Embedded Files
Course Code : PMAT 31212
Title : Mathematics for Computing III
Pre-requisites : PMAT 12212
Learning Outcomes:
At the end of the course the student should be able to
demonstrate knowledge in basic mathematical concepts of calculus
use basic mathematical concepts of calculus for further studies
categorize ordinary differential equations
solve linear ordinary differential equations using appropriate methods
derive the ordinary differential equations for certain applications.
Course Contents:
Limits and Derivatives:
Limit of a Function, Calculating Limits Using the Limit Laws, Continuity, Limits at Infinity-Horizontal Asymptotes, Derivatives and Rates of Change, Derivative as a Function, Differential rules, Applications of Differentiation.
Integrals:
Definite Integral, Fundamental Theorem of Calculus, Substitution Rule.
Applications of Integration:
Areas between Curves, Volumes, Volumes by Cylindrical Shells, Arc Length, Area of a Surface of Revolution, Techniques of Integration.
Ordinary Differential Equations (ODEs):
Introduction to Differential Equations, ODEs, Order, Degree, classification of linear and non-linear ODEs, solution of a differential equation, Family of curves, first order ODEs: Separable ODEs, Exact ODEs, Integrating Factors, Linear ODEs, Higher Order Linear ODEs: Homogeneous Linear ODEs, Homogeneous Linear ODEs with Constant Coefficients, Differential Operators, Special types of ODEs: Bernoulli Equations, Euler–Cauchy Equations, Applications of ODEs.
Method of Teaching and Learning : A combination of lectures and tutorial discussions.
Assessment : Based on tutorials, tests and end of course examination.
Recommended Reading:
Kreyszig, E. (10th Ed., 2011). Advanced Engineering Mathematics, Wiley.
Ross, K.S. (2nd Ed., 2015). Elementary Analysis: The Theory of Calculus, Springer.
Stewart, J. (8th Ed., 2015). Calculus Early Transcendentals, Thomson Learning, Inc.
Report abuse