Topic outline

• General

 Lecturer : Ms Wan Rukaida Binti Wan Abdullah PM Dr Yudariah Mohammad YusofDr Nur Arina Bazilah AzizDr Shazirawati Mohd PuziDr Zuhaila Ismail Semester : 1 2016/2017

Synopsis :

This is a first course in Engineering Mathematics. Contents include topics in basic calculus and algebra. The focus is on differentiation and integration of inverse trigonometric functions, hyperbolic and their inverse functions; improper integrals; series; vectors; matrices including vector spaces, eigenvalues and eigenvectors; polar coordinates; and complex numbers.

Learning Outcomes:

By the end of the course, students should be able to:

• express functions as power series and analyze convergence of infinite series and use Taylor series to estimate limits and integrals

• solve problems using vector methods and matrix algebra.

• analyse and graph polar equations, and solve problems involving polar and parametric equations.

• manipulate complex numbers and solve related problems.

• communicate effectively in verbal and written form

• Topic 1

Further Transcendental Functions:

Inverse trigonometric functions, hyperbolic functions and its inverse in logarithmic form. Solving equations related to the functions.
• Topic 2

Differentiation

Differentiation of functions involving inverse trigonometric functions, hyperbolic functions and inverse hyperbolic functions.
• Topic 3

Integration

Review on integration techniques – standard integral table, substitution, by parts, and partial fractions. Integration of expressions involving inverse trigonometric functions, hyperbolic functions, inverse hyperbolic functions. Using table of integrals to integrate related functions.
• Topic 4

Improper Integrals:

Evaluation of limits including l’Hopital rule, limits of indeterminate forms of type 0/0 and ∞/∞. Improper integrals with infinite limits of integration and infinite integrands.
• Topic 5

Series:

Expansion of finite series, infinite series, power series, and the summations of r, r2 and r3 .Test of convergence – divergence test, ratio test and integral test. Taylor’s and Maclaurin’s series of standard functions including applications to finding limits and approximating definite integral.

• Topic 6

Vectors:

Vector in space and its operations including dot product and cross product. Equation of line and plane. Angle between two lines, intersection of two lines. Intersection of two planes. Shortest distance from a point to a line, a point to a plane. Angle between two planes, and angle between a line and a plane.
• Topic 7

Matrix Algebra:

Minors, cofactors, adjoints, and determinants. Properties of determinants including interchanging rows or columns, multiplying by a scalar. Solve system of linear equations using Cramer’s rule and inverse matrix. Elementary row operations (ERO). Use ERO to obtain inverse matrix and solve system of linear equations using Gauss elimination. Eigen value and eigen vector.
• Topic 8

Polar Coordinates

Point representation in polar coordinates, relationship between polar and Cartesian coordinates. Graph sketching including tests of symmetries. Intersection of curves.
• Topic 9

Complex Numbers

Definition of imaginary number and complex number. Algebraic operations and solving equations involving complex numbers. Modulus and argument. Euler’s formula and de Moivre’s theorem to show some trigonometric identities, to find power and roots of complex numbers.