3. My Teaching
Mathematics in Engineering: Essential Concepts and Tools
Explore the world of mathematics and statistics that fundamental to engineering studies where solving complex problems and equations drives innovation and benefits humanity. Access comprehensive notes to support your academic journey on this page too.
SMJM 1013 - Engineering Mathematics I
Engineering Mathematics I is an introductory course designed to provide students with essential mathematical tools and concepts used in various engineering disciplines. Students will study a range of topics including transcendental functions with differentiation and integration, hyperbolic functions, improper integrals, series, vector and matrix algebra, polar coordinates, and complex numbers. The primary objective is to develop your proficiency in these areas which enable students to solve complex engineering problems effectively.
By the end of this course, I believe students will be able to understand and apply transcendental and hyperbolic functions, evaluate improper integrals, work with series, and utilize vectors and matrices in solving linear algebra problems. Students will also able to convert between Cartesian and polar coordinates, and analyzing complex numbers, where these skills are critical for applications such as modeling growth processes, solving circuit equations, or working with signal processing in electrical engineering. This foundational knowledge prepares students for advanced engineering courses and professional practice.
The link to our textbook: [Textbook of SMJM 1013]
- Chapter 1 – Further Transcendetal Functions
- Chapter 2 – Improper Integral
- Chapter 3 – Series
- Chapter 4 – Vectors
- Chapter 5 – Matrix Algebra
- Chapter 6 – Polar Coordinates
- Chapter 7 – Complex Numbers
SMJM 1023 - Engineering Mathematics II
Engineering Mathematics II is a continuation of the foundational mathematical knowledge introduced in Engineering Mathematics I. This course focuses on differential equations, transforms, and series that are essential for modeling and analyzing engineering systems. Topics include first-order and second-order ordinary differential equations (ODEs), Laplace transforms, Fourier series, and partial differential equations (PDEs). The primary aim is to equip students with the mathematical techniques needed to solve time-dependent and spatially varying engineering problems across various disciplines, such as mechanical vibrations, electrical circuits, and heat transfer.
By the end of this course, students are expected to formulate and solve first- and second-order ODEs using analytical and transform methods, apply Laplace transforms to initial value problems, represent functions using Fourier series, and analyze PDEs in practical contexts. These skills allow students to model dynamic systems, study wave propagation, and investigate heat and mass transfer phenomena. Mastery of these topics provides a strong foundation for advanced courses in engineering, systems modeling, and applied mathematics, which enable students to approach complex engineering challenges with confidence and precision.
The link to our textbook: [Textbook of SMJM 1023]
- Chapter 1 – First-Order Ordinary Differential Equations (ODEs)
- Chapter 4 – Fourier Series
- Chapter 2 – Second-Order Ordinary Differential Equations (ODEs)
- Chapter 5 – Partial Differential Equations (PDEs)
- Chapter 3 – Laplace Transform
SMJM 2043 - Engineering Statistics
Engineering Statistics covers the basics of probability and statistics, focusing on both theory and practical applications. Students will start by learning basic statistics and elementary probability theory. From there, students will go into probability distributions, sampling methods, and how to estimate and test different parameters. Students will also explore further statistical such as estimation, hypothesis testing, analysis of variance (ANOVA), and non-parametric statistics. Correlation and regression are also considered in this course to help students understand the relationships between variables.
The goal of this course is to introduce the fundamental concepts of statistics in a manner that is accessible to students with a primary interest in basic mathematical/statistical concepts. I believe this course is useful for students in acquiring skills of handling observed data, drawing valid inferences, and making profound decision. In addition to the theoretical knowledge, students will get hands-on experience with statistical tools and software, making it easier to tackle real-world engineering problems using statistics.
The link to our textbook: [Textbook of SMJM 2043]
- Chapter 1 – Data Summary
- Chapter 2 – Probabilities
- Chapter 3A – Random Variables (Discrete)
- Chapter 3B – Random Variables (Continuous)
- Chapter 4 – Sampling Distributions
- Chapter 5 – Estimation
- Chapter 6 – Hypothesis Testing
- Chapter 7 – ANOVA
- Chapter 8 – Non-parametric Statistics
- Chapter 9 – Regression and Correlation
Visualizing Mathematical Concepts in Engineering
Common Queries
How can I access the lecture notes?
You can access the lecture notes directly from the button ‘Access Notes Here’.
Are the notes updated regularly?
Yes, notes are updated after each lecture to include the latest information and examples discussed in class.
What should I do if I find an error in the notes?
Please report any errors directly to me, and I will address them promptly.
Can I get additional help with difficult topics?
Yes, I offer office hours for additional assistance. However, I kindly ask students to schedule an appointment in advance to ensure my availability.
Are there any recommended textbooks?
Yes, the lists of the textbooks are stated in the description above.
How can I prepare for exams using the notes?
Review the notes regularly, practice problems provided, and attend classes/sessions before exams.
Will there be any group study sessions?
I do not facilitate group study sessions, as students are expected to independently participate in group discussions. However, I can arrange a session upon request, subject to my availability.
How do I submit assignments?
Assignments should be submitted through the UTM E-learning system by the due date specified in the Course Information.
What if I miss a lecture?
Recorded lectures are available online, and you can catch up by reviewing the notes and recordings.
