Course Info

Course Information

Basic Informations

• Course Code: KIX1001
• Course Title: Engineering Mathematics 1
• Credit: 3
• Medium of Instruction: English
• Course Pre-requisite(s)/ Minimum Requirement(s): No

Course Learning Outcomes

At the end of the course, students are able to:

1. Explain mathematical principles such as derivatives, partial derivative, integration techniques, matrix or vector algebra used in engineering field.
2. Use mathematical principles such as derivatives, partial derivative,integration techniques, matrix or vector algebra in analyzing engineering problem.
3. Solve complex engineering problem and reach a valid conclusion using mathematical principal.

Synopsis of Course Contents

This course attempts to improve the mathematical skills for engineering students. This course covers differentiation, matrix and vector algebra, integration, multiple integrals, line integrals, surface integrals, volume integrals and Gauss’s divergence theorem. This course also introduces the engineering application of the topics taught.

Assessment Weightage

• Continuous Assessment: 40%
• Final Examination: 60%

Main Reference

1. Glyn James, "Modern Engineering Mathematics", 5th Edition, 2015, Pearson.
2. K.A. Stroud and D.J. Booth, “Engineering Mathematics”, 8th Edition, 2020, Red Globe Press.
3. Glyn James, "Advanced Modern Engineering Mathematics", 5th Edition, 2018, Pearson.
4. K.A. Stroud and D.J. Booth, “Advanced Engineering Mathematics”, 6th Edition, 2020, Red Globe Press.
5. Erwin Kreyszig, “Advanced Engineering Mathematics”, 10th Edition International Student Version, 2011, John Wiley & Sons Ltd.

Course Planning

Week	Topic
1	Functions: Limit of a function, limits and continuity Derivatives: Basic ideas and definitions, rules of differentiations, chain rule, Parametric and implicit differentiation, Higher derivatives. Engineering Applications of Functions and Derivatives: Approximating functions, The gradient of a straight line, Concavity, motion and the second derivatives, Curvature of a plane curves
2	Partial Derivatives: Basic ideas and definitions. Domain of the functions, Dependent and independent variables, Higher order partial derivatives, Differentiation of composite functions and implicit functions Partial Derivatives using Jacobians, Differential operators Engineering Applications of Partial Derivatives, Tangent planes and normal to surface in three dimensions
3	Vector Algebra I: Basic concepts, Cartesian components, Vectors in space, Gradient, Divergence, Curl Directional derivatives
4	Vector Algebra II: Scalar Product and Vector Product, Triple Product
5	Engineering Applications of Vector Algebra, Engineering Applications of Vector Analysis
6	Matrix Algebra: Basic concepts, Solutions of a set of linear equations; Gaussian elimination method, Eigenvalues and eigenvectors; Cayley-Hamilton Theory
7	Engineering Applications of Matrix Algebra: Linear dependence, Row echelon matrix, Reduced row echelon matrix, Diagonalization
8	Integration: Basic ideas and definitions, Techniques of Integrations: the substitution method, by parts, by partial fractions Proper and Improper Integrals
9	Engineering Applications of Integrals: Areas of regions in the plane, Volumes of solids with known cross sections, Moment and center of mass
10	Multiple Integrals: Double Integrals and triple Integrals
11	Line integral and work done. Green’s theorem in a plane
12	Surface Integrals
13	Volume Integrals
14	Gauss’s Divergence Theorem

Reference: JKE Guidebook