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2.1 COURSES
C1: CALCULUS
(KUL-code: I725)
Lecturer: MONBALIU J.
ECTS-credit: -
Contact hours: 30 hrs. of practical
Prerequisites: Basic knowledge of calculus and matrix algebra
Time and place: 1st semester, 7 sessions of 3 hours each, K.U.Leuven
Course syllabus: Lecture notes
Evaluation: Exercises (written, closed book, sheet with formulas permitted)
Comparable handbook: Schaum's outline of "Theory and problems of advanced calculus"; "Theory and
problems of matrices"; and "Theory and problems of vector analysis"
Additional information: -
Learning objectives:
Refresh basic knowledge of calculus and matrix algebra. Mathematical models are commonplace and are
widely used by engineers dealing with water resources. Basic calculus and some knowledge of matrix algebra
are needed to be able to understand the more advanced analytical and numerical techniques applied.
Course description:
The aim of the prerequisite is to review basic mathematical techniques frequently encountered and applied in
the field of water engineering resources.
1. Calculus:
- functions;
- series expansion of functions;
- continuity and limits;
- differentials and integrals with one or more variables;
- numerical methods for differentiation and integration;
- zero of a function (Newton's method) ; maxima and minima (generalization towards optimization
problems); and
- differential equations.
2. Linear algebra:
- matrices: definition, add, multiply, transpose,..;
- equivalence: row, column;
- determinant of a square matrix;
- inverse of a square matrix;
- solution of linear equations; and
- Jacobian and Hessian matrices.
3. Vectors and scalars:
- vector fields;
- scalar fields;
- gradient;
- divergence; and
- curl.
Basic theory is given (without rigorous proofs). Classroom exercises and home assignments are given to
assimilate the material.
Complementary studies in Water Resources Engineering / 4