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Mathematics

Course Code: M-1111  |  First Semester
Duration 15 Weeks
Lectures 3 per week  ×  1 hour
Textbook
📚
Required Textbook
Thomas’ Calculus in SI Units, 14th Edition
Joel R. Hass, Christopher E. Heil & Maurice D. Weir
Course Description
This course introduces first-semester students to the fundamental concepts of calculus and mathematical analysis as applied in computing and technology disciplines. Beginning with a solid grounding in functions and their properties, students progressively develop skills in limits, continuity, differentiation, and integration. Emphasis is placed on both theoretical understanding and practical problem-solving, equipping students with the mathematical reasoning required to support further study in computer science, engineering, and related fields.

Learning Objectives

  1. Introduce students to the concepts of functions, their types, graphs, and algebraic combinations including trigonometric and exponential forms.
  2. Develop a rigorous understanding of limits, continuity, and asymptotic behaviour of functions.
  3. Build competency in differentiation techniques including the chain rule, implicit differentiation, and related rates.
  4. Enable students to apply derivatives to real-world problems such as optimisation, curve sketching, and Newton’s method.
  5. Introduce definite and indefinite integrals and the Fundamental Theorem of Calculus.
  6. Apply integration to compute areas, volumes, arc lengths, surface areas, and physical quantities such as work and mass.
  7. Foster logical and analytical reasoning skills essential for advanced mathematics and computer science study.

Learning Outcomes

  • Analyse and graph a variety of functions, including composite, trigonometric, and exponential functions.
  • Evaluate limits and determine continuity of functions using formal definitions and limit laws.
  • Apply differentiation rules accurately to algebraic, trigonometric, and implicitly defined functions.
  • Solve applied optimisation problems and sketch curves using first and second derivative tests.
  • Compute definite and indefinite integrals using substitution and other standard techniques.
  • Use integration to solve geometric and physical application problems, including volumes and arc length.
  • Demonstrate mathematical communication skills by presenting solutions in a structured and logical manner.
Major Topics Covered
Functions
Limits & Continuity
Differentiation
Applications of Derivatives
Integrals
Applications of Integration
Assessment Components
Assignments
Tutorial
Final Exam
Lecture Structure: 3 lectures per week, each up to 60 minutes. Assignments are distributed throughout the semester via LMS, with a Tutorial and Final Exam at the end of the term.
Course Outline
Week Topic
Topic I Functions
Week 01
  • Functions and Their Graphs
  • Combining Functions; Shifting and Scaling Graphs
  • Trigonometric Functions
  • Exponential Functions
    		•
    Topic II Limits and Continuity
    Week 02
  • Rates of Change and Tangents to Curves
  • Limit of a Function and Limit Laws
  • The Precise Definitions of a Limit
    		•
    Week 03
  • One-Sided Limits
  • Limits Involving Infinity; Asymptotes of Graphs
  • Continuity
    		•
    📋 Assignment
    Topic III Differentiation
    Week 04
  • Tangents and the Derivative at a Point
  • The Derivative as a Function
    		•
    Week 05
  • Differentiation Rules
  • The Derivative as a Rate of Change
    		•
    Week 06
  • Derivatives of Trigonometric Functions
  • The Chain Rule
  • Implicit Differentiation
    		•
    Week 07
  • Related Rates
  • Linearization and Differentials
    		•
    📋 Assignment
    Topic IV Applications of Derivatives
    Week 08
  • Extreme Values of Functions on Closed Intervals
  • The Mean Value Theorem
    		•
    Week 09
  • Monotonic Functions and the First Derivative Test
  • Concavity and Curve Sketching
    		•
    Week 10
  • Applied Optimization
  • Newton’s Method
  • Antiderivatives
    		•
    Topic V Integrals
    Week 11
  • Area and Estimating with Finite Sums
  • Sigma Notation and Limits of Finite Sums
    		•
    Week 12
  • The Definite Integral
  • The Fundamental Theorem of Calculus
    		•
    Week 13
  • Indefinite Integrals and the Substitution Method
  • Definite Integral Substitutions and the Area Between Curves
    		•
    Topic VI Applications of Definite Integrals
    Week 14
  • Volumes Using Cross-Sections
  • Volumes Using Cylindrical Shells
    		•
    Week 15
  • Arc Length
  • Areas of Surfaces of Revolution
  • Work and Fluid Forces
  • Moments and Centers of Mass
    		•
    📋 Assignment & Tutorial
    🎓   Final Exam