Course Code : PMAT 31212
Title : Theory of Riemann Integration
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.