blended learning, combining self-paced online lessons, guided practice, and interactive assessments. Upon completing each module, you’ll earn a Micro E-Certificate, and a Macro E-Certificate when all three modules are completed.
This micro-credential is ideal for:
- Engineering undergraduates who want to master essential mathematics concepts.
- Polytechnic or diploma students planning to pursue engineering degrees.
- Working professionals in technical roles seeking to strengthen their foundation.
- STEM educators who want to integrate applied mathematics into their teaching.
By enrolling in this course, you will:
- Strengthen your understanding of key topics: complex numbers, matrices, vectors, differentiation, integration, partial derivatives.
- Gain strong problem-solving skills for engineering applications.
- Earn stackable micro-credentials for academic progression.
- Learn through flexible blended learning with quizzes & hands-on tasks.
- Boost your career and academic profile.
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Apply concepts of complex numbers, matrices, and vectors in engineering problems.
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Apply concepts of differentiation and integration in engineering problems.
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Analyze and solve problems involving partial derivatives in engineering contexts.
Upon successful completion of this course, learners will be able to:
- Module 1 - Complex numbers, matrices, vectors.
- Module 2 - Techniques of differentiation & integration and its application.
- Module 3 - Partial derivative techniques and its application.
Macro E-Certificate is awarded upon completing all three modules.
- Complete each module — start with Basic Algebra, then Differentiation & Integration, and finally Partial Derivatives.
- Watch the teaching videos provided for each subtopic.
- Download and review lecture notes for deeper understanding.
- Complete quizzes or exercises after each module to assess your knowledge.
- Engage in discussions or forums if available to clarify doubts and share insights.
Instructors
DR. NAJAH GHAZALI
DR. NURHIDAYAH BINTI OMAR
DR. ZAINAB BINTI YAHYA
DR. BILIANA BINTI BIDIN
DR. NOR HAZADURA BINTI HAMZAH
DR. NUR 'AFIFAH BINTI RUSDI
ELYANA BINTI SAKIB
ALEZAR BINTI MAT YA'ACOB
Instructors
DR. NAJAH GHAZALI
DR. NURHIDAYAH BINTI OMAR
DR. ZAINAB BINTI YAHYA
DR. BILIANA BINTI BIDIN
DR. NOR HAZADURA BINTI HAMZAH
DR. NUR 'AFIFAH BINTI RUSDI
ELYANA BINTI SAKIB
DR. WAN SUHANA WAN DAUD
ALEZAR BINTI MAT YA'ACOB
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- 1
COMPLEX NUMBER
Instructors
ELYANA BINTI SAKIB
- Learning Outcome: At the end of this module, student should be able to:
- Define a complex number.
- Identify the real and imaginary part of the complex number.
- Explain the meaning of the imaginary unit, \(i\) and use the relation of
- Learning Outcome: At the end of this module, student should be able to represent complex numbers on the complex plane using Cartesian coordinates.
- Learning Outcome: At the end of this module, student should be able to perform basic operations on complex numbers in algebraic form
- Learning Outcome: At the end of this module, student should be able to:
- Define the modulus (r) and the argument (θ) of a complex number.
- Convert a complex number between algebraic form \(a+bi\) and polar form \(r(\cos\theta + i\sin\theta)\).
- Use polar form to carry out multiplication and division of complex numbers efficiently by combining moduli and adding/subtracting arguments.
- Learning Outcome: At the end of this module, student should be able to:
- State and interpret Euler’s formula \(e^{i\theta}=\cos\theta + i\sin\theta\).
- Express a complex number in exponential form \(re^{i\theta}\) and convert back to polar/algebraic forms.
- Compute complex roots using the exponential form.
- Learning Outcome: At the end of this module, student should be able to:
- State De Moivre’s Theorem for integer powers:
(\cos\theta + i\sin\theta)^n = \cos(n\theta) + i\sin(n\theta). - Apply De Moivre’s Theorem to compute powers of complex numbers expressed in polar or exponential form.
- Use the theorem to expand trigonometric expressions .
- Find the n-th roots of complex numbers and list all distinct roots using the formula for roots in polar/exponential form.
- State De Moivre’s Theorem for integer powers:
- Learning Outcome: At the end of this module, student should be able to:
- State the general formula for the n-th roots of a complex number expressed in polar form.
