PMAT 22213: Mathematical Methods for Computing

Course Code            : PMAT 22213

Title                   : Mathematical Methods for Computing

Pre-Requests      : PMAT 12212

Learning Outcomes:

At the end of this course, the student should be able

1. demonstrate knowledge in basic mathematical concepts of calculus
2. use basic mathematical concepts of calculus for further studies
3. classify ordinary differential equations
4. solve linear ordinary differential equations
5. derive the ordinary differential equations for certain applications
6. compute inner products and determine orthogonality on vector spaces
7. apply orthogonal decomposition of inner product spaces.

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, Integration by parts, Partial fractions, 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.

Analytic Geometry: 

• Norms, Inner Products, Lengths and Distances, Angles and Orthogonality, Orthonormal Basis Orthogonal Complement, Inner Product of Functions, Orthogonal Projections, Rotations, Applications in computer Science.

 Method of Teaching and Learning : A combination of lectures and tutorial discussions.

 Assessment : Based on tutorials, tests and end of course examination.

 Recommended Reading:

1. Kreyszig, E. (10th Ed., 2011). Advanced Engineering Mathematics, Wiley.
2. Ross, K.S. (2nd Ed., 2015). Elementary Analysis: The Theory of Calculus, Springer.
3. Stewart, J. (8th Ed., 2015). Calculus Early Transcendentals, Thomson Learning, Inc.
4. Deisenroth, M.P. (2020). Mathematics for Machine Learning Cambridge University Press.