Engineering Mathematics 1

Course Information

  • Course Title: Engineering Mathematics

  • Course Code: MAT 116

  • Credit Hours: 3

  • Semester/Academic Year: First Semester, 2025/2026

  • Lecturer: Ms. Jemima Saah

  • Email: jsaah@aamusted.edu.gh

Course Objective

  • The course is designed to equip students with the basic mathematical principles required to solve day-to-day technical problems.

  • It serves as a prelude to understanding the mathematical basis for the design of some devices.

Course Content

  • Fundamental Concepts and Techniques:

    • Algebra and Number Systems

    • Laws of Indices

    • Logarithms

    • Surds

    • Functions and Graphs:

    • Linear Models

    • Quadratic Models

    • Polynomial Models

    • Exponential Models

    • Logarithmic Models

    • Engineering Applications (Linearization and Experimental Laws)

    • Principles of Mathematical Induction

    • Trigonometric Functions:

    • Identities

    • Equations

    • Applications in solving geometrical and physical problems

    • Hyperbolic Functions

    • Coordinate Geometry:

    • Straight Lines

    • Circles

    • Conic Sections

    • Systems of Linear Equations and Matrices:

    • Methods of Solution:

      • Gaussian elimination

      • Cramer's rule

    • Emphasis:

    • Problem-solving

    • Interpretation of results within engineering contexts

Mode of Delivery

  • The course will be delivered through lectures and discussions.

Detailed Course Topics

  • Indices

  • Logarithms

  • Exponential and Logarithmic Equations

  • Straight Lines

  • Circles

  • Polynomial Functions

  • Rational Functions

  • Exponential Functions

  • Logarithmic Functions

  • Linearization and Experimental Laws

  • Trigonometric Functions

  • Hyperbolic Functions

  • Systems of Linear Equations and Matrices

  • Complex Numbers

  • Vectors

Classroom Discussions

  1. Radical Equations and Rational Exponent Equations

  2. Indices and its Properties

  3. Logarithms and its Properties

  4. Exponential Functions

  5. Cartesian Coordinate Systems:

    • The Distance Formula

    • The Midpoint Formula

    • The Slope of a Line

    • The Equation of a Line

  6. Circles:

    • Standard form of the equation

    • Finding equations of circles with given conditions

  7. Basic Polynomial Functions:

    • Division of Polynomials

    • Remainder and Factor Theorems

    • Roots of a Polynomial

  8. Rational Functions:

    • Domain and Asymptotes

    • Partial Fractions

  9. Mid-Semester Examination

  10. Logarithmic Functions

  11. Linearization and Experimental Laws

  12. Trigonometric Ratios and Identities

  13. Systems of Linear Equations and Matrices:

    • Operations including determinants and matrix inversion

    • Cramer's Rule

    • Gaussian Elimination with Back-Substitution

  14. Complex Numbers:

    • Definition and Basic Operations

    • Polar and Euler Forms

  15. Vectors:

    • Basic Concepts, Scalar Product, and Vector Product

Assessment and Grading

  • Mode of Assessment:

    • Quizzes: 15%

    • Mid-Semester Examination: 15%

    • Attendance and Assignments: 10%

    • End-of-Semester Examination: 60%

Reading List

  1. Aufmann, R. N., Barker, V. C., & Nation, R. D. (2011). College Algebra (7th ed.). Brooks/Cole.

  2. James, G. (2020). Modern Engineering Mathematics. Pearson Education.

  3. Larson, R. (2016). Algebra & Trigonometry. Cengage Learning, Pearson Education Limited.

  4. Malik, A. K., Arthur, P., & Purohit, S. D. (2019). A Textbook of Engineering Mathematics-II.

  5. Stewart, J., Redling, L., & Watson, S. (2002). Pre-calculus Mathematics for Calculus (4th Ed.). Pacific Grove, CA: Brooks/Cole - Thompson Learning.

  6. Stroud, K. A., and Booth, D. J. (2013). Engineering Mathematics (7th Edition). Palgrave Mac.

Academic Integrity Policy

  • Academic misconduct refers to dishonesty in examinations, such as cheating or plagiarism (presenting someone else's work as your own).

  • Students must attend all scheduled classes. Absences without prior permission will result in point deductions.

  • Punctuality to scheduled class sessions is strongly advised.

Grading Policy

  • The weighted total score consists of assignments, class discussions, quizzes, and the end-of-semester examination.

  • Quizzes and assignments account for 40% of the grade, while the end-of-semester examination accounts for 60% using the accumulated weighted score.

Course Schedule

  • Week 1:

    • Introduction to the course

    • The Real Number System

    • Algebraic Expressions

    • Equations and Inequalities

    • Surds

    • Quadratic Equations

    • Other Equations

  • Learning Activities:

    • Discussion on the course and its schedule

    • Discussion on set of real numbers, the real Number Line, Interval Notation, Absolute Value

    • Discussion on Operations on Algebraic Expressions, Factorization of Algebraic Expressions, and Rational Expression

    • Discussion on Solving Linear Equations (all types), and change of subject

    • Discussion on Absolute Value Equations, Mathematical Models, and Linear Inequalities

    • Discussion on the properties of Surds

    • Discussion on solving quadratic equations using Factoring, Square Root Property, Completing the Square, and the Quadratic Formula.