- Compute the modulus and argument of a given complex number and use them to find its principal n-th root.
- Convert each root from exponential/polar form back to algebraic form \(a+bi\) and simplify where appropriate.
- Learning Outcome: At the end of this module, student should be able to
- Describe the locus geomatrically.
- Derive the equation of locus.
- Calculate the voltage using the Ohm's Law.
- 2
MATRICES
Instructors
DR. BILIANA BINTI BIDIN
- Learning Outcome: By the end of this subtopic, students will be able to (1) Define the concept of a matrix and its notation. (2) Identify the order (size) of a matrix. (3) Describe the basic structure and elements of a matrix.
- Learning Outcome: By the end of this subtopic, students will be able to (1) Classify matrices according to their types (e.g., square, diagonal, identity, zero, symmetric). (2) Distinguish between row, column, and rectangular matrices. (3) Determine the properties associated with specific matrix types.
- Learning Outcome: By the end of this subtopic, students will be able to (1) Perform matrix addition, subtraction, and scalar multiplication. (2) Compute matrix multiplication (when defined). (3) Apply the properties of matrix operations in solving mathematical problems.
- Learning Outcome: By the end of this subtopic, students will be able to (1) Compute the determinant of 2×2 and 3×3 matrices. (2) Apply determinant properties in simplifying calculations.
- Learning Outcome: By the end of this subtopic, students will be able to (1) Determine whether a matrix has an inverse. (2) Calculate the inverse of 2×2 and 3×3 matrices using the formula/adjoin method. (3) Use the matrix inverse to solve systems of linear equations.
- Learning Outcome: By the end of this subtopic, students will be able to (1) Form a matrix representation for a system of linear equations. (2) Interpret systems of equations in terms of matrices (coefficient, variable, and constant matrices). (3) Identify types of solutions (unique, many, none).
- Learning Outcome: By the end of this subtopic, students will be able to solve systems of linear equations using Inverse Method, Gaussian Elimination, Gauss-Jordan Elimination and Cramer's Rule.
- Learning Outcome: By the end of this subtopic, students will be able to (1) Define eigenvalues and eigenvectors of a matrix. (2) Compute eigenvalues and eigenvectors for 2×2 and 3×3 matrices.
- 3
VECTOR
Instructors
DR. NURHIDAYAH BINTI OMAR
- Learning Outcome: This module introduces the fundamental concepts of vector. We will cover the introduction and application of vectors.
- 4
DIFFERENTIATION & INTEGRATION
Instructors
DR. NAJAH GHAZALI
DR. ZAINAB YAHYA
DR. NOR HAZADURA BINTI HAMZAH
- Learning Outcome: This module introduces the fundamental concepts and techniques of differentiation, a cornerstone of calculus. We will cover the derivatives of common functions and the essential rules for differentiating more complex functions.
- Learning Outcome: This module introduces the fundamental concepts and techniques of differentiation, a cornerstone of calculus. We will cover the derivatives of common functions and the essential rules for differentiating more complex functions.
- Learning Outcome: In this topic, we will learn the essential rules for differentiating more complex functions that involve multiplication, division or composition.
- Learning Outcome: In this section, you will learn the basic ideas of integration, its notation, the types of integrals, and how to compute simple integrals.
- Learning Outcome: In this section, you will learn how to use standard integration formulas and apply basic rules such as the constant multiple and sum/difference rules.
- Learning Outcome: In this section, you will learn how to evaluate definite integrals using the Fundamental Theorem of Calculus and apply basic properties to simplify calculations.
- Learning Outcome: In this section, you will learn how to use substitution, apply integration by parts, and use the tabular method for repeated integration by parts.
- Learning Outcome: This module introduces the fundamental concepts and techniques of differentiation, a cornerstone of calculus. We will cover the derivatives of common functions and the essential rules for differentiating more complex functions.
- Learning Outcome: This module introduces the fundamental concepts and techniques of differentiation, a cornerstone of calculus. We will cover the derivatives of common functions and the essential rules for differentiating more complex functions.
- 5
PARTIAL DERIVATIVE
Instructors
DR. NUR 'AFIFAH BINTI RUSDI
ALEZAR BINTI MAT YA'ACOB
- Learning Outcome: This module introduces the fundamental concepts and techniques of differentiation, a cornerstone of calculus. We will cover the derivatives of common functions and the essential rules for differentiating more complex functions.